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Les cartes, planches, tableaux, etc., peuvent dtre film6s d des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est film6 d partir de Tangle sup6rieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images n^cessaire. Les diagrammes suivants illustrent la mdthode. 32 X 1 2 3 4 5 6 i\ PREFACE The New Method A»,t„.met.c is what it, a new n,eth«i of presenting the subie., f ' ""''"'==- The authors have not been ,!sp rl; by 1 'l'"'?^^ -"'""^'- to the already large „u„,ber o, pLfcar H " ''" °" ""^ 'he market, but, rather, to turn o ,t oT f""" "'' "^ "" -bieet in a way that must conn ; ; : 'Z"^' ^'^ P'^" ">e student. """^ "*" to every teacher and We think it will be conceded th.f ■ the mam idea should be to imnr« ""^ ™"* "' '"""tion ^;'ails that the Princplesl::: t.''™';;''::^^; -^ '" - -n.e of detail. Who has not met the bov . "" ""'"^'"S "'ass strong on profit and loss bl ,o T "'" '"=" '"^' "^ "- was always a diiBculty. 'is thi att '°r''"°" '"" ''"''"''S^ -ndor Which he has LnV^Z^T I'^l ""f " - 'he system "US. shoulder the blame. C; Jh^" "'' '"^ ^^^'^"■ arrangement of the study of arithnL T "■™''' " "■ P™!*^ oomm,ssion and brokerag Wh 1 ' "" ''™*' ^"^ '°^^ '"^ «ons of percentage as se^arat! depJLI'roft^ \ '''''- siniply transgressing a first nrin . ^ ''°'^' ^« ^re -''iect. Thedetaifofp™ : :\':P™'-^'^.P-"ti„g the age is made to overshadow the p Zin^ , '"" ""^ ''""'"■ such work is a mere apphcatio" ' "' ^"^"'^«^' °' -"ich Perhaps no better idea ran h» u. ■ -Pon which the Whole s L" is °' *' ^™'^' P'» to that section of the w k'^i^i f 7'^^'^" "' ' «'-»« i" a systematic order under . . ™* P'''^'^^'^- There. Second, Third, and C !^^: ' ^ "f '"""""^ """^ ^-'' usual applications of percental " P''""*^"^ ^" *= QAiou « PREFACE taxes, insurance, and stocks and bonds. These are not presented as so many different departments in the work of arithmetic, but simply as so many appUcations of the percentage idea. We have called attention to but one section of the book by way of illustration. A reference to others will show a consistent working out of the same plan. It may be new, but it has been tried and proved. P. McIntosh. C. A. Norman. I CONTENTS Simple Rules Definitions ^''^% Notation and Numeration Arabic Notation ..... 6 Roman Notation . . Addition . 5 5 Subtraction j^ Factors .... Highest Common Factor Definitions ..... Reduction of Fractions . Reduction Ascending Reduction Descending Reduction to Common Denomi'- nator Complementary Numbers Multiplication . . Division .... Cancellation .... Combinations of Processes Methods for Proving Work Factors and Multiples • . 38 Multiples • . 41 Lowest Common Multiple Common or Vulgar Fractions 47 Addition Subtraction .... Multiplication ... Division .... Review of Fractions . . Sharing .... 48 SO 51 52 Decimal Definitions ^2 Numeration no Notation .....*.' Reduction .... Addition Subtraction . 74 75 78 79 Fractions Multiplication Division Repeating or Circulating Deci- mals Review Pane 15 19 23 31 33 34 44 44 53 54 56 58 60 66 80 81 82 84 T, , , , , Denominate Numbers Reduction . ■ ■ ■ • Q? J^."l.*\Pl^cat'o° 104 Addition . . ; ; ; ; ; ^l] ^'^^'^'^^ 105 Square Root Surfaces Solids . Involution and Evolution • . . 108 Cube Root j|g Practical Mensuration • • . 117 Miscellaneous . . ioa ... 122 • ... 1.44 f, ^. Practical Measurements p"?'^*^"^ 134 Roofing . . Jraperme . . iq- t i. . Lumber . \lt i^^^"^^ ^°^ Plastering *^ Bnck and Stone Work 141 143 144 CONTENTS ,f Percentage PROFir AND Loss Trade DiscouNr, Commission and Rrokkracf Insdranck Taxes, Duties, Kxciianoe, Stocks, Interksi Term' Used 147 Basis of Calculation . . . .153 Questions of the First Aspect . 154 Questions of the Second Aspect 166 Page 171 Questions of the Third Aspect Questions of the Fourth Aspect 176 Keview . jg2 In Decimals Short Methods In Multiplication .... 201 In Percentage oil In Division 205 Bilhng ..'.'.'.[', 2I8 . . . . 206 Cash Storage Bills . . . , 233 Applications of Simple Interest 236 Averaging Accounts . . . .271 Averaging Account Sales . . 277 Interest on Partners' Accounts 281 Accounts with Banks . . .284 Accounts with Stock Brokers . 288 Negotiable Papers Bank Discount . True Discount Partial Payments Cash Balance Equation of Payments 245 249 257 263 269 Compound Interi-st Questions of the First Aspect . 292 Questions of the Third Aspect 297 Questions of the Second Aspect 296 Questions of the Fourth Aspect 298 Annuities Questions of the First Aspect . 301 Questions of the Third Aspect . 306 Questions of the Second Aspect 304 ^ Foreign Trade ni'ri^V^''?""^' .... 310 Indirect or Circuitous Exchange 317 Direct Exchange 314 Custom House Business . . . 318 Average and its Applications -, ,. Alligation, Storage, Investments Questions of the First Aspect . 325 Questions of the Second Aspect 331 Definitions The Metric System Partnership . 336 Adjustments Appendix 337 347 NEW METHOD ARITHMETIC fVspect . 306 SIMPLE RULES DEFINITIONS rn.^b^^i^l\!!'" '?"" '' """^^^- '' ^^-^he^ how numbers may De applied to produce required results. or fit"""'"' " "" ""'""'°" "' ' ""»'''>'' ^y -^'"^ ol character, Thi''i„",f °'^ """"'^ i^ ™^ <" 'he things which it expresses by the thousand the int^if oVorur/relT'etc'" ^'"""^ '^^'^'^ An abstract number k a number not nssociatpH wifh particular thing or qtiantity ; as 2. 7, 10 .;c ^"^ The fundamontal operations of Arithmetic are • Nnf f a„d^_Nu„»ra.ion, Add.tion, Snhtraction, M^.ti^lati^r^r NOTATION AND NUMERATION Notation is the art of writing numbers. .p^^Uof ^ '-' '' -^'y -P--^ --bers whe. Numbers are written in three ways : t. By words ; as, one hundred, twenty-five. 2. By hgures, called the Arabic Method ; as, 125 3. By letters, called the Roman Method; as. CVXV 6 SIMPLE RULES ARABIC NOTATIOIJ This system received its name from tl.e fact that it was intro- duced m to Europe by the Arabs. It employs ten figures or characters by vvliicli numbers are represented. 12 3456789 O One Two Three Four Five Six Seven Eight Nine Zero or Naught. 1. 2, 3, 4. 5. 6. 7. 8. 9, are significant figu: :s. They represent value. anotSr figure!" ^'^"''^°' ^^''- ^' ^^P^''^^^^ °° value, unless used with . J^'f '* ^'i' """^^^'•^ ^'^ ^"tten With the figures 1. 2, 3, 4. nr L ^f ' ;^^"" ""'^''''' ^'" expressed by combining two or more figures. Thus, the number seven is written by using ttie^figure 7. while seventeen is expressed by combining 1 and with^trfif '' ^l"^*'"^*'^"' ^« «^« that the figure 1. when used tT. Jh T^u V° '''^'''' ^^' ""'""y '■^P^^^^^ts ten. If we reverse whil. fh' 7 . ^T ^^ """*" ^^' '^' ^S"^^ ^ has a value of one. while the 7 has a value of seventy. wh^!.^^^'^ T^^"^ °^ ^ ^^^'' ^' *^" ^^"^ ^'hich it expresses dumber! ^^ ' "' '" '^' ^'"' ^^^'' *^ *^^ "^^^ °^ ^ ^^ole The Local Value of a figure is the value which it has when associated with other figures in expressing a number. orHp?" Tu'^ ^^^'^ ' ^^"'" °''^P^'^ ^" ^ ^^"^ber is called its whil\J '' u ""' ''' ^°''" *^^^ ^^''''' 1 1 11 we know that dvfn tn' T^' ''""''' °^ ^°"' ''' '^''' ^' ^ ^'g^ifi^a^t value ^ven to each figure according to its position. Starting at the right and going to the left we have one unit, one ten. one hundred. r^ . I . ^" ''"^'"^ ^^^ ""'"^^ ^« begin at the left and read to the right as follows : One thousand, one hundred, eleven (ten and one) Even this reading is shortened in business to : liieven hundred, eleven. When there are four or more figures in a number it is divided into periods of three figures each, beginning at the right side. The f 4 I I Name 4 I I Express 1. 592 2. I71i 3. 745; 4. 392 S- 65i: 6. 8721 7. 219= it was intro- :n figures or O 'o or Naught. present value, iless used with !s 1. 2. 3, 4. ubining two in by using ining 1 and when used f we reverse alue of one, it expresses of a whole : has when > called its know that cant value ing at the e hundred, le left and ed, eleven isiness to : NOTATTON" AND NUMERATION • following table ual .ho.v the order of the u.nts and the ua.ucs of the periods, for a reasonabk- distance up tlie scale : Periods. Name NUMERATION TABLE 6th 5th 4th .'ird 2n1 1st Orders of "^ Periods. Number. units in the '«,„,„ ^ C iG ^ ^ 'f>. f> The number written below the 37 quadrillions, 406 trillions, thousand, 3 hundred, eighty-four. 2 3, 7 1, 3 0, 3 8 4 table would be read as follows : 523 billions, 71 milhons, 300 SERIES t Express by written words, the following numbers : 8. 9127438. 9- 5375816253. 10. 29285. 11. 92162715208508. 12. 4000273001. 13. 180005107. 14- 8000000026. 1. 59285. 2. 1718219. 3. 745364. 4. 39219283. 5- 65175. 6. 8721293592. 7. 2195629837. 15. 1900107500. 16. 400034. 17. 2900107. 18. 9800001800070. 19- 31768290005. 20. 2831000. 21. 91000146. SERIES 2 Express, by means of figures, the following numbers : I. Five thousand, two hundred and forty-seven ^' V^Z^Z' ^^''i,''"'^' ''^^'^ ^^""^'■^^ ^"d seventy-one. 3. Jiight thousand and fifty-three. 8 SIMPLE RULES 4. Twelve J.iousand and nine. 5. Ninety thousand and thirty-six. 6. Tm.o hundred and eight thousand, and ninety-four twenty-fiv" ""'"' '"' '""'"' ^"' ^^^^ ^^--n^, and forty. ^' ^'"' "''"'''"' ^^''^y-'"''''' ^^^^"^^"d- five hundred and 9. Two mUlion, five thousand, seven hundred and six thirty-hv^' "''^''°"' '""^ ^'""^''"^ ^""^ ''^^' ^h^"^^'^"^' ^"d forty'eigh^r '''"'°"' "^^^^y-five thousand, one hundred and 12. Nine billion, forty-three million, and seven thousand. 13. Ninety-six trillion, thirty-five thousand and nine 14. Fifteen trillion, seven hundred and thirty-nine billion fifty million, one hundred and ninety thousand, and seventy-six' h„ ^'^; '^^f''^ !""'°"' ''"^ ^""^'"^ ^"^ twenty-nine million, two hundred and twelve thousand, five hundred and sixty-one fonr'f; ^'"'?"*''\'^"'^'""°"' "S^^* ^""^°"' two hundred and lour thousand, one hundred and forty. ROMAN NOTATION The Roman Method of Notation uses letters instead of figures to express numbers. It employs seven characters or letters as loilows : ' I V X L C D M ^ ^ 10 50 100 500 1000 As in the Arabic Notation, each character has a definite value when standing alone, as noted, and a varying value when written m certain positions in combination with the other characters The principles which govern the use of these characters in expressing numbers are as follows : .. I. Repeating a letter repeats its value. Thus. X represents 10, XX represents 20, XXX represents 30. Roman . VI I c II 1 III 1 IV t V I VI s VII s VIII E IX ^ X T ADDITION 9 hundred and hundred and 2. When a letter of less value is placed before one ol greater <^alue, the number expressed is the difference between the values of such numbers. Thus, IX represents 9, XC represents 90. 3. When a letter of less value is placed after one of greater value, the number indicated is the sum of the values of such letters. Thus, CX represents 110. 4. A bar placed over a letter multiplies the letter by one thousand. Thus, V represents five thousand ; T, one hundred usand. 5. A letter should not be repeated more than three times in expressing numbers. 6. A bar is never placed over the letter I. COMPARATIVE NOTATION TABLE Roman. Words. Arabic. I II III IV V VI VII One Two Thr^ Four Five Six Seven VIII Eighi IX Nine X Ten 1 2 3 4 5 6 7 8 9 10 Roman. Words. Arabic. XI XII XIII XIV XV XVI XVII XVIII XIX XX II 12 13 Eleven Twelve Thirteen Fourteen 14 Fifteen 15 Sixteen 16 Seventeen 17 Eighteen 18 Nineteen 19 Twenty 20 Roman. Words. Arabic. XXX Thirty 30 XL Forty 40 L Fifty 50 LX Sixty 60 LXX Seventy 70 LXXX Eighty 80 XC Ninety 9G C One Hundred 100 D Five Hundred 500 M One Thousand 1000 ADDITION Addition is the process of uniting into one number all the units contained in two or more oth-^r numbers. The number obtained by addition is called the sum, amount or aggregate, ' 10 SIMPIiB RULES The nunnlxTs to b. addod are called addends, or parts. The sign + signifies addition, and is read plus. The sign = signifies equality, and is read equals. and^lhdrr"''" "'"" """'"' '"* °' ™"^ = -' « >PP'- Like numbers only can be added. If unlike numbers can be made like, they may be added. For instance, we may add 6 tons and 6 Dounds bv fir«t fi„ r u pounds there are in 6 tons. ^ ^ ''* ^'"'^'"^ how many ILLUSTRATION.-Add 456, 5187, 45, 278, and 7302. SOLUTION.-First ^vrite the numbers, placing units of the same^order in the same column, units unu'er unL. teL undt: Then add the right-hand column. 2+8+5+7+6-28 Place the right-Iiand figure, 8 (units), under the tolumn a"^ded The tens column added in hke manner, 7+4+8+5 and the 2 tens from units' column, will produce 26. Write the , .. , .' °' "S^^*-^^^°d fig"'-'^. "nder the tens" column and carrv the 2 or left-hand figure, to the next column ^ ^' tens' Toln^^^flVTZ ' ^' -^^ ' '""^ ^''^ " ''-^-^«' ^^^ t^^ lens column. = 12, or 1 thousand and 2 hundreds tho,^^"?.*''!, ^ '^"'''^'"^' "°'^''' *^' hundreds' "column and carry the 1 thousand to the thousands' column. ^ column'- Tf "?',"'"""' '"" '• ""^ *^' ' ^'^^"^^"^ ^-"^ ^^""dreds' column 13. which written under the thousands' column, completes the work and gives 1326o, the sum. ^ ^mIT^'TTTI^ ^'^^ '^""^ """""^ "'^^"^'^'^ "'"^ *° °^™« results only in only. as. 6 10. etc. In the above example, begin at the bottom of units' counin and add upward-10, 15. 22. 28. Write 8 under units and ca!^ -J to the tens— always adding the carrying figure first A very good plan to follow, when the question to be added is a large Slow ond' H T\"u '''" """°"' '°^""°^ ^°"° ^° *^« -^'^"^ i»"«trated below and then add these totals together. Then, the necessity of remem- benng th. carrymg figure is removed ; and if one is interrupted while aTd'ng 456 5187 45 278 7302 13268 Ad I. 4 2 3 1 3 5 ADDiTIOU ■ Paris. 5 ; as, 5 apples s ; as, 5 apples )e added, finding how many 502. ing units of the jnits, tens under 5 + 7 + 6 = 28. le column added he next column. 7+4+8+5, J 26. Write the and carry the 2, dreds' from the md carry the 1 from hundreds' , completes the results only in name the sum ottom of units' Jnits and carry dded is a large nner illustrated sity of remem- :d while adding u a question, he will be saved the trouble of adding the whole question again . to find the carrying figure. Thus, in the question above : ^ ^^ 28 24 10 12 13268 RULE 1. Write the numbers, placing tmits of the same order in the same column. 2. Find the sum of units' column first mid place the right-hand ngure of thts sum under this column and carry the left-hand fisure or figures, to the next column. ^ 3. Ad upon the remaining colmnvs in regular order and in a under the column from which the sum was obtained, and carrv the left-hand figure, or figures, if any, to the next column.. 4. Under the last column write the last amount. Add the following : I. 4 2.3 3. 34 2 6 51 3 5 25 1 6 32 3 1 43 5 4^ 14 7. 4751 8. 8267 9. 3675 6958 5483 4592 8527 3796 8147 3489 5864 6328 6476 4394 7465 3547 8936 3726 4368 7453 4857 5936 2718 8395 SERIES 3 4. 46 63 38 57 82 74 5. 346 572 465 537 724 316 10. 6435 II. 78643 7582 85972 4617 43289 3874 76541 6293 63748 7436 62862 3548 26875 6987 49386 6. 635 853 674 359 482 375 12. 34625 87394 51786 46937 84394 68479 75648 49576 12 SIMPLE BULES farmtosVme p"'"^ '''' '"'"^ ' '""" '""^ ^^■*^- ^h^' did «>0 •,„.'?' ^'^'" ''"Ssheads of tobacco weigh respectivelv Tls aiK 794. 8,6^768, 857, 783. and 837 pounds. 'Findfhe 2 IILT' .6. A grocer's shop is worth 81,980, and his goods areworth S765 more than the shop. What is the value of toth > Monday 113,643 feet on Tuesday; 108.581 feet on Wednesday 86,572 feet on Thursday: 126,416 feet on Friday and iTs^Q feet on Saturday. What was the week's - cut " of fte mill ' ' '' 18. A man bought four farms. For the first he paid S5 87n • Ztirrt f''''j '"' "" ""^''' ^ ™- ftan ffti; dM ;it f / °"''*- ^''^ ™^= """ '°f 'he second. What aid the four farms cost him ? 19. What is the sum of five hundred and ninetv-one dollar, two thousand three hundred and eight dollars, sixty-seven doUaJ and nmeteen thousand one hundred dollars ? * f. fT* ^'""i *^' ^''^'^ ^''^^'^"^ ^^«"«d a rectangular field 1 62q feet long and 1,574 feet wide. ' '^^^ 21. A farmer sent to a cheese fartnrv t i^a-? j , in Marrh . 9 Qi« • a •, ^^^^ lactory 1,587 pounds of milk n Tulv i 4 1" ^"^ ' '''^' ^" ^^^y ' ^'867 in June ; 4,634 rndto52lf Nov T'' '^''' ^" "^P*^""^^'- 2>714inO tober; factX set;T'^^- "°^^ --^ -^^ ^^ ten. w.,o .o.„ ., , ../:-■ ;- -; i:z:7\zr^-i SUBTRACTION 15 May 994 917 793 714 June 917 889 719 658 Total 947 939 324 783 397 786 651 727 ;rc:ice between 'om which the •umber to be obtained by 4 s, or less. 235 and 858. d, the number the number to "ne order under md, as 8 ones ten from 3 tens Dnes= 15 ones, es. As 5 tens ens and add to 2 tens leaves 7 m 1.' hunir'Td which leaves 3 hundred. Hence the answer. 3 hundreds, 7 tens, and 7 ones or 377 ones, or 377. ' This process is caUed " borrowing tens." Having mastered the theory, the ordinary and most convenient method for practice is to leave the minuend in its original form, and, when borrowing is necessary, add 1 to the succeeding subtrahend figure. RULE 1. Write the subtrahend under the minuend, placing units of ths same order in the same column. Draw a line beneath. 2. Begin with units and take each figure of the subtrahend from the figure of the minuend just above it, and xvritc the remainder beneath. 3. // any figure of the minuend is smaller than the corresponding figure of the subtrahend, add 10 to that figure of the minuend' and then subtract, after which take 1 from the next figure of the minuend and proceed as before. COMPLEMENIARY NUMBERS Complementary Nxombers are any two numbers whose sum is equal to a unit of the next higher order. Thus, 6 c .d 4. 7 and 3, 8 and 2, etc., are complementary numbers, as the sum of each of these pairs is 10 ; and 36 and 64, 27 and 73, 42 and 58 are complementary, as the sum of each pair is 100. A number is said to be the complement of another when the sum of the two is a unit of the next higher order ; thus, 7 is the complement of 3, 26 is the complement of 74. and 364 is the complement of 636. In all complementary numbers of more than one figure the sum of the unit figures is 10, while that of the other corresponding orders is i?. Example ; 4632 5368 999,0= 10000 247 V53 99,0= 1000 By applymg the foregoing principle, a little practice will enable one to name, at sight, the complement of any number. The ahilitv to do this IS very useful m the business office in making change, 16 I.l '!■ SIMFLtE AUXitt SERIES 4 1. Write the complements of fi.« f n • f4. 73, 28c. 83. 42, 3^4. 65c 48 126 ^'""""^""^^^^ •' 3^' 26c. 83. 55, 22, 31. 43, 82, 53. ' ^' ^^' ^^'^ ^2, 63. 76. 19. 2. Write the complements of f>,^ r n ■ 475. 643. 764. 238. 753^ 146 3 ^rLf 458 TSslc!, T' '''' '''' 3. In case a ten-doUar bill is oVrfd If ' ^^• amount of change required for l.T ^ t Payment, write the «2.75, $1.45, $3.56. $8 2713 42 «« 9Q J '/ '°"°^^^"^ ^"^^^nts : «6.15, a38, $7.23 $Z9i,'^5t$?74'/«^'''^ ^^'^S' «8-21. In each of the foUovJine nrnhf ' l^^' ^•^^' ^^-37. S2.85 by subtracting the sum Tt1.e' iemT^ V'' ^'^"^^ ^^^-^ possible, find the result mert^ly! ' '""^ P^^^' ^V^^<^^e 4. I5c, 12c. 50c. $1 5. 24c. 36c. 18c. 6. 45c. 15c, 36c. $2 7. 21c, 18c. 12c. $1 8- 45c. 55c. 48c. $2 9. 23c. 34c, 25c. $1 10. 63c. 8c, 4c. $1 Subtract the folloWing : I. 68549 2. 97568 34236 23415 Items 11. 75c, 24c, 47c. 12. $1.25, 60c, 22c 13- $3.25, 50c, $1.25 14. $4.60, $2.25. $1.20 15. $1.20. $1.50. $2. 16. $3.60. $4. 55c. 17. $4.25. $5.50. $&20 Paid $2 $5 $5 $10 $5 $10 $20 SERIES 5 S. 438649 6. 870215 7 183756 158634 235746 184693 824316 257948 4. 329145 235648 8. 354182 173659 '■ S "• ^~ "• ^2006398 „. 32405708 37587439 16578345 13- If a man receives a how much will he save per' ve2^?°^ ^^^ ^ ^'^' ^"^ ^P^^^s $568, per year ibers : 36, 26c, 32, 63. 76, 19. 125. 236, 328. 637. 'ent, write the ^ing amounts : •• «5.75, $8.21, $3.37, $2.85 ange required paid. VVliere 354182 173659 32405708 [6578345 ends $568, J SXJBTBAOnON *- ^l of 113.4^'' """''' "'"'' "^ '''^' *° "^'^^^ ^« ^-^ - -suit 15. From a carload of coal containing 53,247 lbs., 34.865 lbs ■ '''''^'Z'"'"^'''^' "°^^ "^^'^^^ ^°^^ ^^"^-in^ ^n the c^r p : 16 What number must be subtracted from 86,023 to leave 19,362 as remamder ? . ^^ lu leave 17. A man deposited $19,075 in a bank inri oU.. a withdrpw «ft^ 19Q u , . , ^"" afterwards withdrew 85,129. How much had he remaining in ,hc bank ? 8197 3 J^° ^''""ng price oj a business was 8346.238.75 anc- 8197^,4.50 was pa,d on .t. What amount rentain,, unpaid .> paJL'i t^-nvL'JdVLtrirr'' - ^'■««' '- '^» • and'^,4'y,379terrS"BvT'''''' ^' °' '"'""^^ » '«•« the n,i,. ina-eased d^ingle yl^"'" "" "^ """"^ °' 21. A speculator bought real estate for fi97 Qfio 4-7 j ,, t at a loss of «fiQ7 SQ T? u 5>^/,368.47 and sold 11- a loss ot *b97.89. For how much did he sell it ? and^he'a^ea'S C^ "r'^tsSrsa '■^'T ^""^ ""-■ ■arger is Europe than th": Uni^Ses >' " """• """ ■""'" 8.7S3.45.^t Augt'*t*h!n? "^"^ "^r^^ ^™""''^ '» was the amount ol the ncrelse ' th b' T *"■''*•'"• '^'>'" 24 In 18C« ,v, , , '"'■ '"'"'' ''"°™' ''"ring July ? s.a.:t ivzz rs'" rzt '^-^ 'rr "' '"^ ^-'-» State was 359,879 acrer TOa ^Ib' "T'" '""^ '" '"^ ^^"« the decade .> ^l"^' ""mber of acres was sold during C mS a1d'D';2^^'°'^' '"'^"'^■^"^^^ " ^ °- A «5, B 85^, andt^aThrju^h t to*;:-^ ?• " ' °- ^ ^- B ''«'. Bro^^- rel' ^S.TnestvS^r ^-^--WP- Todd as much a^ Rr^„ Jones mvests $375 more than Brown: of the firm ? IS the total capital 18 SIMPLE BULBS 'iil ;or ufe t^t^^i:zt;^\ 'r^'' --- ^-^ for the fourth. What did he pav f!r'r i^^ !^'' "'''"^' ^^"^ ^«'^75 29. A man bought a Jot ^or s/i. "^'/i'^^ ^""^''^ ? «75 to have it endosed. and the^soVf .''? ^" '^^^ ''' ^'^'^'- niuch did he receive for the iot ? "" '' '^ ^^^^' ^"^'^ 30. I bought a house for «4 «<;« rJ.-JtuS'^lt '" '""'"' ' ™" '" «'3-85. What wa. .he 'or !!; :i'°°,^Ttr tr.':f -' ^-^- " '■= ^o<,„,Ves, support of his faraiy, $775 "tf'^""''' *""' """^ '" '"a the end of the year f ' ^'" ™°""' "«1 h'^ have left at 'hefetVa^"tg'2fe"d J25'^^:'^r•'^ - -. During -ond year. How If ^i ha^e T th'^'-'f ••'*« ''""'« «■' year? . ""^ ^"he end of the second «»a£[s'':6,^^r;CTXCr''^- '^ "^^ ^d the 35- On Ncvember I F-i^r /tr n i ■ cantile Bank was {J947 60 On r f ^"^""'^ ^* ^^e Mer- ^256.75. and on N embe?27 ;2^°^'" '" ''' 1'^^ '^^^^^^^^ withdrew on their cheques % 159 S* wk"?^ '^' ^^^^^ they balance on December 1 ? ^^'^^^■^^- What was their bank ^^ 36. A ranchman being asked how many cattl. h u ^ If you give me 67 and I buv TAQ fT ^x ^^ ^^^' '"^P^^^d : 258 left." How many had he^ ' '" ^ '"" ''^^ ^^ -"^ have is tS'^LZT'"' '' ''''' ^"^ ^'^^ -bt-hend 1,216. What 38. The cost of mv lot wac «r -rcn x my house, $1,210 • LJrZl , ^^'^ ^^'^ "^^^°n work ot ^85; for dec.at;ng!%r6STtr;:-'^^^^^^^^^ ^^ P^-^ing! soddmg and fencing grounds \IZ tk ^' ^^^^ ' ^°^ ^^^^ing, date of sale was |3l| ^ I then .oldTh '"''""'* '^^ °"«^ys to receiving cash $6,000. and 7 note 1 ^rr^'^^^ ^ ^^^^ ^' ^^'250. face of the note ? • note for the remainder. Wh at was the ►0, paying §3,800 tJ^rcl, and <;i6,97vS use ? have it graded. ■> of $275. How for repairs, and What was the If he requires, ; and for the le have Jeft at cash. During >.36 during the of the second 7,896 and the - at the Mer- sey deposited e month they 3 their bank had, replied : 56 and have 1.216. What Lson work ot »r plumbing, for grading, 1 outlays to i 1 of $1,250, '''hat was the inTLTlPLTCATrON 19 39. Which of the two numbers 78 Tifi ..„.i ocno< • [to 47,215, and how much? ' '^ ^^'^^^ '' "^^^^^ liS^I'i '\,"^''^''^«"V'\'««^^Pt.s for the first half of a year were i\>ti,^io. Ills receipts n Januarv wpro *«»= • i "T. ^ ^®^® in March, $1,050 in AvTt^z^Tf ir''^'^'''^''y'^^^^' I were his I'eceipts in June? ' °^ ^" ^^"^' ^^'^^^- ^hat i yeat':l'AlZ '''' ' ^^^^^^"^^ ™ '' ^-- old. In what l*60o''rett"?e'$i2rrd" f'' "^^ ^^ ^°"«-= ^ages I bank $42 His erenditn;. '""'T' "^ ^""^« ^^ ^ ^^vings i$75, /rocer'7$oS ins-- '''^'^ *'^'''' ^'" *^^^' ^"^'^ ' ith;r\.;e;se!l70."k™:^^^^^^^ '''' f'^^^^ ^^^O, and j ^ ^"^^"^'^^^ did he save during that year? MULTIPLICATION ^^^^^^^i:.:^'--^ "' «"^'n« the su. When The Product is the result obtained by multiplication, mJm^l^ "*"*" «**!«.«»«, and is read, ti„e., or The product has always the sa„e unit as the multiplicand, ine Factors of u Vumber «-- <' jquals the given num^r th^' 7 anT. "' V"'"' P^°^"«* because 7 and 3 multinli J '+n .i: ^ ^""^ ^^«*o^« «* 21, ' ^ multiplied together equal 21. SIWPLE RT7t.ES MULTIPLICATION i . iDLE aa a4laa Call the figures in the column at the left the multipliers and those arranged horizontally at the top or bottom the muhipl 'p.^s The product of any two factors will be found in the line to the nght 01 the multiplier and under or over the figure mult pli d For Illustration, the product of 20 multiplied by 20 (400) m b found by following the black lines to the r oint Lre thVy me;^ Illustration l.-Find the product of 2416 x 7. SoLuxroN.-Write the multiplier 7 below the unit figure of the mulhplicand as shown in the margin, and be^n at the nght to rnultiply. 7 times 6 units equafs 42 units.^o^ 4 tens -u 2 umts Wnte 2 units in the place of units, and reserve 4 .. to ada to the product of tens. 7 times 1 ten equals and 1 ten W^; "- "'tK ;' ' ", t *'"' ""'''''^'^ ^""'^ ' ' *^"^- °^ ^ hundred hundred resen^e. g.ves .^ Zdred, :. t'^onsand " d. '"' fT' *'^ ' Q i_ xi,„ •„ X L. J , '-^''=-'-' ""^ - '^nonsand^i and 9 Hundreds, Write 7 timt ^r. "f'""'- ""'^ '''''''' 2 *° ^^d t° th^ Product of thousands 7 t;me3 2 thousands equals 14 thousands, and adding the 2 thousand 16912 resei aire; 16,9 unit r^nd and ; I Ti th' c( a] way I. nniis i 2. the m\ right-h multip 3. produc lultipliers, and multiplicands. the line to the are multiplied. (400), nu.y b'^ ! they mee'. the unit figure md begin at the units, or 4 tens aits, and reserve les 1 ten equals ;ns, or 1 hundred d to the product d adding the 1 undreds. Write ct of thousands. be 2 thousands MULTIPUCATION 21 iLLusTRATir.N 2.~-Fmd the product of 417 x 356. and 30U r«n .f , ^^ r ^- ^'"'t'P'ying the multiplicand by 6, 50 and .0 respectively and adding the products, the results are as folLs : ' la) FULL Partial Products. (fc) Abbreviated Partial Products. 19??nn 0"""^^ S'"^'"^' ^y 50 2085 '■^^^"" Partial Pro "^y 6. obtaining 5 (tns)aTh"' '^"'^ *^^ --'* and 3 (tens) as the next remainder r.J ! , ^ "'^* *J"°tient figure. mT:V: *'" "^'^^ -^- of t e":,,,^;„7. "- .'ast remainder (3 tens o (^« -'ts) by 6, Obtaining 6 units as the^t^u^S ^rt'"' ''' '''^'' LONG DIVISION DIVISION 25 lumber when the in exact divisor, an exact divisor. d mentally and divisor consists one's thorough of the dividend, 3 below the divi- id by the divisor, ied. Thus, 2 is vrite the 4 below ireds, 2 hundred 3 contained in 6' s contained in 2 ing the division, d) and 3 (hun- nder the order '0 tens) to the ^ide the result juotient figure, der (3 tens or vide the result ted mentally i; 37)81449(2201 J^ 74 74 74 49 37 ■*2 Remainder. Illustration.— Divide 81449 by 37. Solution.— Write the terms as in short division, and place a line after the dividend to separate it from the quotient, which is now to bo written at the right. Then divide the fiut two figures of the dividend, 81, by the divisor, 37, and obtain 2 a: the first figure of the quotient ; then subtract from 81 the product of - x 37, or 74, obtaining 7 as a remainder ; to this remainder annex 4, the succeeding figure of the dividend ; which gives 74 as the next partial dividend,' the divisor is contained in this dividend twice, or 2 times, giving 2 as the next or second quotien. figure ; subtracting the product of 2 x 37 from 74, nothing remains ; then brmg down 4, the next figure of the dividend, and as it is less than, the divisor, place a in the quotient ; next bring down 9, th; remaining figure o.' the dividend, which gives 49 as the last partial dividend ; the di-.isor iscontrined in this dividend once, or 1 time ; writing this 1 in the quotient and sub- tracting the last partial product from the last partial dividend, Y2 remains ; write tliis remainder in the form of a fraction at th2 right of the other figures in the quotient, and 2201 Jf is the result of dividin^ 81449 by 37. Italian Method By the Italian Method of dividing, the divisor is placed on the light of the dividend, and the quotient immediately beneath it. The advantage .in this is that the numbers concerned in the operation are closer together. To illustrate 28260(36 30 785 18 Divide 1978 by 7. Divide 8976 by 6. Divide 10274 by 8. Divide 7861247 by 4. Divide 20761201 by 5. 6. Divide 1217294C by 9. 7. Divide $8673.57 by 3. 8. Divide S407232.4S by 9. 9. Divide 9706421 by 11 I. 2. 4- 5. SERIES 7 11. 21786 ^ 19 = ? 12. 87463 -v 28 = ? 13. 10271086 -r 146 = ? 14. 94207658 -r 67 = ? 15. 560217563 -r 496 = ? 16. 85205617 -r 649 = ? 17. 417601924 -f 4567 = ? 18. 93681596 :- S37 - ? 19. 170215862 -r 299 = ? 'in 10. Divide 201634596 by 12. 20. 37021675 -i- 7019 = ? 28 SIMPLE Rt7l.Ea 21. U a train moves n -.m how long vvi], it .equ.e to go 336 1^^: ^ °' '' "^'^^^^ ^^ ^^^ vaIu?of^a^arm'er's''rrf ''"^' ^'^ ^"^^^^ ^" «^^ "market price th. ri,vi u ''^rmer s crop is increased £ 27* If S350 be nairl fr^- e:n u can be bough, for sLe 2 af tht"™ ''°"' '■°" "^"^ barrels . ^o- 1 bought a fa™ f„, S6;3 "orr":^ •' ga.n,„g J2,75 pe, acre. How'l'fy I'ljid f, "/" ''■''«■^^■ 29. I bought 24 varH. f . '" '''™ ™"'ain ? Bl30acres,a„dCtherematad r the, A"^ " '^ """^ '^ acres, 3r. If 37 sheep and 4,, n ""^ °' """°™ """= ? are worH, S2iO. what are! pJHrr* *'"'■"• '"" ^ =»«? centfpet^rd\S\'80^;j-t ,ta'':t ^^^ '"^""^ ^' Pe- pound. At what price per D„,md ^''■A"*'' "^""6 35 cents 33. A farmer sold a„ I'L . t , ""^ ''" " '°«''™ «"-7S ? receiving S3,540 for th whot V r"""""^^' ^""^ ^"^ calves, - »37,a„daca,fat S.^td the ^'Xroft?: " ^'^^ ^ "^ 34- Ten cents will buv •? nr n„ ^ , many apples are worth as much Ts d "'' " ' "^^^^^ ' ^°^ temons ? """"^ "^ 5 dozen oranges and 7 dozea DIVISION i^-iles per hour, rket price, the many bushels >f the numbers of 575 gallons or $42,360.75; the value of Tiany barrels 'r $7,218.75, ■m contain ? iend bought 'ard, paying g 420 acres . ^ 75 acres, >rni value ? i 28 sheep costing 25 ? 35 cents n $11.75.? nd calves, 39, a cow 5les ; how f 7 dozea 27 are there in each chest ? '°- '^ *' l3-7o. How many pounds on what he sold What dW^h',^ «"'"'"^ '^ "=■="'= P« bushe 37 A bush! n/ I '"'''''' "" "'" P"^' '•"^el ? weiS .ae^r if3;;r„ :r,„i',V"v;"^' -' «°" barrels of flour can be u.de iro^'^tl^-f^Z'''^ """' L^^an'; ::-r;,-^ f --el-, .^^r-xi thaf'i iSl by'SitaJf:'' " t'-^" "" r ' «="" " -"= ™- seUing 800 yaMs 7suo pe'^aS?"'^ ''''' ™""' ' «"'" "^ be reinforced by 250 men ? "^ ""^ ^ "^°"^^^ t^ej 41* A horse worth .^170 anri q exchan d,„,,,^^^f™^-.^3;^ows^w„^^^^ wf£°«;pTXinrer^:,:?t*:iif"°-t"^"^^ only $3.60 per gallon ? ''^'''^ "'^^ ^^ ^^orth .he^';t'tr:^ir r:,::;'^^rri,ie:rt --^ '-- '-- --^ -« on 1 1 boxes each containing 20 dol." "'" ""'' '"' ' «^'" num'bJisSolS "^^^'^ f/'» -d "- P^duct of two other. ^'^^''^W- One of the numbers is 9.402; iind the U=fellnT3.tt\tTrlt'r^^^ Find his gam on the whole lot. ^^ ^^^*' 46. What is the least number th..t must be adied ' ^ millions to mak'p it o^^^f-i i- • •, , aaded lo five nineteen ? '"'^^ ^^"'^^'^^ "^^^ -^^n thousand and ! ill 28 SIMPLE RULES 47. A drover bought a number of cattle for $4,375. and sold IZT ""''Lo ''^" '"^ ^' P^^ ""^ f°^ the total sun S $3,655 gaming $680; for how much per head must he sell the remamder so as to gain $400 on them ? ^ 48. A merchant bought a number of barrels of flour for $4 600 and sold them for $5,200. thereby gaining 75 cents per bari^ hovv^n^ny barrels did he buy. and what did they cost him pi; 49. A person, after paying out of his income for a year a tax oU cents m the dollar, has $7,200 left Find his income for a 50. A residence property rents for $35 per month. The annual taxes average $75 and the reoairs IS'.O tL « , ^"""^ rate of «i 7^ rl. ,/"^ ^f P^'.^^ ^^' The owner pays the water rate of $1.75 per month ; what is the net income from the propertv durmg a period of five years ? property 51. A committee has a certain sum with which to purchase nrit $U0 nef 'T\. ^'"^n' "' '''^' '' ''^'^ purchasfcat^ ^ :;7re;2d7 ''■'' '' ''- ^- ~- "rr; HeSd'^$27'/for"f ' '"?!!' f ''""^ "°°' '°* ^^ ^^6 per acre, ft $^^0 Ir A Tl '^' ^"'' '°^^ ^^""^ '' '^ ^°^ds of wood at $1.50 per cord, and then sold the lot for $950. What did he gain on the speculation ? ^ 53. An orchard contains 26 rows of trees, with 42 trees in each row. The apple crop from the orchard was sold for ^95 What was the value of the yield per tree ? .n ?"*■ ^-,1^™'' ^^' ^^^-^ ^" '^^^h' ^"d by selling his crop of apples at 75 cents per bushel. 3 calves at $8 each, 7 lambs at $4 25 and borrowing $72 from a neighbor, he is able to pay off a :^or4,e per pou^d'^^tT^."'' T '°""'' ^' ^" ^^^^^ ^-^^^^S ^2 cents per pound with 175 pounds costing 16 cents per pound At what pnce per pound must he sell the mixture to gain $&75 ? $4,375, and sold the total sum of Tiust he sell the flour for $4,600 ints per barrel ; ;y cost him per or a year a tax is income for a h. The annual pays the water m the property :h to purchase urchase carpet- tiaving enough it 95 cents per 1. How many $26 per acre. cords of wood What did he ! trees in each 4,095. What g his crop of tnbs at $4.25, If a mortgage lels of apples :ing 12 cents d. At what 5? DIVISION 29 sold 465 bushels, then boul, ,2, u"" ^""^ht 340 bushels, then to reduce his sto k of corn fo eau v, f ''' .""'' ""■'" ^"'^ ^'"""Sh (of his last sale at 68 ce,rper b "sM > *' ^''* ^^^^ '"^ -'-"' a";rprr^^;sr - ™- "^ -> *":::s:ri*^if 59. A farmer sold to a merchanf i<; j . cents per pound, 25 dozen eggs at 4 Ir' 1 '""" '' ^8 chickens at $2.20 per dozen fn/ ' ^^' ^°''"' ^ dozen of molasses at 55 ceL per Jallon 9 P^^'™'/"^^"^^ ' S^"°- per pound, 1 barrel o^ Zf t^sS ^h T' '' '' ^^"^^ sugar at 8 cents per pounds How ' ""^ ^^'' remainder in [farmer receive ? ^ ^°'' "^^"^ P^""ds of sugar did the 60. A contractor engages to buUd a house for «2 «7«: I he uses lumber costing '• «^'-'5; paper, S3,a25 ; printing and binding i, S T '' ""'""^ ^ ■ K tl>e books are sold at 50c each wtf ^ ' ''^''""^ «'5-95. J '**■"'"''■ ™'>^"= "ic gain on each book ? 4 07. A speculator bought a nior» „« ■ 1 • soM the property at an S^^f^^Sm ' 'T''' ''' ^'''''' I and invested the money in wla !t 687" f P^^^^ P"ce. wards sold the wheat at 74c a tsh.l ' "'^''^- ^' ''^'''■ other charges to the amount of $62 75 It ^'^^"^ ^^^^^^^ion and capital increased ? ^^"^ "'"^^ ^as his original :rreirhi'r;ru!d ^r-" -^ ^-'--- would remai; unLpendedT ' "' P""''^^^"' ^'i "'-''™ JohS SLt ef 'Lttr 'rr ^^^ "' «>* fathers, made the calculatio;, "a; 'thaf 4 '^aT^ "^^ J''''''^' "^-^ average of the four iust w ,„ ,.f. "" ^^c "ill make the father ? '"" '^ y^"=- What is the age of James's -ided b. 3.3, the retf. X'^-^:^ i ^ ^ ^ f^^' werrx";:d'rdot '^'tsf "^" " ^^^'°™ "-- '* ™- CANCELLATION lid he ride on his @ 19c., and sold peculation in pork • a pound. What Dalhousie College Board and room, Haundry, $41.15; lily expenses ? 3ks are as follows : packing, $15.95. in on each book } Perty for $2,650, e purchase price, ishel. He after- commission and ^ was his original i a certain sum bicycles at $27 bought bicycles I, and what sum of their fathers. James, having will make the age of James's 1 multiplied by the remainder number } what 180 men 31 72. A young man graduated from college when he was 25 years old. His mother was born in 1835, and his father is 4 years older than his mother. If the father was 32 years old when the son was born, m what year did he graduate ? 73. What is the least number that must be subtracted from one million to make it exactly divisible by 359 ? $12 per M. f.o.b. cars at mill, and shipped same into Toronto paying freight at the rate of 19 cents per cwt. The lumber on being unloaded and measured is found to be as follows • 2 M feet basswood, 3 M. feet red pine, and 4 M. feet ash. Estimated weight of basswood is 2,700 lbs. per M. feet, pine 3,000 lbs. per M kmd:f\u':r^- '-' "• "" '-' '-'-' - ^^- ^- "each 75. A Toronto merchant wishes to purchase a car of hard coal and receives two quotations ; one naming price of $5.25 per short ton f.o.b. cars Toronto, and the other naming $4.60 per long ton f.o.b. c::rs Suspension Bridge, New York. On latter there would be no duty but there would be freight to Toronto of 60 cents per ton to be paid by purchaser Which quotation is cheaper and by how much per short ton ? ' 76. A Toronto merchant wishes to ship 11,150 lbs of m^r chandise to Brantford, Ontario, by the cheapesi route HeZ two options : 1st, to ship in the ordinary way and pay freight at rate 01 25 cents per cwt., plus ^ cents per cwt cartage at Toronto and the same at Brantford ; 2nd, he can ship in a car at rate of 11 f f^L''^^' °'' ^ "Minimum weight of 20,000 lbs., and pav a flat rate of $5 for cartage at Toronto and $4 at Brantford Show cos of shipping goods by each method. CANCELLATION Cancellation is the process of shortening the operation of di^W^ion or the combmed operations of multiplication and division, by' omiStmg or stnkmg out equal factors from the dividend and divisor 32 SIMPLE RULES X s'Zr.'V'^'!;"^'* " '^'' 'J"^*'^"* of 25 X 6 X 8 . 9 X 27 ^odivided by 4x3x3x5x4x2x9x6? ^ "" ^ $ 3 ^>c3x3xyx4x2xOx0°"4' "'^ ^^* Solution.. -Place the divi. dend above and the divisor below a horizontal line ; cancel all factors common to both dividend and divisor. Tlie pro- duct of the numbers above will u *, fHvidend and divisor. Tlie pro- numbers below w^l^:: TiZrV^^T. !:[ 'V^""^^ ^'''^ ciivisor. divide the dividend by the hvisor and ^ ' V''. ''■^^" '''" ^"^^ be written above the divi.or. " reniamder, if any, may SERIES 8 1. Divide the product of 21 x 15 x Q h„ +h 5x7x3. ^* ^ 13 X y by the product of 2. What is the quotient when 24 x lOft s, lo -, divided by 18 X 4 X 8 x 14 ? x 108 x 12 x 7 x 5 is 3. Simphfy 81 X 25 X 34 X 30 ^ by 21 X 5 X 6 . ,- ^^4.^I^.de72x210x95x60x42\y2lVl9:;2xI0 by el'Tul'l TuT '" '^^^'^"^ ^^ ^ 7 ^< 9 X 27 . 40 X 56 given';n?x:;aTg7for4T?^^^^^^^^ ^ '^. ^^"^^ ^ ^^^^ ^^ould be nge 45 bushels of wheat worth gO cents a bushel ^ bushels each, a. 35 cents a bushe^ * °' ''°'"""=^- "' * P yard. How many pieces of calico did he receive ? .s^t/ruia Thr™ti'„vr,^r ^™--« barrels of sugar of 225 pounds erchatS '^' ™* '2 Price per bushel was allo3 for the t " ' "" """"^ ''''"' 10. If 8 loads <-'f rnrn co -1^ ■ • ■ -ush.s, .ere.ven=:;:rr^- tS »-^^^^ CANCELLATION 88 5 X 8 X 9 X 27 —Place the divi- and the divisor ontal line ; cancel omnion to both livisor. The pro- fie product of the ' larger than the tier, if any, may le product of 2x7x5 is 6 X 17. 19 X 12 X 10 27 >. 40 X 56 tid should be Its a bushel ? 18 yards, at tatoes, of 60 I, averaging >r a number tnd worth 5 ceive ? ■; averaging rye with 12 ind. What d each bag , averaging 250 pounds per barrel, and worth 9 cents per pound, what was the corn worth per bushel ? COMBINATIONS OF ARITHMETICAL PROCESSES It is often desirable to express in one formula, or statement, several arithmetical operations; also to indicate the order iil which these operations are to be performed. This is accomplished by means of the four arithmetical signs + , -, X , and -r , used in connectio n with the comma, the parenthesis ( ), and the vinculum Thus, the expression 6 + 7, x 9 indicates that 6 and 7 are to be added, and the sum multiplied by nine, the result being 117; while the expression 6, + 7 x 9 indicates that the product of 7 X 9, or 63, is to be added to 6, the result being 69. The parenthesis is used to inclose one or more indicated opera- tions, the result of which is to be considered as one quantity. Thus, 5 + (12 -r 3) + 8- (2 X 3) indicates that the quotient of 12 -f- 3,* or 4, is to be added to 5, that 8 is to be added to this, and that from this result, 17, the product of 2 x 3, or 6, is to be subtracted, givmg the result, 11. . ^ The vinculum may be used instead of, or in connection with, the parenthesis. Thus, 27-24 - (12^- 8) indicates that the whole quantity, 24 divided by the quantity 12-8, is to be subtracted from 27. 27 — !4 Solve the following : 1. (17-8) ^ 3. 2. 51 -r 17 +9- (2 X 4). SERIES 9 3. 4- 34 -=-, 15 + (3 x 2) -r 3> (7 5_^ 15) + 9. 2 5. (98-7) -r (8-4 X 28^9). 6. 54 ^ (12 + 78 - 13) + 15 - (8 - 4). 7- (25-6) X (52 -r 13) . (3 X 13) - 37. i n 84 SIMPLE BULE&l METHODS FOR PROVING WORK Addition may be verified by reversing th. «r i . , , TZtT "'" " "'""^^' """ "- ""-"d, the work Multiplication may be verified in two ways ■ remultiplvi^rif ';f"' "^ """""'" "'^ ■"""''•'-'"<' -''=■ '^ "- greater than 2, so the tosTHATVoN 2.-Cast the elevens out of 5160459674. -,. , ^ Solution The sum of the digits in the odd places = 4 + 6 + 5 + o x t ,. The sum of the digits in the even places -iZ 111 .^ ' "= ^^■ From 16 subtract 11 and 5 are left -7+9+4+6+5= 31. From 31 subtract 22 and 9 are left result is ! 1 - (8 - 5) = 7 °' *^' ''«"» " the even places, so the METHODS FOR PROVING WORK 37 g the excess uotient. If 3SS of nines hen there is »f any other case of the -k figure is ;in with the 1 we begin Then, if the sum of :e between ices is the ^ese sums, eleven, we itains and I. 1=10. 5=35. St multiple a 2, so the = 16. = 31. now less s, so the There is no short method of casting out the thirteens, seven- teens, or nineteens from a number. To do thii, it is necessary to actually divide the numbers by these various check figures. But a little practice will enable the student to divide by any one of these numbers mentally. Probably the best check figure to be used is 13, although the adherents of each one will advance various reasons why their particular choice is the best. There are numbers of errors that 9 and 1 1 will not detect. On the other hand, the process of casting out nines or elevens is much easier than that of casting out thirteens, seventeens, or nineteens. Of course, the smaller the divisor the easier the division is effected. So that, all things considered, probably 13 is the best one to be used. Many bookkeepers and accountants use a check figure in doing their posting and in taking off a Trial Balance. In fact, some will make no calculations thr.t they do not verify in this manner. The check figure 9, however, should for obvious reasons be avoided by the bookkeeper. SERIES 10 1. Find the product of 8467 and 359 and vtiify the work by casting out the nines, 2. Divide 367452 by 627 and prove the correctness of the work by casting out the elevens. 3. Add 3685, 2736, 4985, 283, 34756, 23754, and 9136, and verify the work with the check figure 13. 4. Subtract 458367 from 923645 and verify by casting out the nines. 5. Multiply 37546 by 963 and verify by division. 6. Divide 7436254 by 397 and verify without the use of a check figure. 7. Find the difference between 3782654 and 4253263 and verify without use of a check figure* M,' FACTORS AND MULTIPLES FACTORS itselt r^d'r ^ ■"'""'' -^ -y --' divisor of that number, except muwS by lrpr2certr„u„tr "^ "'•'"'°'' **■ -»» Thus, 3 and 2 are co-facton, i„ relation t .1, APrimeN„n,h. ■ ""'"'"«» the number 6. .tc "' """^^ '^ °- *^' has no factors ; as 2. 5. 7, ni3 - s'foXt ^""^^ '^ - '"- - be resolved into factors ! 1 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 TABLE OF PRIME NUMBERS FROM 139 233 149 239 151 241 157 251 163 257 167 263 173 269 179 271 181 191 277 281 193 283 197 293 199 307 211 311 223 313 227 317 337 439 557 347 443 563 349 449 353 457 359 461 367 373 379 479 599 383 487 601 389 491 607 I TO 1000 569 571 577 463 587 467 593 653 659 661 673 677 809 769 883 773 887 787 907 797 911 683 811 691 821 701 709 919 929 937 823 941 397 401 409 499 613 503 617 509 619 ^19 521 631 42' 523 641 431 541 oAo 229 33) 133 547 2' ' • ^°^ ^ ^"^^ Pnme factors of 105. 827 947 719 829 953 727 839 967 733 853 971 739 857 977 743 859 983 751 863 991 877 997 881 757 761 FACTORS 39 LES ' imber, except 3th said to be vhich, when 5, 7, U, 13, nto factors ; 769 883 773 887 787 907 797 911 809 919 811 929 821 937 823 941 827 947 ?29 953 J39 967 J53 971 157 977 !59 983 63 991 77 997 81 A Composite Factor is a lac cor which is a composite nuiiiLior. Thus, 15, 21, and 35 are composite factors of 105. Tests of Exact Divisibility.— The following tests of exact' divisibiUty are often useful in a search for the factors of a number. (1) A number is exactly divisible by 2 if its right-hand figure is zero or a number exactly divisible by 2. (2) A number is exactly divisible by 4 if its two right-hand figures are zeros or express a number exactly divisible by 4. Examples.— 173528 is exactly divisible by 4, for 28 is exactly divisible by 4 ; but 319378 is not a multiple of 4, for 78 is not exactly divisible by 4. (3) A number is exactly divisible by 8 if its three right-hand figures are zeros or express a number exactly divisible by 8. Examples.— 536 is a multiple of 8, therefore 1397536 is exactly divisible by 8 ; but 356 is not a multiple of 8, consequently 4679356 is not exactly divisible by 8. (4) A number is exactly divisible by 5, 25, 125, if the number expressed by the right-hand figure or the two, three, right-hand figures is exactly divisible by 5, 25, 125 (5) A number is exactly divisible by 3 if the sum of its digits is exactly divisible by 3. (6) A number is exactly divisible by 9 if the sum of its digits is exactly divisible by 9. Examples.— Test whether 18637569 and 7385621 are divisible by 9. 1 + 8+6+3+7+5+6+9= 45 =9x5, .-. 18637569 is exactly divisible by 9. 7+3+8+5+6+2+1 = 32=9x3+ 5, .-. 7385621 is not exactly divisible by 9. (7) A number is exactly divisible by 6 if it is exactly divisible by both 2 and 3. (8) A number is exactly divisible by 10 if its right-hand figure is zero. (9) A number is exactly divisible by 12 if it is exactly divisible by both 4 and 3. (10) A number is exactly divisible by 1 1 if the difference between the sum of its 1st, 3rd, 5th, 7th. etc., figures and the sum of its 2nd, 40 FACTORS AND MULTIPLES 4th, 6th, 8th, etc., fieures is 7prn nr - u by U. ^ ^^'"^ ""' ^ "'^"^ber exactly divisible ExAMPLEs.-Test whether 729583624 and 45798'^fl9I . by 11. ^* '*"" 4a/98J621 are exactly divisible X 2' "■.^L'sL'i^ '='''■ 2+3+5+2=12; 34-12-22-n K ^, . . 729583624 is exactly divisible by 1 1 * 1^- 22-- H 1 + 6+8+7+4=26; 2+3+9+5=19 26 19-7 • ,.^ notexactiy divisible by 11. ^^' •"• 457983621 is SERIES II I. 2. 3. 4. 5. 345672. 2143560. 3657247. 281)3652. 5329170. 6. 4362416. 7- 3758362. 8. 43621545. 9. 213654829. 10. 3267037021. ^^^-.H„«..Hep_o.sepa.«;rZ^':„.„,^,„^ ILLUSTRATION.-Factor the number 1260. SoLUTioN.-Since the number is even dmdeuby2. 1260+2=630. The first quot^nt being even, divide again by 2. 630 (3l^H\ I """^ °^ ^^'^ '^^Sit^ in 315, 3 W.H -^^'k^'"^ ^' ^^^'^^ '« divisible by ?05 tl'' ' '"^ ''' '''' *h'^d ^l"°tient aLin and "''°" '"^* ^'^^"' ^^^^^^^ ^y 3 again and we get 35. Now divide bv 5 -ce 35 e ,3 ,,,, ^ ^^^^e J,y 5 work th -^"t"'' "'^^'^ '^"'^P^^t- the work, the prime factors being 2, 2. 3, 3, 5, Rule rf^w^e ^/^. ;'«w/^«,. guoiieni ' aJl I ^ f'''^''' 'i^il^rly is obtainecl THe^ZTLsZt 17^^^^^^^ ""'' ' ^''"^^ ^-^-«' factors. '''' ^""^ ^^' ^^'^ ^»of.iml are the prime 1260 630, first quotient. 315, second quotient. 105, third quotient. 35, fourth quotient. 7, last quotient. FACTORS 41 ictly divisible xactly divisible ■12= 22= 11 457983621 is :tly divisible ■) n, (;) 12, o its prime ber is even, ). The first 1 by 2. 630 igits in 315, divisible by rd quotient, divide by 3 ivide by 5, thus we get npletes the 2, 3, 3, 5. similarly 'e quotient the prime Proof The continued product of all the prime factors should equal the given number. SERIES 12 Resolve the following numbers into their prime factors : I. 64. 6. 1575 2. 144. 3. 512. 4. 1050. 5. 1527. 7- 2376. 8. 2744. 9. 4367. 10. 6435. II. 15625. 12. 18216. 13. 21659. 14. 25785. IS. 38577. A Common Factor, or Divisor, of two or more numbers is a factor which belongs to each of them. Thus, since the prime factors of 6 are 3 and 2, and of 10 are 5 and 2, it will be seen that 2 is a common factor of 6 and 10. The Highest Common Factor (or, as it is sometimes called, the Greatest Common Measure c . Greatest Common Divisor) of two or more numbers is the largest factor common to the numbers. Thus, all the exact divisors of 12 are 2, 3, 4, and 6 ; of 18, are 2, 3, 6, and 9 ; and of 30. are 2, 3, 5, 6, 10, and 15. The divisors common to the three numbers are 2, 3, and 6. The Greatest Common Divisor or Highest Common Factor of the three numbers is, therefore, 6. Numbers are prime to each other when they have no common factor. Thus, the prime factors of 9 are 3 and 3, and of 22 are 2 and 11. 9 and 22 are, therefore, prime to each other. Illustration 1. — What is the g.c.d. or the h.c.f. of 30, 45, 60, and 75 ? 30=2 X 3 X 5 45 = 3 X 3 X 5 60 =2x2x3x5 75 = 3 X 5 X 5 H.C.F. = 3 X 5= 15 Solution 1. — Factor each number and pick cut all the common factors. The product of all the common factors will be the h.c.f. Solution 2, — The g.c.d. of these numbers cannot be greater than 30 ; if 30 is an exact divisor of the rest of the numbers it is the n.c.D. By inspec- tion it is found not to be a divisor of all the numbers. Dropping the smallest factor, 2, out of 30, and using the other one, 15, as a divisor, we find by 42 FACTORS AND MTJIjTIPLES .1, /V^^""""^^'" ^'^ ^^'^^ ^"^ the factoring, therefore difficult the following method is commonly used : * Illustration 2.-Find the g.c.m. of 1645 and 1833. Solution — First Method : 1645)1833(1 1645 188)1645(8 1504 141)188(1 141 G.C.M. = 47 47)141(3 141 Rule Dtvtde the greater number by the less, and the last divisor by the lastremmnder, and so continue to divide until a quotient is obtained wUhout aremamdcr. The last divisor obtained will be the greatest common divisor. ^rtme!>i Where more than two numbers are given, first find the G.C D IZleL ' "'"" '^ ''' ^•''•''- ^'"^ ^^"^'^ ^"'^ ^^- ^^-^' The following arrangement of the work necessitates the placme of fewer figures on the paper : ^ Solution.— Second Method;: 1833 1645 G.C.M, = 47 / lerefore, it is. the efore, difficult, nd 1833, FACTORS 43 *a( ' Uvisor by the it is obtained s the greatest ■ the G.C.D. md the third the placing SERIES 13 Find the g.c.d. of the Mentally. 1. 12 and 18. 2. 15 and 25. 3. 18 and 24. 4. 20 and 36. 5. 24 and 72. By Factoring. 6. 48 and 84. 7. 60 and 90. following numbers : By Division. 11. 964 and 1272. 12. 729 and 1701, 13. 513 and 1368. 14. 4125 and 6750. 15. 8778 and 9702. 16. 4853 and 5697. 17. 1177 and 1498. 18. 2827 and 10537. 8. 75 and 125. 19. 1027, 2133, and 2449. 9- 84, 96, and 120. 20. 1157, 2047, and 2937. 10. 48, 72. and 360. 21. 1268, 1472, and 1684. 22. A man has four large lots, containing respectively 675, 1125, 1575, and 1800 sq. ft. He wishes to divide them all into smaller lots of the largest possible size to contain an equal number of sq. ft. How many sq. ft. will each of the smaller lots contain ? 23. How many ft. in circumference is the largest locomotive drive-wheel that will make an exact number of revolutions in going a distance of 513, 608, and 1368 ft. respectively ? 24. Find the largest number that will divide 49, 73, 97, and 121 and leave a remainder of 1 each time. 25. What is the largest number that v;ill divide 179 and 301 and leave remainders of 17 and 13 respectively ? 26. At the intersection of three avenues is a triangular piece of ground whose separate sides -.re 64, 80, and 112 ft. What is the length of the longest boards that can be used to build a fence around it, if the boards are of equal length and no allowance is made for waste ? 27. A carpenter is directed to make the widest possible side- walk, no wastage, out of "the following planks each 1 foot in width and 2 inches in thickness : 9 planks 20 feet long, 8 planks 16 feet long, and 6 planks 12 feet long. What will be the length and width of the walk ? (Planks to run crosswise of the walk.) 44 FACTORS AND MUIiTIPLES 'I! MULTIPLES A Multiple of a number is a number which will co-itain fh given number exactly. coxitam the Thus. 12 is a multiple of 4, of 3, of 6, or of 2. eight multiplet of iS E^inf,; « ' ' *' ""• """ '^O »" *= ii„t «;a. 60 J „„ a„ ;o'rs4rr;r,^^r„T,r ".u.«p.e, ». „„. the i.c.M. of the three numbers. ^^ '^' therefore, ^ ^ILLUSTHAXIOK ..-What is the L.C.M. of 5, 6, .0, ,2, .8, and 5 X 24 is 120. The nexfnlbt; T'T"?' ' "' " """ "'»* >» "'I. The last number 18 LSZ . '/ """ '° '^ " ='"'« <«"»' »f 120 be increased by 3 as a factor 3 x 120 11^ \,T"'°'"'."'' "" '"°°" t.c.M. ^ X i^u IS dbO. the required number, the SERIES 14 Find the l.c.m. of the following : 1- 3, 4, 5, 6, and 8. 2- 2, 6, 8, 12, and 24. 3' 3, 9, 12, 6, and IS. 4. 12, 18, 24, 36, and 48. 5- 6. 24, 32, 28, and 18. 6, 8, 12, 24, and 32. 7. 4, 8, 16, 32, and 128. 8. 4, 6, 14, 21, and 42. ■ i MULTIPriES 45 ill contain the number which lumbers is the them exactly. 120 are the first and 120 are the 120 are the first mltiples we find 60 is, therefore, >. 12, 18, and exact dividend inspection it is By comparison a prime factor ■ must be used, divisor of 120. 3, 3, and 2. 9 tly. 120 should i number, the and 18. i, and 32. I, and 128. 1, and 42. Illustration 2.-What is the l.c.m. of 75. 120, 150, and ISO ? ?o= 3x5x5 120=2x2x2x3x5 150=2x3x5x5 180=2x2x3x3x5 2x2x2x3x3x5x5= 1800 1800 is the l.c.m. It is, therefore, I ^^^ *^° ^'^' °^ i' must be 1800. Solution l._Set the numbers down in a column, and opposite each one set Its prime factors. Scanning this list of factors, we find that they consist of 2's 3 s. and 5's. The most 2's we find in any number is 3 ; the most 3's is 2 ; and the most 5's, 2. The L.C.M. of these numbers, then, must contain three 2's, two 3's Short Method Solution. 150. 180 Solution 2._Set the numbers do^vn in a row as for short division. Strike 75 out of the Ust, as it is contained exactly in 150 and we know that any number that will contain 150 will contain 75. Beginning with 2, the lowest prime number (except 1) we see that it will divide all three numbers so we divide each number by it, setting the Again, we see that 2 will divide 60 andTo ln""^'''i' '^'^'°" *'^ °"™^^"- 2 will not divide 75 exactlv .n I , ' ^-^ ^'""'"^^ ^^""^ ^^ '* ^^ before. Now. we see'thit 2 ^mnll H I T^ ^/'* '* ''°"" =^"^°"S ^^e quotients, will divide all Of them Then Jfn 1 n''^ """'""' ^° "^ ^^^ '• -^ich again, we try 5, the n"xt nrim: n K ""/°' ^'"^'^ *"° °* ^^^ '^"'"bers Of them. Afte; d' viding 'by 5 wetr'that Th ^''^ '' ""^ ''^'^' ''' *^^^^ divide any of the two quotients The l cm is th" "° ""'"^^^ *^^* -'» quotients and the various div sors 2 X 2 ^ 3 x | x'2 S °'.*'' '"^' It will be noted that these factor? prp ^/ "^ ^ ^ ^ x 2 x 5 x 3= 1800. SERIES IS Find the l.c.m. of 1. 32 and 88. 6. 12, 44. 60. . 2. 34 and 60. , 7. 44, 88, 100. 3. 57 and 95. 8. 3, 5, 8, 9. 10, 15. 4. 81 and 117. 9. 5, 6, 10, 12, 15. S. 36 and 150. 10. 4 8 12, 16, 50. 11. 144, 1728, 60. 12. 56, 512, 128. 13. 11, 33, 66, 165. 14. 9, 18, 45, 63. IS- 14, 49, 77. 22. 46 FACTORS AND MULTIPLES .':;():. 1 6. A boy has four boxes full of money. The first contains 3-cent pieces ; the second, 5-cent pieces ; the third, 10-cent pieces ; and the fourth, 25-cent pieces. What is the smallest bill that he can pay and take the money from any one of the boxes ? 17. A committee appointed to decorate a hall found that a pretty effect could be secured by stretching wires whose lengths are respectively 12, 15, 18, and 30 ft. Before deciding which length to adopt, they sent for the wire. What length of wire must be bought that no loss be sustained in the adoption of either length ? 18. John can walk around a circular path in 14 min., James m 18 min., and Frank in 21 min. If they start directly opposite a point on the inner side of the path and at the same time, how long will it be until they occupy the same relative position ? 19. What is the least number that can be divided by 30, 34, 51, and 85 and leave a remainder of 7 each time ? 20. Four travelling salesmen meet in Toronto ; they visit the city regularly every 2, 4, 6, and 8 weeks respectively. Kcw long will it be until they meet again ? irst contains cent pieces ; bill that he 5? )und that a lose lengths iding which gth of wire or of eithei Tiin., James tly opposite } time, how ition ? by 30, 34, 2y visit the Kow long COMMON OR VULGAR FRACTIONS WHAT IS A FRACTION? A Fraction is simply a part. Cut an ordinary twelve-inch ruler in two at the six-inch mark, and you have two equal parts. Pick up one part and you call it one-half of the work' nl ; ,? ,*=°"'-^'^' ^" Arithmetic you do not represent this part by 2, °Z '^''y ""^^^ t'^-" y°" would use the word "one" to repre^ sent 1. We use figures to represent fractions just as we use figures to represent whole quanfties. One-half is v^itten in figures as '/,. or as J. Next, suppose you cut each of ;..ese parts again in two. Your original s^l tl',. H n P''"'' '"^ " y°" "^''^ "P °"^ °"* °f the four you might say that you held one-quarter, or. expressed in figures, it would be i If you pick up three pieces you have three-quarters, or }. of the ruler So we see that we can have different fractions just as often as we can find parts mto whicn to divide anything. Cut your rule;- into eight equal parts and you have eighths-J, g, I and so on. Cut it into nine equal parts and yo. h. ve ninths-^. «. j. and so on. The bottom part of the fraction always tolls the number of parts into which the thing is divided, and is caUed the dc::ofmna.or. while the top part tells the number of these parts that are held in mind, rnd is called the numerator, thus : 3 numerator. 4 denominator. If we understand how fractions are made— by dividing things into parts-we should, to a certain extent, be able to handle fractional numbers as easily as whole numbers. We know, for instance, that a fifty-cent piece represents one-half of a dollar. Suppose then that we place a row of fifty-cent pieces before us in this fashion : ' Soc soc 500 50C 50c 50c ^^ ^^ H H U $i 'f we stop to pick them up and as we go along to call out the sums, we should say as follows : 50c, $1.00, $1.50, $2.00, $2.50. and so on ; or agam, we might speak of the different amounts as follows: %\, $1, $1J, $2, $2i, and so on. { 4Q «» COMMON OR VULGAR FRACTIONS It should not be much harder if we introduced some twenty, five-cent pieces : ' 25c 2SC see 25c soc ^i H U $i ^ Picking them up in order and calling out the sums by fractions we have $J, $J, $1, $1^ si|. 'fo see that you have thus far grasped the idea of fractions, we would like you to consider the following exercises, giving in each case the sum total of the fractions which are indicated. Find the 1. J bus. 2. i yd. 3. i rod 4. I ton 5' J and 6. J bus. and f bus. 7. i yd. and I yd. 8. I rod SERIES 16 complete amount of and f bus. and § bus. and J bus. and J bus. and J bus. and I yd. and f yd. and | yd. and I yd. and f yd. and I rod and i- rod and f rod and | rod and f rod. and f ton and f ton and | ton and ? ton P.nd | ton. J and I and i and ^ and ^ c.nC J. and ^ bus. and J bus. and f bus. and i bus. and }- bus. and i yd. and f yd. and | yd. and f yd. and i yd. T rod. and ^\ rod and ^V rod and A rod and ^-^ rod and REDUCTION OF FRAC TQNS Cut an apple in two equal parts, and each of the parts is known a. one-half of the apple. Put the two parts together, and we may written # ^' two-halves of the apple, or in figures it would be In our first lesson we learned that a fraction is a part. One- ha f IS. therefore, properly speaking, a fraction. Two-hal'/es is not a fraction, for it represents a complete amount. ^ is a Proper Fraction. I is an Improper Fraction. / ome twenty- 50c by fractions ve thus far :onsider the he fractions MIDUCTION OF FRACTIONS 49 and J bus. nd f yd. and f rod. and I ton. and ,{ bus. and i yd. jy rod and > is known d we may : would be rt. One- halves is A Proper Fraction represents a part less than a whole. An Improper Fraction represents either a whole amount, or more than a whole amount. If we cut several apples of the same size each into halves, we know that every time we take up two of these parts we have one whole apple. This we could represent as 1, or as ?.. Suppose we pick up 3 pieces. We woukl then have three-halves, or we could speak of them as one apple and one-half apple. Expressing this in figures, ^ = IJ. In the last expression we have a combination of a fraction and a whole number, or we speak of it as a Mixed Number. Now that we know what a mixed number is, we should be able to tell what impvr.r-s fraction it is equal to. We have seen that 4 and U represent the same value. In other words, the mixed number IJ is equal to the :mproper fraction #. We explain it as follows : The whole number I is equal to k, nnj this along with the } makes •. ° Again, 3| = Y. The whole number 3 is equal to V- and thin along with » mr.kes up ■^. Our rule may therefore be stated as follows : F:nd how many parts of Che seme kind as indicated by the fraction arem the whc': number, and add the parts expressed by the fractiofi to them. Of course, it should be quite aa easy for us to reverse this work That is, we should be able to tell that J^ = 3|. This may be Ulustrated by putting before us 15 twenty-live cent pieces, or quarter-dollars as we sometimes call them. We know that as often as we can get four quarters we have Sl.OO. Now we can Pick up 4 quarters three times out of 15 quarters, and stUl there wUl-be 3 quarters left, or, in otlier words, $Y are equal to $3i ; it IS just a matter of division-4 into 15 goes 3 times and 3 over. In the same way V" equal 5f, nnd so on. This work of thus changing the form of an expression is sometimes called Reduction of Fractions. ,.: 50 COMMON OR VULGAR FRACTIONS ! " SERIES 17 Exercise 1. -Divide a sheet of paper by ruling into three columns, heading the first column " Proper Fractions," the second Improper Fractions." and the third " Mixed Numbers " Sort out the foUowmg expressions by placing each one in the column to which It belongs. Put the expressions one beneath the other m straight lines down the columns : h I. 4i I -V. 21, I, ^1, 61 41 I .y., 6^. -. I, 51 -V, I 21 141, ?, ^, in, I V, ^\ t, if, A, 5,v, n, 7a, a. u, s^, il> 23i 7f, 4-A, if, 9,V, 2/,, ft. 9/^. ,- , 29,i^, 10,V^, ,- . Exercise 2.---G0 down your list of Improper Fractions, and set opposite each one the Mixed Number or the Whole Number to which It IS equivalent. Exercise 3.— Go down your column of Mixed Numbers -^nd set opposite each one the Improper Fraction to which it h equivalent. REDUCTION ASCENDING on/h.r ri'" ^?^' I" '^° '^"^^ P^'"*^' ^^^ h^^« in each part one-half of the apple. Should we take one-half of the apple and cut It m two equal parts, we have in each half two-quartersf Now th^ two-quarters are just exactly equal to the one-half. There is a difference in form, but not in value. If we continue cutting, and give each of the two-quarters a cut into two equal parts, we wouM have, out of our one-half apple, |. From this simple eiampTe we !^:\ k ^' '"' ^ "' *'^ ^^"^ ^" ^^^"^- This shows us th! Wem^n 7/ '? ^^^'^ ^' "^^y ^^""S^ °^ ^^duce fractions. We may change the form without changing the value. This is of great use to us in such operations as addition and subtraction. We cannot add 16 ounces and 1 ton, if we leave them as th.v ar" If w. consider that 16 ounces equals 1 pound, and that 1 ton equal's 2.000 pounds, we may say that the total is 2.001 pound.. In the Ch I. f 3. f 4. f REDUCTION DESCENDING 61 into three the second ;rs." Sort he column the other * 16 4 91 15 01 ' TT> <>TT> 3_12 1 7 -'2 2T> S'BT* ions, and 5 Number ibers and lich it ia :ach part pple and *s. Now 'here is a :ing, and v^e would niple we 5 us that ractions. This is traction, hey are. n equals In the same way we add i and I by figuring that ^ is equal to |. The sum of f and i is |. Illustration.— Reduce f to sixths. Solution.— Dividing 3 into 6 we get 2. which tells us I X § = J *^^* ^^^^^ ^'■^ always twice as many sixths in any amount as there are thirds. If we have |. we must have twice 2 or four sixths. Rule Divide the required denominator by the denominator of the given fraction. Multiply the numerator of the given fraction by the quotient thus obtained and write the product over the required denominator. The result is the fraction in higher terms. SERIES 18 Change I. f to ISths. 6. J to 36ths. II. xV to 52nds. 2. {- to ISths. 7. 1 to 36ths. 12. i'j^ to llSths. 3. f to 21sts. 8. 1 to 27ths. 13. A to 128ths. 4. f to 21sts. 9. f% to 120ths. 14. ^j; to 192nds. 5- A to 36ths. 10. 1 to 88ths. 15. H to 147ths. REDUCTION DESCENDING We have seen that it is possible to change the form of a fraction without changing its, value. This we did by multiplying both parts of the fraction by the same number. By reversing the process we should be able to change a fraction of a higher denomination into au equivalent one of a lower denomination. Illustration.— Reduce A to its lowest terms. Solution.— To get the fraction in its lowest terms ^ -f § = J we must know the largest number that will divide both 8 and !6. In a simple case of this kind we can tell by mspection that this number is 8. Dividing both 8 and 16 by 8 we produce the fraction J, which is an expression sf £g in ita lowest terma. M '■ I 52 COMMON OR VULGAR FRACTIONS I I Illustration.— Reduce Hf to its lowest terms. Solution.— Where the fraction is large, we find 48o - § — f ? the largest niimber that will divide both terms by ^ ooA . ^ finding the highest common factor. The h.c.f. of 192 and 330 is 6. .Hivide 6 into each of the numbers and we get the fraction f|. Rule Cancel all factors common to both numerator and denominator; or divide both terms by their greatest common divisor. SERIES 19 Reduce to their lowest terms 1623 SIST 2 '! 9 6 r. 008 TTfT 3178 5^2 r 3 5 2 11 Fr2iir REDUCTION TO A COMMON DENOMINATOR To reduce a series of fractions to the same common denominator. Illustration.— Reduce J, ^, J to 12ths. Solution.— The number expressing the denomination to which we may reduce halves, thirds, and quarters must be a number which will contain 2, 3, 4 exactly. This, in other words, must be the l.c.m. of 2, 3, 4. The l.c.m of these three numbers is 12. | reduced to twelfths gives us A : 4 reduced to twelfths gives us j^ ; and i reduced to twelfths gives us ^. I. 16 6. 3 9 TYiT II. 549 16. 2. 28 7. 504 TF2- 12. 930 Tsrg- 17- 3. 78 8. 39fl TTT2" 23. 485 B'TF 18. 4- 50 9. 385 14. 1 080 19. 5. 112 ID. 498 IS. 6184 20. h X S=A *x l=A t Rule 1. Find the L.C.M. of the denominators. 2. Divide this L.C.M. by the denominator of the fraction that ts being reduced and multiply the terms of that fraction by the Quotient wus obtained. ADDITION OP FRACTIONS 53 I. i and § 2. J and J 3. f and tV 4. 1, T^, and n 5. I, ^V, and Itf 51- 6* TIT. rs> and |^ 3. Continue with the fractions in regular order until all have heen reduced. Before beginning the above operation, each fraction should be in its lowest terms, and mixed numbers should be reduced to improper fractions. Whole numbers are written in the form of a fraction by writing 1 for th3 denominator. SERIES 20 Reduce to equivalent fractions having the l.c.d. 717 35 11 „_j 43 • 35^. ¥F» 1^. ana f§ 8. Ih f i n, and If 9. A. ii hh and e 10- IF. ^T, A. and |# TT S 11 43 „_ J 14 **• u» 'S's> B^(T» ana ^^y ADDITION OF FRACTIONS Ileustratign 1.— Find the sum of f, f, f. Solution. — First Step — S X t = A Change these fractions to equivalent fractions having J X 1= -^.j the same common denominator by the process akeady S X § = i§ illustrated. As a result we have ^, ^, Jg. Solution. — Second Step — Having once changc-d the frac- tions to the same common denom- inator the addition may be just as easily carried out as the additicj of eight pounds, nine pounds, and twelve pounds. Note that it is the numerator or the part which shows how many that enters into the addition. After we have found that there are 27 twelfths in the sum of these three fractions, we reduce this improper fraction to a mixed number, 2^, which in turn we reduce to its lowest terma, 2^^, /g may be expressed, ^ may be expressed, j-§ may be expressed. 8 twelfths. 9 twelfths. 10 twelfths. The sum of these is 27 twelfths. 27 twelfths = f 5 a = 2,^ or 2J isr I 64 COMMON OB VTTLGAR FRACTIONS Illustration 2.— Find the sum of 3j , l;j, 4.1.. 3+1+4=8 SoLUTioN.-Find first the sum of the whole numbers, which is 8. Next find the sum of the fractions, by the method already illustrated. Thev amount to H or l^^,. Add 8 and l,^, and we have the complete sum, 9j»g. 9A Rule .Reduce to equivalent fractions of a common dmominator ; add 1:^:^ ~^^^^^'- ^^^ ''-' ^'^ -- -- ^^^ ^ommon reduce°d ""to i;rr,f r "'''''''^' ^" ''''''''■ '' P^°P^^ fr^^«°"^. should be numbers ™' ' '°^ " ^"P^^P^"" ^^^^*^°-' *« ^^-valent mixed SERIES 21 Add I. 3. 5. 7. 9. II. 13. I, f and I- 4i 2J, 5| and 6| ?' 6» T6-' T(T and /^ li 2f, 3 J and 4| 7. 8i, 9|, 6.^-, and 8 f. I, 2t''t> 1 7 2. 4. 6. 8. ID. T"6-» tt and -g^g- 12. 32?T. 4 6?^ and 8j-|j 14. 15- 16. 17. 18. s> I, T5- and /^ i i, #, tV and 11 I, f, I, I and I- . 4i, A. 5 1 and ^ 3i 9^?^, 8, 7^ and 6f -'^li 9JII, If, ItV and 1^ i, I, i, ^- and J^. 364|, 243«, 327.V and 162^?^ 123vV, 247f, 842iA and 375.^ 3251, 426t«^, 342^V and 136/^ 243tV, 327^, 4363-V and 244/^ SUBTRACTION OF FRACTIONS Illustration I.-Find the difference between | and § SoLUTioN.-First Step-As in the case of addition, we first change our fractions to equivalent fractions ftavmg the same common denominator. By this we find that S is equal to Jf, while g is equal to A? SoLUTioK.-Second Step-Subtracting Jf from J* we have a remainder Qt ^. ^ '* SUBTRACTION OF FRACTIONS 55 f the whole sum of the rated. They and we have lator : add ^e common rs : add the , should be ilent mixed and 6f r and l^^ [ addition, fractions y this we Illustration 2.— Find the difference between 8| and 3|. _ Solution. — As in the previous case, we change the °S— 8JI fractions to equivalent fractions having the same ^ — 3JI • common denominator. Having done this, we compare - fractions and find the diffsrence to be ^, while a S^ comparison of the whole numbers shows a difference of 5. The complete result is therefore 5.4, Illustration 3.— Find the difference between 7f and 3|. Solution.— As in the previous cases, we change 78 — 7JI our fractions to equivalent fractions having the same 33— 3jf denominator. Next we proceed to compare the --- fractions with the idea of subtracting J| from Jf. ^^ This, we see, is impossible unless we borrow one unit which is equal to §|. Adding this U to U we get U. Now we subtract }f from if, getting a difference of S|. When we start to compare the whole numbers with the idea of getting their difference, we must remember the one that we borrowed, so that we are really subtracting 3 from 6, which leaves us 3. The whole answer is therefore, 3S|. Rule 1. To Subtract Fractions. — IF/ien necessary, reduce the fractions to their least tommon denominator. Subtract the numer' ator of the subtrahend from the numerator of the minuend, and place, the difference over the common denominator. 2. To Subtract Mixed Numbers.— TJ^rfwce the fractions, if necessary, to a common denominator, and if the fraction in the sub- trahend is smaller than that in the minuend, subtract one fraction from the other, and the smaller whole number from the larger whole number. But if the fraction in the subtrahend is larger than that in the minuend, borrow one from the whole number. After changing tt to the same denominator as the fraction, add it to the fraction in the minuend. Then subtract as before. SERIES 22 Find the difference between I. f 2 ^ TT and f 6. f and i II. 3| and 2| and /j- 7- f and tV 12. 5| P.nd !4 and j\ 8. i and -l 13. 8;i and 9| and 5. t and 11 9. f and ^ 10. f and t 14. &§- and 4^- 15. 5| and 7^ 56 COMMON OR VULGAR FRACTIONS From ! 'I 1 6. 25 J take 16^ 17. 83J take 19| 18. 150 take 13 J 19- 144| take 50| 20. 25|^ take 15 J 21. 51^ take 18| 22. 75 take Uf 23. 62]| take SJ 24. 72f\- take 16t\ 25. 195 take lOl^V MULTIPLICATION OF FRACTIONS If we attempt to take 3 times 2 pounds the operation would be expressed something as follows : 2 pounds. 3 , 6 pounds. The figures alone concern us. 3 times 2 are 6, whether it is 2 pounds, or 2 gallons, or 2 boys. If we take 3 times 2 quarters it will be just the same. 2 quarters. 3 6 quarters. ^ Instead of using the word " quarters " we represent the fraction m figures, as f. Then 3 x f = «, or what is the same thing, >< 3 - y. There is no difference between 3 times 2 quarters and I of 3, as far as the work of finding the result is concerned.' Suppose again that instead of multiplying f by 3, we have # to be multiplied by f. The answer is not | as before, because our quarters are each to be divided into 8 equal parts. When quarters are thus divided into 8 equal parts, we get thirty-seconds. Our work would be represented as follows : f X t = 1^. MULTIPLICATION OP FRACTIONS 07 would be ther it is fraction ■ thing, uarters, icerned. have f use our [uarters i. Our Multiplication ot motions is therefore a matter ox multiplying the two numerators for a numerator, and the two denominators for a new denominator. If we have to deal with mixed numbers we can bring them under the same rule. Illustratig:-.— Multiply 2J by 3|. Solution.— 2i=|. 3J=jyi 5 X J#=:^=8g=8J. Cancellation.-In all work of this kind, we can often shorten the operation by cancelling the factors that are common to both numerator and denominator, before proceeding with the multiplication. Illustration IrluLTiPLY -} by |. « 3 Solution.— It will be noted that 2 is a common factor |X ^ = lV °* 2 and 8. We. therefore, divide 2 into 2, placing the 4 result above the original figure after putting a cancellation stroke through it. In the same way we divide 2 into 8 placing the result, 4, underneath, after cancelling the 8. We next multiply the two figures of the numerator, 3 and 1, producing the new numerator, 3. We also multiply the two denominators. 4 and 4. thus producing the new denominator. 16. A Compound Fraction is a fractional part of a whole number or mixed number, or another fraction ; as | x i ^ x 2J, f of j%. Compound fractions may be reduced to simple fractions by the process of multiplication. Thus- (1) jx 4=^ (2) |x 2i=S X i = A (3) §ofA=^x^=^ Rule I. Change all whole or mixed numbers to fractions. 2. Eject all factors common to both the numerator and denominator. 3. Multiply the numerators together for a new numerator; multiply the. denominators together for a new denominator. 58 COMMON OR VULGAR FRACTIONS 4. // the new numerator is equal to, or greater thun the new ienominator, reduce the fraction to a whole or mixed number. Note l.-If one of the factors is an integer, change it to the form of a raction by writing 1 under it for a denominator, or by imagining 1 to be thu3 written, and then apply the rule. Note 2.-The word of written between fractions, or betwocn fractions and integers, indicates that they are to be multiplied. fractions thus connected are called compound fractions. or III I-!' SERIES 23 ' Find the value of 'j;: I- 18 X 1 8. 93 X 3| IS- TT X 128 !' 2. 23 X § 9. 125 X 4§ I '. A X 35 3- 125 X 1 10. 625 X 3,^ 17. TiV X 36 4. 240 X y\ II. 1825 X 2§ 18. il X 84 I 5. 84 X ^ 12. 124 X 7^ 19. V X 36 ■ I 6. 25 X 1 13. 1 X 21 20. 2^ X 47 7. 36 X V- 14. A X 125 21. 3J X 64 22. 1 X 1 X A X 1 x| 26. 5J ^ 5J X 7i X 1 23. 2i X 4J X 6| X § 27. 3|. < 4i X 18| 24. 16f X 9 X 24| X m 28. 88J X 9J X 7J. 25. 12^ X 12i X 8 X 4i 29. 16§ X 30| X l\» DIVISION OF FRACTIONS When we know how to multiply fractions, there is little to learn m mastering the division of fractions. Suppose we wish to divide ^ by I. or as it is indicated, ^ - f. We know that 4 means 7- of 4. Let us make two operations of the work. First, we will divide | by 4. or what amounts to the same thing we will take i of f . which by the process of multiplication already illustrated, will give us |. ^ new «• DIVISION OF FRACTIONS 59 ^ Thus lar we have just divided by 4, while our real divisor is T or ^ of 4. The divisor we have used is therefore 7 times too large, or the quotient we have obtained is 7 times too si .all Our second operation therefore will be to take our quotient, thus far obtained, and multiply it by 7. ' X 7 = KS 7 If this work is all put into one operation it means that we must multiply I by 7 and divide it by 4, or expressed as a multiplication question, it appears as follows : ?x^=V = i|. Our rule for division may, therefore, be shortly stated as follows • Inveri the divisor and proceed as in midtiflication. Illustration 1.— Divide | by |. ^X- = i SoLUTipN.— Following the rule, we set down the figure H 3 to be divided, g, followed by a multiplication sign, and t\ ,. ^^^"'^ ^'^'^ *he flivisor, in an inverted position. The balance of the work is straight multiplication. Illustration 2.— Divide 2| by 3J. Solution.- 2J= §, 3J= ;yj, § ^ ;^_ § ^ ^^^ ^^ A Complex Fraction is a fraction having one or both of its terms fractional; as, ^, -J-' — .— • 9 f 'I 9 Complex fractions may be reduced to simple fractions by the process of division. TllUS, (1) 5. (2) =iH=ixi=^ (3) i (4) 2i , fi I: ■*■! 60 Divide : COMMON OB VULQAR PBAOTIONS SERIES 24 2. 3- 4- 5- 6. 7. 8. 10 IT 32 US 7 Xf 8 21 by 3. by 5. by 8 by 6. by 16. by 11. 8by |. 7 12 by Find the value of 25. (f of ^ X t) 9. 10. II. 12. 13. 14. 15. 16. 6 by f . I- by i H by S. ii by «. .'I by tV by ' by 1 IT T^' 3J by ». 26. 27. 28. 29. 30. 31. 32- 33- 34. 35. 36. (|of f of^,). (3^ x"^of71f)-4Jx|oil6. 7A - i of f of ^. 2| of 5^ 4- 6| of ^. (I - I) -f (« - 2t\). (I of 2i X ^1) -. II. (^ of f) X (I - I). I of /^ of 1| ~ I of /r of 3^ of 9. H -f (f X 5^ X 7). m - I) X f of >- of 11 . 3J + 27#-6J X 3i (f of 25j^) + (I of 27) 75J + 8J + 7|-1| 31i ~ 6i i6§ by ». 21 1 by 6. 2i by 2i. 8J by 2^. 18, by 4]?. 283^ by 32|. 202i by 125. 24. 3614/^ by 144i. 17. 1 8. 19. 20. 21. 22. 23- REVIEW OF FRACTIONS SERIES 25 i«, ,1* ^ ^°^^'" P^^^^^ '" ^ ^^'^ ^°^ shipment ISf lbs. sugar 191 lbs. coffee, 2^ lbs. tea, 17f lbs. ham, and 25^ lbs. bacon! What was the total weight of the contents of the box ? 2. If 18| gallons were sold from a barrel of molasses containing 453J gallons, how many gallons remained in the barrel ? 14. 17. REVIEW OP FRACTIONS 61 by 4j?. 3. The average yield per acre of j field I 1 bushels I wheat was "-ac was lue total yield if tne field contained 13^ acre be bo';gXll^:^T'^ °^ '''''' ^' ''' -"^^ P- P-d can woul^ A ffl: ^i:; ;;:1J^'^^'^-^^^1^ of Wheat, how many bushels 6. A merchant sold 75 pounds of butter at 245 cents oer pound. 93 dozen eggs at IGf cents per dozen, and 4.^ XlZ mjlk at 20 cents per gallon. What was the total amount of thl cost r " ^^ ^'''^' '^ '^''" '°'' ^^2-^^' ^^^* ^i^l 23^ yards vor ^'.yiif "^^^ ^"^ ^^ ^^'- °^ *'"' ^°^ "^^^y Jbs. can be bought 9. What fraction of a short ton is « of a long ton ? f../^;,,^ r'!- ^^' '''°^'" °^ ^2 feet from the top. leaving 28 feet stfil standing. What part of the pole remained ;tandTg ? 39 "mL^s' "^f "'' ^\''^ ^'^^^ ^^^''"^°^^ *^ Washington is jyry mUes If a waystation on the road is ISA- miles from Baltimore, how far is it from Washington ? 12. I sold I of a piece of goods containing 39| yards How many yards remained in the piece ? ^ 13. A person owns f of a ship and sells f of his share for /I 260 What is the value of the ship ? «^orii,^w. 14. A man invested | of his capital in bank stock | of the remainder m real estate, and had still §6.000 left. Find Ifi^ cap!tL 15. After taking out of a purse | of its contents, f of the re- wh^rumT ^"^' " '' ''-' '''' ^^^* P- «^ ^3 W.S the 16. What fraction of ^58 5s. 6d. is |-« of £17 2s. 3d ? ^JJ' 'n «,r"^' '''''^'''"' ^^^ '"^^'^ ^"'^h^S' how many gallons of hZ ttp? ' "'"" ' '' ' "• '°"^' ' '*• ' ^"- ^-^^' -d 1 ft. '• COMMON OH VTJLQAa A'lUCTlONS e A 3i 18. A re( .ves yj of an estate and B ^ of ^| of the remainder. C gets what is left and finds that hi share is worth $872 more than A's. Wliat is the value of the estate ? 19. The divisor is 3| + 3? and the quotient isJ-^ Find the dividend. ^' of fj^ 20. liow many boxes, each holding | of a quart, will be required to hold 12 bus. 3 pk. I gal. 2 qt. of strawberries ? 21. A man earns $280 in 2 J months. If lie ^pend in 4} months what he earns in 3^ months, how much will he oavo in a year ? 22. A produce merchant exchanged 48if bushels of oats at 39| cents per bushel, and 13^ barrels of apples at $3.85 per barrel, for butter at 37J cents per pound. How many pounds of butter did he receive ? 23. What quantity taken from 159} will make it exactly divisible by 12f ? 24. What must be the length of a plot of ground, if the breadth is 15| feet, that its area may coi.tain 46 square yards ? 25. A merchant bought a number of barrels of flour for $1,800 ; he used 20 barrels, and sold | of the remainder for f? 1,568, which was $224 more than cost. How many barrels did he buy ? 26. A, B, and C own a vessel, each having equal shares. They sell respectively I J and ^ of their shares to D, who dies and leaves his share equally among them. If B's and C's interests in the ship be now worth $37,300, what is the value of A's share ? 27. A merchant sold 20 barrels of flour for $127^, which was U of what he received for what he had left and which he sold at $6J a barrel. How many barrels in all did he sell ? 28. After spending $10 less than | of my money, I had $15 more than j\ of it left. How much had I at first ? 29. I had a sum of money of which I paid away |, then J of the remainder, then § of what was still left, and found that I had still left half a dollar less than | of J of the whole. What sum had I at first ? RBVIEW OF FaACTIONS 63 remainder. $872 more r Find the r- :t, will bo ? 4J months year ? of oats at per barrel, > of butter it exactly le breadth )r SI, 800; 68, which es. They ind leaves its in the I ? ^hich was le sold at had $15 ;hen J of I at I had hat sum money and found that A had le remainder. How much had 30. A, B, and C counted their f of the total amount, B J, and C U B and C if A had $30 ? 31. A pedestrian travelled 32| miles on Monday, 23,«, miles on Tuesday, 37i miles on Wednesday. 19| miles on Tlmrsday. Z4l miles on FriHav nnH Iftl „,il„^ e_i..._i__ »»,. . / What was the 24J miles on Friday, and 16J miles on Saturday average distance travelled per day ? 32. If coffee loses iV of its weight in roast og, how tj ich green coffee will be needed to make 252 pounds of roc."i,;.d cof e ? 33- What is (a) the h.c.f. and {b) the l.c.m. 34. Divide the L.C.M. of 4^ and 9J by their h.c.f. 35. How many times does the sum of 12| and 8| contain their difference ? 36. A certain number divided by 8/7. the quotient increased by 21, the sum multiplied by 2J . ^nd the result diminished by i of ^ of 14^, gives 2f. What is the number ? 37. One-fourth of M of the length of a pole is in the mud, two-thirds of the remainder is in the water, and there are 5^ feet in the air. What is the length of the pole ? 38. I of A's stock was destroyed by fire, | of the remainder was mjured by water and smoke ; he sold the uninjured goods at cost price, and the injured goods at J of cost price. He realized $1,155. What did he lose by the fire ? 39- A can do a piece of work in 35 days ; B can do it in 40 days ; C can do it in 45 days. In what time will they do it, all working together ? 40. A and B can reap a field of wheat in 3 days ; A and C in 3J days ; and B and C in 4 days. In what time would each working alone do the work ? 41. A can do a piece of work in 27 days, and B in 15 days ; A works at it alone for 12 days. B then works alone for 5 days, and then C finishes the work in 4 days. In what time could C h^ve done the work by himself ? 64 COMMON OR VULGAR FRACTIONS iiii Tn ^l' A^^" ^"^ ^ P'^'^ °^ ^""'^ ^" * «^ a day and B in * of a day In what time can both together do it ? If $1.40 be odd for th^ work, how much should A receive ? ^ spectLfvtn7 '" f !f K^^ '"'" P^P^' ^" '^ ^"d 20 minutes re- spectively and emptied by a tap in 40 minutes. What part of Jt^wiU be filled m 10 minutes when all are opened atlhe sLe 44. I bought 481 pounds of tea at 63| cents per pound How many pounds more would have been received, if the price had bee^ 7J cents per pound less, for the same money ? ^^ ^ ^^a Deen coal at $5i per ton. How many tons of coal did he receive ? 47. If a fruit vendor buy lemons at the rate of 5 for 3 cent., how many must he sell at the rate of 6 for 5 cents to gain U ce^i an/Lt\-.%! -"/ ;:x- -- rj 7:^^ r and 6| hours per dav an<1 R J tu ^ ^'^^' P^"" ^^^^ hour. How 4nyt;:"^f ;;*= T^ZlT °' '' "^^^ ^ c-fatenr'oXrthe'rs ^nf r-' rT- " °"'^ ">^ and if both are opened it !ht. T 1-^ ™P''^ '" * ™™'^ : yard. How many yards of calico should B receive > "^ and'witt = *:, rr:: i:':;:,tr" '- .^-.'-ings ba„., wasJU How much mo-LXsrs^rdr^^it'T ^^"'' ""'=- I of a day. lid for the linutes re- at part of the same tid. How had been r ton for ve ? 5 pounds quantity nsurance, total net 3 cents, 4 cents ? ch other 3er hour liles per •nly the linutes ; tn what pened ? s goods ■nts per 3 bank, which REVIEW OF PBACTIONS 65 52. A speculator invested J of his money and $200 in bonds, i of his money and $500 in railway stocks, J of his money and $600 in real estate, and the balance, which was $1,200. he deposited in a Dank, now much was he worth ? 53. I sold 5 jars of butter weighing 35^ 32i, 31|, 291, and 36i pounds ^spectively, at 18^ cents per pound. The jars weighed 9n 7' 7' 1 ^ P""""^' respectively. I received in payment 20 pounds of coffee at 33^ cents per pound, 5 pounds of tea at 62* cents per pound, and the balance in sugar at 4 cents per pound tiow many pounds of sugar did I receive ? .K ^t ^u ^'i^^^ "^^^ ^'^'^^^ ^"'^"g t^o t>^others and a sister : the e.der brother received | of the estate, the younger I and the sister the remainder, which was $5,740 less than the elder brother received. What was the value of the estate .? 55. A tank whose capacity is 126 gallons, is | full; if 113 gallons more be poured into it, what part of the tank is full ? 56. How many suits of clothes containing 7| yards each can be cut from UOf yards ? 5 s jr u» eacn can 57. How muo -onstone ore must be raised from a mine, so hat on losing ^ m roasting, and A of the remainder in smelting. there may result 506 tons of pure metal ? ' 58. Reduce to its lowest terms the fraction ^V/t^- 59. Two wine glasses are filled with a mixture of spirit and water, one containing 3 parts of water and 1 of spirit, and the o her 4 part3 of water and 3 parts of spirit. When the contents ot the two glasses are mixed in a tumbler, find how many parts of pe whole mixture are spirit and water. 60. Find the total number of bushels that can be put in five bms based upon the following : f of 1st bin equals 150 bushels. U of 2nd bin equals 850 bushels. xV of 3rd bin equals 95 bushels. ^ of 4th bin equals 120 bushels. U of 5th bin equals 260 bushels. : L« decimals thus produced are caUed / f ^ '^"^"^" ^*" "°t ^"d. The repeated. Repetends. ^^""^ ^"'^""^"S Decimals, and the figures Illustration 2.--ReducP > t« 3)1000 ^ ' *° ^" equivalent decimal. '^'^ end.'X'r^J^er"'^" '" *'^^^ ^^ -"»<^ never * = -333 + culating de ima. ^hi T '^""""^ ' "P^^«"« ^ «=-■ = .^ Placing^ period^abo?; th': tlrrrhtl. ^""^*'"^^' '^ ^^^STKATio.3.^Heduce, to an equivalent decim^^^ = .8d SERIES 30 si«%';:f "'"' ''"'™'^- ""> ™' -'»d beyond f„„r z. 2. 3. 4. s. I 4, f. I 8 T' 8 XT' 6. 7. 8. J. 9. I 10. 1 TT* Reduce the following to decimals of II. 12. 13. 14. 15. s rj- lis I 9 "ST' 1 2 rf^c. places. 16. 19f. 17. 415i 5 ll,-»*-tr« tank at the end of 27 days ? 86 DECIMAL FRACTIOlfa I,'. B i' is.2'o';.tde"-^a.t"'"^ """'P''^" "^ '«» "l-'^ -65. What' Ko^rV ^'? i?^^ ^"'^'*' ^^ ^^^^"^ 24.08 bushels of wheat How many bushels of wheat have I ? are 7J.05, 31.009, .4158, and 8.3, what is the fifth ? 32' A man bequeathed .125 of his nrnnprt,. +^ was the value of his property ? ^u„d that they had 3«).,2 acres. HowtaTact" a^Uchl: ^^34. Multiply . of .175 by .285714 and divide the result by Enjiihtr^ "'^' ^' " ^'-^^^ ''"^ *^ ^^- "' «2,3(X) i„ he pd/sitrt"""**"/?-"^ """ '•' ""^y- '" 20.25 tons of it ne paid $16 per ton, and for the rest $18.2625 per ton • he sold wSt t:: -''"''' '"'- °^ '■''' ^^ "'■■ "- .u'rdid tl,=t^^™' r^'^?" °^ " ™'''"^ '""=^ 0' ™«<»- is 253.17 grains and tacL f^ ' '"*, "' ""■ '^ -^'^'^ grains. How ^ny ^ubt ,« 1ji;'r: '^"'^, '" ™«" '° ""^ '^"'"<= '»<" °' water p"^ A, i r7ttd'":6r"""'^' '' '^^ ^" ^^- *^ -» -^ t. ^r^'^'' ^'"= P""'"'^' 0' 'hr^e vulgar fractions is 4 ; two of them .hrerpL\L7nrhrt7ranra:r^^^^^^^ much money fails to the share of the third partner 7 65. What gallon and ntain ? ng rcspec- tons, and of wheat. e addends ti orphan e. What A added is, it was i each at esult by . '2,300 in 3ns of it he sold luch did ins, and y cubic n of f , >f them ion will BBJVIBW OP DEOIMALS 37 than .d of the cost of the horse; for harness .185 of the cost of horse and buggy. Fmd his entire outlay. 42. The metre ,s 39.371 inches in length. Express the length ot 25 metres as a fraction of a mile. ^co-'}\ir''''^ °^ '"^'' "'''* -^^^^25 of S8, find the value of .0623 of 16 barrels of 200 pounds each. ^^'!:t^ T" "^^ °'''"''^ ^ °^ ^ steamboat sold .7 of his share for $1,400 ; what decimal part of the boat does he still own. and what was the boat worth } and of s, how DENOMINATE NUMBERS TABLES OF VALUES, WEIGHTS A^D MEASURES Canadian Money 10 Mills 100 Cents TABLE = 1 Cent = 1 Dollar ct. or c. dol. or S The mill is defined by statute, but is not recognized in ordinary com- mercial transactions. Its use is practically confined to stating rates of local taxation, which are generally described as so many mills on the dollar of assessed value ; thus, a rate of .015 is described as 15 mills on the dollar. The dollar is defined by statute to be of such value that four dollars and eighty-six cents and two-thirds of a cent shall be equal in value to one pound sterling ($4.86 J =;£!). The silver coins are the fifty-cffit piece, the twenty-five-cent piece, the twenty-cent piece, the ten-cent pifCi a-vl the five-cent piece. The Copper coin is the ceni. The gold coins are the five-dolkbi, isc ten-dollar, and the twenty-dollar. United States Money U. S. Money is the legal currency of the United States, and is often called Federal Money. Its denominations are Eagles, Dollars, Dimes, Cents, and Mills. The Gold coins are the double eagle, eagle, half-eagle, quarter-eagle. The Silver coins are the dollar, half-dollar, quarter-dollar, and dime. The Bronze and Nickel coins are the one-cent and five-cent pieces. TABLE 10 mills =1 Cent 10 Cents =1 Dime 10 Dimes or 100 Cents . = 1 Dollar 10 Dollars . . . . = i Eagle ct. d. dol. E. or $. British Money British or Steriing money is the currency of Great Britain. The unit is the Pound Sterling, vvhich is represented by a gold sovereign, and is equal in value to $4.86f. TABLE OF VALUES, WEIGHTS AND MEASURES 89 TABLE 4 Farthings {qr. or far.). = i Penny . ^ ^^ l?;"'' =1 Shilling . . : : ,; 20 Shi mgs . . . . = 1 Pound or Sovereign £. 21 Shilhngs ....=. 1 Guinea. The Gold coins are the sovereign and the half-sovereign The Silver coins are the crown (- 5s.), the half^rown (2s. 6d ) the two shilling, the shilling, and the sixpenny piece. The Copper coins are the penny, halfpenny, and farthing. The standard purity of the gold coins of Great Britain is 22 carats fin.. • thatiMi pure gold and A alloy. That of silver coins is mllTe'::^ Avoirdupois Weight weigtnf '''" ''"''''' '" "''' '''■ ^^ ^'^ °^^^^^^y P^^P-^- of The measuring unit is the pound, which is equal to 7,000 grains. TABLE 7000 Grains = 16 Ounces (oz.) = 1 Pound . . lb 9Z p°""? = ' Hundredweight cwt. 2000 Pounds, or 20 ca/jf. . . = 1 Jon ... T. coIhT!"" ^""^'^'^'^ Weights and Measures Act declares that "all articles ^W by weight sh,ul be sold by Avoirdupois weight, except that gold s1^^ r p at num. and precious stones, and articles made thereof, may be sold by the ounce Troy or by any decimal part of such ounce - th.!r ^'■^^^* f"*^^°^'"d I'-^J^nd the gr.:n, the ounce, and the pound are (lonJTon) ' '""'^"^-^^g^* ^^ '^'l"- -' 1^2 lbs., and the ton to'^2.240 lbs British or Imperial Avoirdupois Weight 7000 Grains (gr.) = 16 Ounces (oz.) = 1 Pound 14 Pounds .......= 8 Stone ....'.'.' = 20 Hundredweight . . . . = Troy Weight Troy \\ Bight is used in weighing gold, silver, and jewels; in philosophical experiments. , The measuring unit is the pound. . . lb. 1 Stone . . . St. 1 Hunflredweight cwt. 1 Ton . . , T. IMAGE EVALUATION TEST TARGET (MT-3) 1.0 ^Ki I.I 1.25 2.5 2.2 1^ 6" 1.8 U IIIII16 Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 V 4v r<\^ \ :\ ''^\ ' ^'^ # ^' .V .^ iL ^ 90 DENOMINATE NUMBERS ^^1 .;' dwt, oz. lb. TABLE 24 Grains (gr.) . . . , . = i Pennyweight . . 20 Pennyweiglits. . . . = i Ounce . . ^2 Ounces = i ^^^^^ ^ ^ \ The value of diamonds and other jewels is estimated by carats A carat is the weight of four grains. Apothecaries Weight Apothecaries Weight is used by druggists and physicians in compounding medicines, but drugs and medicines are bought and sold by avoirdupois weight. The measuring unit is the pound. The pound, ounce, and grain are the same as in troy weight. TABLE ^I'f''^] =1 Scruple. . . ..cora ^5f'"P''^ =lDram . . . , dr. or t, 8 Drams = i Oiinr^ io r^ .... - 1 uunce . . . . 0^ or \ *2 Ounces =1 Pound . . . . ;j_ * Apothecaries Fluid Measure Apothecaries Fluid Measure is used in mixing liquid medicines. TABLE 60 Minims, or Drops (m). . = l Fluid Drachm. . /, S F uid Drachm.s . . . . i Fluid Ounce . . fl 20 Fluid Ounces . . . = 1 Pint . q ®^^"*' =1 Gallon .* .* ; ; cmg. Comparative Table of Weights TROY. AVOIRDUPOIS. APOTHECARIES. = 5760 Grains = 7000 Grains = 5760 Grains = 480 Grains = 437^ Grains = 480 Grains. 175 Pounds = 144 Pounds = 175 Pounds. Measures of Capacity TABLE • • • • = 1 Quart . . . • • • • = 1 Gallon . . • • • . = 1 Peck . . . 1 Pound 1 Ounce 2 Pints ipt.) . . . . 4 Quarts 2 Gallons 4 Pecks A gill equals i of a pint. = 1 Bushel. qt. gal. pk. bush. dwt. oz. lb. ;s. 'sicians m ought and weight. . sc. or 8 . dr. or s . oz ox "i^ . lb. nedicines, f% 0. Cong. iins. ains. jnds. qt. gal. pk. bttsh. TABLE OF VALUES, WEIGHTS AND MEASUBHS 91 m J!"^ •^""''' "°'* °'' '*'^"'^^'-'l '"^asure of capacity is the gaUon. containing 10 Domimon standard pounds of distiUed water weighed under ^S conditions. Under these conditions, "^"* 1 cu. ft. of water = 62.356 lbs. 1 gallon (10 lbs.) = 277.118 cu. inches. Agdn, since 1 cu. ft. of water = 62.356 lbs., which is 997.696 ozs the weight for ordinary purposes is taken as 1000 ozs ' Cisterns, reservoirs, and the hke are often measured in barrels. 1 barrel {bbl.)= 31 i gaUons. 2 barrels = 1 hogshead 'hJid.). 1 barrel of flour = 196 lbs. 1 barrel of pork or beef = 200 lbs. The legal bushel of grain and some other substances is deter- mined not by measure, but by weight, as indicated in the following 14 lbs. Blue Grass Seed 34 lbs. Oats . . 36 lbs. Malt . . 40 lbs. Castor Beans 44 lbs. Hemp Seed 48 lbs. Barley . 48 lbs. Buckwheat 48 lbs. Timothy Seed 50 lbs. Flax Seed . 56 lbs. Indian Corn 56 lbs. Rye . . . 60 lbs. Wheat . . 60 lbs. Beans. . . 60 lbs. Red Clover Seed 60 lbs. Potatoes , 60 lbs. Turnips 60 lbs. Carrots 60 lbs. Parsnips 60 lbs. Beets . . 60 lbs. Onions . . 70 lbs. Bituminous Coal . . ^»^,,^, 480%T^''' ^^ ^^'''''' ^^"'"'^ ^^'''''''^ '' ^^"^^"*^^ 8 bushels or = 1 Bushel. = 1 Bushel = 1 Bushel = 1 Bushel. = 1 Bushel. = 1 Bushel 1 Bushel 1 Bushel 1 Bushel 1 Bushel 1 Bushel 1 Bushel 1 Bushel 1 Bushel 1 Bushel. 1 Bushel. 1 Bushel. 1 Bushel 1 Bushel 1 Bushel 1 Bushel 11 92 DEJIOMINATE NUMBERS Measures of Extension Measures of Extension are those used to ascertain how long a hne is, or in calculating the size (extent) of a surface or solid. A line has only one dimension — length. Linear or Line Measure , In measuring length, linear or line measure is used. TABLE 12 Inches {in.) . . . . = i Foot , . . ft, 3 Feet = i Yard . . . yrf. 5i Yards, or 16J Ft. . = 1 Rod . . . rd 320 Rods =1 Mile . . . mi. EQUIVALENTS 1 Mile = 320 Reds = 1,760 Yards = 5,280 Feet = 63.3&J Indies. Surveyors' Measure Gunter's Chain, used by land surveyors, is 4 rods, or 66 feet long, and consists of 100 links, each 7.92 inches long. TABLE 7.92 Inches = i Linl: . . . Ik. 25 Links = 1 Rod . . . r<;. 4 Rods, or 66 Feet . . = i Chain . . , ch, 80 Chains = j Mile . . . mi. The following measures are used only occasional!,, , or for special purposes . The line = ^ inch. The size= \ inch, used by shoemakers. The nail = 2\ inches = ^ yard, formerly used in cloth measure. The word is now obsolete as a term of measurement. The hand = 4 inches, used in measuring the height of horses. The fathom = 6 feet and 1 The cable-length = 120 fathoms, /"^^^ ^y sailors. The rod, pole, or perch = SJ yards, used in measu, Ing land, but not by surveyors. The furlong = 220 yards = | irile. The league, not a fixed length, but ij« England commonly = S miles. IS ow long a lid. TABLE OP VALUES, WEIGHTS AND MEASUKES 93 ft- yd. rd. mi. 50 Indies. )r 66 feet Ik. rd. ch. mi. I purposes . ure. 3ut not by 'o miles. Square Measure Square Measure is used in measuring surfaces; as of land boards, painting, plastering, etc. ' Area or Surface has ler.gth and breadth only, and is the space or surface included within any given lines. ^ A square inch, square foot, or square yard, is a square each Side of which IS respectively 1 inch, 1 foot, or 1 yard in iTngth. TABLE 144 Square Inches {sq. in.) 9 Square Feet . . 30J Square Yards 160 Square Rods . . . 640 Acres . , 1 Square Foot . 1 Square Yard . I Square Rod . 1 Acre . . . 1 Square Mile . sq. ft. aq. yd. sq. rd. A. sq. mi. Surveyors' Square Measure ^^ Jhis measure is used by surveyors in computing the area of 625 Square Links 16 Poles {sq. rods) 10 Square Chains 640 Acres . . TABLE 1 Pole (sq. rod) P. I Square Chain, sq. ch. 1 Acre . . . A. 1 Square Mile . sq. mi. Cubic Measure Cubic Measure is used in measuring solids or volume. A solid is that which has length, breadth, and thickness. Hence length, breadth, and thickness are equal to each other. 94 DENOMINATE NUMBEBS TABLE 1728 Cubic Inches (cu. in.) . = 1 Cubic Foot . cu. ft 27 Cubic Feet ....=, Cubic Yard . cu. yd. 40 Cubic Feet of Round ^ Timber, or ... 50 Cubic Feet of Hewn Timber 16 Cubic Feet . . .' ." 8 Cord Feet, or 128 Cubic ^^^' =1 Cord of Wood. Cd 24| Cubic Feet . . . . = 1 Perch of Stone = 1 Ton . . T. = 1 Cord Foot . cd ft. or Masonry 1 Pch. Note 1.— A cubic yard of earth is called a load. NoiE 2.-A pile of wood 8 feet long. 4 feet wide, and 4 feet high, contains 1 cord ; and a cord foot is 1 foot in length of such a pile. Note 3.— A foot of lumber, or a board foot, is the unit of measurement in lumber. It is 1 foot long, 1 foot wide, and 1 inch thick. Measure of Time Time is the measure of duration. Time is naturally divided into days and years. The former are measured by the revolution cf the earth on its axis ; the latter by its revolution around the sun. TABLE 60 Seconds {sec). 60 Minutes . . , 24 Hours . . . , 7 Days . . . , 365 Days . . . , 366 Days . . . , 12 Calendar Months. 100 Years . . . . 1 Minute . . min. 1 Hour . . hr. 1 Day . . . da. 1 Week . . . wk. 1 Common Year c. yr. 1 Leap Year I. yr. 1 Civil Year yr. 1 Century. C. The unit of time is the solar day; it includes one revolution of the earth on its axis, and is divided into 24 hours, counting from midnight to midnight again. V-;, TABLE OF VALUES, WEIGHTS AND MEASURES 95 minutes, 49.7 seconds, or about 3^ da^~^ ''' ''°'"^' '^ .0 the .non'h ol FeZyZZtLTcT^ 7\^'' '' '""'''' the fraction that is disregarded wheTi^ d»! " "^ T' ^»« is less than one fourth of a div thJ^.^, ^'!' """"''' ^ " y^^' year is not exactly accu ate The r m °" °' " "'"^ '=^"5' '»""•> rected by excluding from ,1; I ^''Sl" "™'- ^'"1 existing is cor. diviSd iX' .iz^x :r°" ^"^ '-•''^-- -^ ^ 31 Days Ju]y (July) . January (/««.) . . ^, ^^^^ February (F^fiy.) . 28 Days In Leap Year 29 Days March (Mar.). . . 31 Days April (Apr.) . . . 30 Days May (May) . . . 31 Days June (June) ... 30 Days August (^«g.) ^ September (5^/)/.) October (Oc/.) . November (Nov.) December (Dec.) 31 Days 31 Days 30 Days 31 Days 30 Days 31 Days Standard Time tuae, 7J of which are east and 7i° are wp^f .^f +1.^ ^ ^ that belt. governing meridian of a„d^the'°;^[hTc"t^ofTrc "^ 'f • '"^ ^''- '-^ >»«'"• Bngland, and ^^^'•^^::tT:^^t^ 96 DENOMINATE NUMBERS difference in time of exactly one hour between any one of them and the one next on the east, or the one next on the west ; the standard meridian next on the east being one hour faster, and the one next on the west one hour slower. Hence, the 60° of longi- tude is four hours, the 75° five hours, the 90° six hours, the lOS© seven hours, and the 120° eight hours slower than Greenwich time, making five different standards of time between the Atlantic and the Pacific Oceans, viz. : Intercolonial, Eastern, Central, Mountain, and Pacific. Circular or Angular Measure Circular Measure is used principally in surveying, navigation, astronomy, and geography, for reckoning latitude and longitude,' determining locations of places and of vessels, and in computing difference of time. Every circle, great or small, is divided into the same number of equal pwts ; as quarters, called quadrants ; twelfths, called signs ; three hundred and sixtieths, called degrees, etc. Consequently the parts of different circles. although having the same names, are of different lengths. _ The unit is the degree, which is gj, part of the circumference of any 60 Seconds (") 60 Minutes . 30 Degrees 12 Signs, or 360" 12 Things 12 Dozen 12 Gross 20 Things 24 Sheets 20 Quires 2 Reams TABLE - 1 Minute = 1 Degree • . . = 1 Sign . • • . =1 Circle Miscellaneous Tables COUNTING = 1 Dozen. = 1 Gross. = 1 Great Gross. = 1 Score. PAPER = 1 Quire. = 1 Ream. = 1 Bundle. S. c. 5 Bundles = 1 Bale. REDUCTION OF DENOMINATE NUMBERS 97 e of them >vest ; the ister, and of Jongi- , the 1050 jreenwich c Atlantic , Central, avigation, longitude, omputing er of equal 2e hundred ent circles, ice of any BOOKS 2 Leaves = 1 Fohq 4 Leases = 1 Quarto, or 4to. 8 Leaves = 1 Octavo, or 8vo. 12 Leaves = 1 Duodecimo, or I2mo. The terms folio, quarto, octavo, denote the number of leaves m^o which a sheet of paper is folded in making books. REDUCTION OF DENOMINATE NUMBERS In reduction the unit or denomination of a number changes but not the value. When the change is from a higher to a lower denommation the i)rocess is called reduction descending, and when from a lower to a higher, reduction ascending. To reduce denominate numbers from higher to lower denominations. ILLUSTRATION.-Change 1 bushel, 1 peck, 1 pint to pints. 1 bu. 1 pk. qts. 1 pt 4 4 pecks 1 p eck 5 pecks 8 40 quarts 2 80 pints 1 pint 81 pints. Solution.— Since 1 bushel = 4 pecks, 1 bushel and 1 peok= 5 pecks. Since 1 peck = 8 quarts, 5 pecks =5x8 quarts = 40 quarts. Since 1 quart = 2 pints, 40 quarts = 40 X 2 pints = SO pints, and 80 pints + 1 pint = 81 pints ; therefore, 1 bushel. 1 peck, 1 pint = 81 pints. Rule Multiply the units of the highest denominatio^i given by that number which will reduce it to the denominatio>i next lower, and add the units tt any of that denomination. Continue in this manner until the required denomination is reached. ^^ D»5N0MINATB NUMBERS SERIES 37 Reduce to the lowest denomination named : X. 4 mi. 17 rd. 3 yd. 1 in. ii 4 T. 5 cwt. 3 lb. 1 or. 2. £52 10s. 4d. j2. 6 lb. 8oz. 11 dwt. 3- *' bu. 5pt. J3. 20 rd. Sin. 4. 6 bu. 1 pk. 3 qt ,4. 15 sq. rd. 5 sq. yd. 3 sq. ft. ^- '^^'' ^' 23^ 15. 10 A. 31 sq. rd. 5 sq. yd. 4 sq. ft. 6. 15 gal. 3 qt. 1 gi. 16. 7 ,vk. 210 hr. 5 min. 31 sec. 7. 6 l.t. 50 lb. 2 02. 17. 8 cu. yd. 2 cu. ft. 8. 7 cu. yd. 4 cu. ft. 11 cu. in. 18. 6 lb. 3 dwt. 4 gr. 9. 190 sq. rd. 15 sq. in. 19. l bbl. 2 gal. 1 pt. 10. 2 mi. 10 eh. 43 Ik. 20. 2 mi. 15 rd. 11 ft. 10 in. Reduction from a lower denomination to a higher. ILLUSTRATION.-Reduce 473 pt. to bushels. Solution.— Since 2 pt. equal 1 qt.. 8 qt. 473 pt. 236 qt. + 1 pt. 29 pk + 4 qt. 1 pk., and 4 pk. 1 bu.. the successive divisors for reducing given pints to bushels are 2, 8, and 4 respectively. -7 u„ . , - . ^'^''le 473 pt. by 2 and the result b 236 qt. 473 pt =7 bu 1 Dk 7u^^ ^ "-eniainder of I pt. ; divide 236 qt. by 8 and 4 at ^^" *^' "■"'"'* '^ 29 pk. with a remainder 4 qt. • qt. 1 pt. divide 29 by 4 and the result is 7 bu. with a remainder 1 pk. «o,r^*rJ^!-^,*u'^"f'°*^''^ ^^' '"^"^* remainders in order and the required result is 7 bu. 1 pk. 4 qt. 1 pt. Rule Divide the given number by the number of the same denomina- txm reqmred to make one of the next higher denomination, and consider the quotietU as units of the higher denomination, and the remainder as umts of the lower denomination. Proceed in like manner with each successive quotient until the required denomination is reached. The last restUt and the several remainders written in order xmU oethe answer required. BBDiJcnON OF DENOMINATE NUMBERS 89 Reduce : Z. 813551 2. 47920 3- 23769 4. 17150 5. 4276 6. 185760 7. 278644 8. 32359 9. 477960 10. 213546 zi. 12. 13. 14. '5. To SERIES 38 ounces grains inches pounds pints seconds cubic inches farthings cubic feet sheets of paper pence grains, troy, mills 2368 23754 45630 4700356 links 2562 pints reduce a fractional denomination. ILLUSTRATION.—Reduce denominations. to tons, etc. to pounds, etc. to miles, etc. to long tons, etc. to gallons, etc. to days, etc. to cubic yards, etc. to £, etc. to cords, etc, to reams, etc. to half-crowns, etc. to pounds, etc. to dollars, etc. to miles, etc. to bushels, etc. denominate number 12d. X 20 X /fl = 105d. I05d. = 8s. 9d. or 20s. X A = ys. = 8|s. 12d. X J = 9d. ••• ;iA=8s. 9d. or 7 20 16)140(83. 128 ^tV Solution to a lower (.4375) to integers of lower 12d. X 20 X .4375= 105d. lOSd. = 8s. 9d. or ;g.4375 20 8.8.7500 12 d.9.0000 .'. i;.4375= 83. 9± 12 12 16)144(dd. 144 100 DENOMINATE NUMBEflS SERIES 39 Reduce to lower denominations : I. i of a day. 3. tV o^ a mi. 3. T of a mo. 4* IT o^ an acre. 5" rs of a cu. yd. 6. ff of a gal. 7. ^js of a bu. 8. irtff of a rod. 9. .625 of a mile. 10. .727 of a ton. Zi. .625 of an acre. 12. .4225 of a cord. 13. .5375 of a gal. 14 r of a pound, Apoth. To reduce a fractional denominate number to a hieher denomination. Illustration 1. -Reduce 9s. 6d. 3 far. to the decimal of a pound sterling. 4 12 20 («) 3Jar. 6.75d. 9.562SS. ;^.478125 (ft) Solution (a).— -The successive divisors to reduce farthings to pounds are 4. 12, and 20 respectively. Dividing 3 far. by 4, the result xs .7Sd. Putting with this the 6d., the result is 6.75. Dividing 6.75d. by 12, the result is .5625s. Putting with this the 9s., the result is 9.5625. Dividing by 20, the result is .478125 pounds sterUng. Or, Solution (/>).— In 9s. 6d. 3 far. there arr 459 far., and in £1 there are 960 far. Hence, 9s. 6d. 3 far. = 459 far. £1 = 960 far. _ 459 + 960 = ^.478125 9s. 6d. 3 far. is ^ J 3" of a pound sterUng.' /m = ;^.478125. ^ **" Illustration 2.-Reduce £19 9s. 6d. 3 far. to doUars and WvIXLS* ti& Js. 6d. 3 far. = ;^19.478125 £1 = J4.86I ;J19.478125 = 19.478125 times $4,863 =» $94.79354 + = $94.79 Solution. -- By previous illustration 9s. 6d. 3 far. are equal to ;£.478125. Then ;£19.478125, at the par value of £\ (S4.86§), are equivalent to $94,79, sq 7( Sp ADDITION OF DENOMINATE NUMBERS 101 a Ji'^^^'*'^"^-"^ a. -Roducv A yd. 2 ft. 6 in. to the fraction oi Solution («)._T».c successive divisors to rtduce inches to rocis are 12. 3, and 5t respec- tivdy. (i in. divided by 12 equal J ft. Putting Willi tiiis the 2 (t., tlie result is 2J ft 2} ft chvided by 3 equal Jj yd. PuttinR ^itli this the 4 yd., the result is 4g yd. 4} yd. divided by 5 J (a) 6-^ 12= i It. 5(21) -^ 3=3 yd. V{4;])-r 5J=ij|{ rd. 4 yd. 2 ft. 6 in. = 174 in. '•'•1"'^1 i^ rt'- Or. 1 rd.= 198 in. Solution (/>).- 174 -f 198= fy = J J I rd. equals 198 in. I. 2. 3. 4. 5- 4 yd. 2 ft. 6 in. equal 174 in. ,,, , . 4 yd. 2 ft. 6 in. is. therefore, tU oi 1 rd., or ijlj rd. SERIES 40 What fractional part of a buslicl is 3 pk. 4 qt 2 pt ? VVhat decimal part of a pound troy is 8 oz. 10 dwt. ? What fractio:ial part of 2 hhd. 20 gal. is 30 gal. ? What decnnul part of 2 J mi. is 10 rd. 4 ft ? Reduce 3d. 3 far. to the fraction of a shilling 6. Reduce 8 oz. 2 dr. 2 sc. 10 gr. to the decimal of a lb. 7. Reduce 20 rd. 12 ft. 10 in. to the fraction of a mile. squa'- rod " ' ''• ''• ' ''' '• ''' ^^- '"• ^^ ''^ '•--^- o^ ^ Reduce to Canadian Currency. 9. ;f47 12s. 6d. 13. £176 9s. 8^. 10. £250 I5s. 9d. 14. £29 17s. 7fd. 11. P5 10s. lid. 15. £212 9s. 5id. 12. £124 12s. 9d. * Addition of denominate numbers. iLLUSTRATION.^Add 1 bu. 2 pk. 1 pt., 1 bu. 1 qt., 1 bu. 3 pk. 7 qt. 1 pt. -1 i' Solution.— Add each denomination separately, and the simple denominations are 3 bushels, 5 pecks, 8 quarts, and 2 pints. Changing to equivalents, the 2 pints = 1 quart, which added to the 8 quarts = 9 quarts ; 9 quarts = I peck and 1 quart remaining. Write the 1 quart remaining under the column of quarts and add the 1 peck to the 5 pecks. Write the 2 pecks under the column of bu. bk. qt. pt. 12 1 10 10 13 7 1 3 4 5 2 8 2 = first sum. 1 = equivalents. 6 pecks = 1 bushel and 2 pecks. 102 DENOMINATE NUMBERS tl 1 quart. '''' P'*^^' « *1"^' and 2 pints = 4 bushels. 2 pecks! In practice o.it the first sum and write only the equivalents. Rule I. Wriie the numbers so that unit^ nt tu. in the same column. ^ ^^ "''^' '^^^^ ^^«^^ ^icmd the juoli^ u,ith the Mxt colZ^ """"'^"' '' ""y- ""^ -^ SERIES 41 I. £ s. d. 75 5 8 13 16 5 96 8 H 52 13 9 7 2 4 33 18 8 far. 3 1 2 I 2 3 2. lb. oz. dwt. gr. 5 9 12 9 13 4 16 8 41 6 8 15 71 11 18 22 56 7 13 19 72 8 14 16 mi. rd. yd. ft. in, 5 175 3 1 8 17 248 4 2 6 25 315 1 1 11 41 214 3 1 7 50 16 2 2 9 48 296 4 1 5 ^ ^4. Add 5 ga,. 3 ,t. , pt.. , ,., 2 ,,. 2 ,, , p,. „, 3 ^^ listtmT'"'-^^^ ^'" *• ^- '°^ » »™i« <" cutlery i^i 5s. 8d. for an invoice of files, and ^73 1 7. ft, , ^^ of saws. Tlie cliaros. *„, . *'■ ''"' ™ "TOce What was Z r.? 'ran^Portation amounted to f 19 2s 4d What was the total cost of the goods in sterling money ? .toti'r ;:;:',;:• ::,:- ^ - >« -■ «« '^- ^ «. 1 oz., and 5 ton 12 cwt. 94 lb 7 oz 7. Whatisthesumof|bu..|pk..andiqt? 8. Add ^.832. .0125s.. 5.275s.. and .17d. , 9. What is the sum of .9675 gal 2 125 ^;,l ^ . . Sai., ^ 1^5 gal.. .5 qt., and .25 pt. , y rherefore, the shels, 2 pecks, ■s. ■ shall stand J sum to the y, and add ft. in. 1 8 2 6 1 11 1 7 2 9 1 5 o rd. 71 15 yd. 3 5 ft. 2 2 SUB-nUCTION OP DENOMINATE NUMBERS 103 Subtraction of denominate numbers. 2 ,,!^3t:^----^- '' ''■ ' y^' 2 ft. 6 in. take 15 rd. 5 yd. SoLUTiON.-Write the numbers so fh.f .», take'77t '(12"i„Tr ''o '"'*^^^*^^ *--" 6 in., whichUSin:L:^--i^,:^-ioin.. but rT"'"" "" ' "• " ^^^^d t° 6 in., there is cannot be suotracted from 1 ft J^TT"^^^ l"" '"^ minuend. Since 2 ft. it to the , ft., making 4 ft 4 ft ^us 2'ft "'^ ^^ *'^ ' ^'^^^ ^^ ^^^ m the remainder. "' ^ ^*- '^^^^s 2 ft., which write as feet Inasmuch as 1 yd. was added to 1 ft tj, in the minuend. Since 5 yd cannot h. k! ' ^'' •""* ^ yd. remaining (H yd.) from 71 rd. and add to the ol'^ '-''*''' ''°'" ' ^^•' *"^' ' '"'^ eaves 2^ yd., which write as ya'ds in t'h" °'- '* ^^^ '* ^^^ -'°"« « yd. leaves 55 rd.. which write ^ rSs n the r^'^''^^^'"- '« ^^- ^'^^^ '5 rd. Reducinij 4 vd tn lo,. 5°^^ ^° *°e remainder. is found to l^y^d. 3 ydUt'Jt''''^"' '"' ^'"^^' "^^ ^-I'^^i r-ult 55 2i 2 i=l 55 m. 6 8 10 6 nd 8 gal. f cutlery, n invoice 9 2s. 4d. !b. 5 oz. 25 pt. r I. lb. oz, dwt. gr 75 6 13 12 42 9 18 23 SERIES 42 2. mi. rd. yd. ft i2 75 3 2" 8 318 4 1 3. --^ bu. pk. qt. pt. 18 1 3 1 16 3 2 1 4. A merchant sold 25 eal 2 at 1 r.^ f ■ ' had he yet to deliver ? ^°- ^°^ "^"ch hay 6. An English merchant's salPQ f«r o 5s. Sd 9 far °,n 1 I,- ^'^ ^ y^^r amounted to /!S "^QP — oc. „ Tar., and his purchases /18 352 2<; q,i w „ £io,^bv greater were his purchases than.his Ses ? ^°^ '""^^ 104 DENOMINATE NUMBERS lb. oz. d\vt. gr. 15 5 13 16 7 7. Find the difference between .522 yd. and .02345 mi. 8. SuhtKict J sq. yd. from § sq. id. Multiplication of denominate numbers. ILLUSTKATION.-Each of seven bars of silver weichs 15 lb 5 02. 13 dwt. 16 gr. Find the total weight. Solution.— Write the nniltiplier under the lowest denomiiuition of the ,„ ; '""Itiplicand, and multiply as in simple 1081b. 3oz. 15(hvt. l(>gr. numbers, thus : ' Carry Vtour- ^^"^'^^^^^ ^^ ^^ = ^ '^- '^ - ^:i'< ^lo.n 3 under oz. 15 lb. X 7 + (3 lb. carried) ^ 108 lb. Put down 108 under lb. RULS ,' ' ' ' MuUipiy each dmomination separately afut change the partial products to units of higher denominatimis. SERIES 43 ' ^ ' 1. Multiply 7 bu. 3 pk. 5 qt. 1 pt. by la 2. 24 times 8 gal. 3 qt. 1 pt. equals what ? ^^ 3. How much wood is there in 36 piles, each measuring 3 Cd 40 cu. ft. 1020 cu. in. ? ^ 4. Multiply 1 wk. 5 da. 6 hr. 30 min. 45 sec. by 80. 5. If 60 acres 40 sq. rd. 9 sq. yd. 6 sq. ft. 100 sq. in. be multiplied by 72, wiiat will be the product ? 6. Find the product of 2 ton 8 cwt. 40 lb. 12 oz. multiphed by 50. ^ -^ 7. 32 acres of oats averaged 42 bu. 3 pk. 5 qt. 1 pt. Find the entire crop. 8. What quantity of wine will be required to fill 48 barrels if each barrel holds 31 gal. 2 qt. 1 pt. / '/ betv i( aver E numi I] bi 4)^ peck n 11 qua 3 quar Di: to loW( She units tc Fin 1. ] i. i 5. 1 of equa 6. F different Canadia 7. I lost $98 mi. ghs 15 lb. multiplier .tion of tlift as in simple Carry 4 to ur down 15 3 under oz. DIVISION OP DKNOMINATE NUMBERS 105 av::^.^i;a:;"LrL^;r numlLT'°" "^ ''"°"''"''' """''^^- ^'^ ^^^^^ ^'^'^°^ - abstract iLLUSTRAriON.-Divido 5 bu. 1 ,,k. 3 qt. by 4. bu. pk. qt. pt. 4)5 1 3 1 1 2 Snr.irTioN.-DivUling 5 buslids by 4 dves a quotient of 1 ,,„shel and an undivided remainder of 1 bushel ; reduce ti.is remainder to pecks (4) and add to the . peck of the dividend, obtaining 5 pecks, which chv.ded by 4 gives 1 peck an^ sq. rd. 12 sq. yd. ? ^ ^^^ containing 684 acres 72 57 L"^^"'^''^ ^''''^°"' °^ '^"^^' ^^^h ^q«al to 1 day 14 hr 57 mm^ 33 sea. are contained in 365 days 5\r. 48 min. 45 sec ? 7. Among how many persons must /641 14s ITH i f u ' make the trip ? '^ "" '"'" """"y "^^^^ «*" " take her to sd to the lowest ne result would ny of the other luart. and divide in ■i; ! INVOLUTION AND EVOLUTION INVOLUTION involution is the operation of finding any power of a given nnni^T' °^ ^ "''"'^'' ^' *^' P'^^^^t Obtained by using it a number of times as a factor. ^ ^ A Square of a number is the second power of that number or he product obtamed by multiplying the number by'tself Thus the square of 4 = 4x4=1 6. ^i-scii. mus The Cube of a number is the third power of the number or the product obtamed by multiplying together three facto" each of which IS the number. Thus the cube of 4 = 4 x 4x4=^ and\''liftrarl">' '5"" """^" *° '^^ "^h* °f the number and a httle above it, indicating the number of times the factor SERIES 46 What is the square, or second power, of 25 ? What is the cube, or third power, of 5 ? 24 ? 168 ? What IS the fourth power of 4 ? 8 ? 16 ? 25 ? What is the third power of | ? f p | p Expand the following : 6^, 92, 8*, 10^ 23^. 6. Find the required power of the foUowine •* (l)Mm(3J)3,(14|)^(5.06T)3^- 7' rind the difference between SS^ and 902. EVOLUTION Evolution is the operation of finding any root of a given number. squart'is^r'' ^°°* °l^ ^''"'' """^^^^ '' '^^' """^ber whose • square is the given number. I. 2. 3. 4. s. Examples. — 4 is the square of 2, sauarp /if •* . 1 • i.- * . ■ • 2 is the square root of 4 ; 9 is the square of 3, .-. 3 is the square root of 9 ;>""-- -- square root of 100. 100 is the square of 10, .-. 10 is the EVOLUTION 109 JTION ver of a given by using it a hat number or V itself. Thus he number or ! factors, each < 4 X 4 = 64. 'f the number les the factor hat the factor 38? iven number, mber whose 3f 4 ; 9 is the 0, .-. 10 is the The Cube Root of a given number is that number whose cube is the given number. cube^oft'^'s"^.^' *'r"'' °' '• •■• ' " '''' ^"^« -°* °* « : >25 is the «, h ; ; l!! * ' '"''" '°°* °^ ^-^ • '•^•^^ ^^ ^he cube of 10. .-. 10 is the Cube root of 1000. *"® There are two ways of denoting Evolution. In the first or older notation, the square root of a given number is denoted by refixmg the symbol V to the given number; the cube root is denoted by prefixing v^. root^f r"''"'''' '"°'" *'^ ^'""^ "°* °^ '' -• ^'' ^-°*- *^« -be The second method employs fractional exponents. ^^ Jhus. 64 denotes the square root of 64; 64* denotes the cube root To extract the square root of a number. Rule I. Point off the given number into periods of two fimres each begtnu.^g at the decimal point ^^ ^'^^' 4. Double the part of the root already found for a irul DmsOH. 1 110 INVOLUTION AND EVOLUTION Illustration.— What is the square root of 22420225 ? 87 943 9465 22 I 42 I 02 I 25)4735 16 642 609 3302 2829 47325 47325 n Solution.— Here 22 is the left-hand period and the highest square in 22 is 16, of which the square root is 4. We place 4 in the root and subtract 16 from 22. This leaves a remainder 6, to which we bring down the next period, 42, and thus obtain 642 for the new dividend. Our next step is to find the trial divisor, which we obtain by doubling the part of the root already found. This gives us 8 {= 4 doubled), and we ask how many times 8 will go into 64 (the dividend exclusive of the right-hand digit). Bearing in mind that we are to put the digit thus obtained both in the root and in the divisor, and that the complete divisor will be over 80, we find that the required digit is 7, which we accordingly place both in the root and in the divisor. The complete divisor is 87, which multiplied by 7, gives 609 and this subtracted from 642, gives a remainder 33, to which we bring down the next period, 02, and thus get 3302 for the next dividend. Again, doubling the part of the root ahready found, we obtain 94 (= 47 doubled) for a trial divisor, and as this wiU go into 330 (the dividend exclusive of the right-hand digit) 3 times, we place 3 both in the root and in the divisor. Multiplying the 943 thus obtained by 3, subtracting and bringing down the next period, we get 47325 for the next dividend. The next trial divisor is 946 (= 473 doubled), which wiU go into 4732 (the dividend exclusive of the right-hand figure) 5 times ; and we therefore place 5 both in the root and in the divisor. Multiplying and subtracting, we find no remainder. 4735 is therefore the square root of 22420225. Proof.— 4735 x 4735 = 22420225. Note 1.— If there is a remainder after the root of the last period is found, annex periods of ciphers, and proceed as before. The figures of the root thus obtained will be decimals. Note 2.— If the trial divisor is not contained in the dividend, annex a cipher both to the root and to the divisor, and bring down the next period. Note. 3— It sometimes happens that the remainder is larger than the divisor ; but it does not necessarily follow that the figure in the root is too small. tl 55 EVOLUTION 111 0225? eft-hand period is 16, of which :e 4 in the root This leaves a ring down the ain 642 for the is to find the ay doubling the id. This gives ask how many idend exclusive aring in mind thus obtained visor, and that ver 80, we find in the root and by 7, gives 609 we bring down btain 94 (= 47 idend exclusive i in the divisor. bringing down !xt trial divisor ad exclusive of )th in the root no remainder. )eriod is found, tf the root thus idend, annex a next period. arger than the the root is too To extract the square root of a decimal. Rule Begin at the units' place, and proceed towards the left and right, to separate into periods of two figures each, then extract the root as in whole numbers. Note 1. — The left-hand period in whole numbers may have but otie figure ; but in decimals, each period must liave two figures. Hence, if the number of decimals is odd, a cipher must be annexed to complete the period. Note 2. — It must be kept in mind that no period should contain an integer and decimal, and that, if there is an odd number of decimal places in the given number, the last period must be completed by annexing a cipher. To extract the square root of a fraction. Rule Reduce the fraction to its simplest form and find the square foot of each term separately. Note 1. — If the denominator of the given fraction, when reduced, is an imperfect square, reduce the fraction to a decimal, and proceed as above. Note 2. — Mixed numbers should be reduced to improper fractions, or the fractional part to a decimal. SERIES 47 Find the square root of z. 2. 3- 4. s. 6. 7. 8. 576 1225 2025 4356 11025 18225 15129 103041 9. 10. II. 12. 13. 14. IS- 16. 39601 88209 751689 106929 225 TS^ 169 F15T 256 3T5T IQfl FIT 17. 18. 19. 20. 21. 22. 23. 24. 11.9025 41249.61 .697225 54.6121 3 376.4 12.823 4367.2 25. Find the length in rods of a square 10-acre field. 26. A park, in the form of a rectangle 220 yards wide and 528 yards long, has a path around it and from corner to corner. 112 INVOLUTION AND EVOLUTION It: How much will a person, who wishes to cross the park diigonullv save by " cutting across " ? b""any, 27. An electric light pole broke in such a way that the top struck the ground 33 feet from the base of the pole What was the height of the pole, the broken part being 65 feet long ? 28. A ladder, 41 feet long, stands uprigiit a^amst a wall. Find Lp'l f'ool'' *''' ^''^'^'' "''''' ^' P'^^'^ ""^ *° ^'"^'^ the 9i f^; Vf'^""' ^ ^'"' ^""^' '^ P^"^^^ '^ ^ t° '^^'^^ a window 24 feet high on one side of a street, and from the same spot it will reach a vvmdow 32 feet high on the other side of the street. i dividing 5960P by 7500 ( ike ft fnr "- « -w. i„ ...1 ,, '™;r oT "^^"" " ^• MuUipiy i ^tt that i, fh. 1. • ''"''"""'• and add result t; 7500/ ' Thus t'.eTsTse '' '"' ' '" ^^'^^^ (^). "y 6. Now multiply 8436 by 6. and we get 50616 the ^t:::^, '-- ^^^^ - o. re.ainde;i3 S^.. to wH.H we attach (3) Now to find third figure of answer Thus we get in column (a) 168 Square 56. and multiply result "by 3C0 = 940800. This divided into 8992795 gives 9 Put down 9 in column (.) as third'figure of answer, resulft Ko"JSo"l^^^^ -'"- ^ ^ --) ^. ^. = 15201. and add = 3^7^-'tiply 956001 by 9= 860400, and subtract this from 8992795 (4) To 388786 attach fourth period Multiply 168 by 10. and add 9 x 3^ or 27 Thus 1680+27=1707 Pnf th- ■ multiply by 300= 97128300! "' ^'^^ '° column (a). Square 569, and Divide this into 388786384 = 4 Thus our answer is 5694 exactly. obtained „m be ii.*^...«fc: P'""'" « ^^'o"- The root figure, thu, Penod. «"• "' *« divisor, and bring down the neil Nora 3.— i; til. .,-... „; V,, J. . placed in the roc. , , ■, ,1. ,,.5° I'T' ""'l"=*«' '"'o the figure last times th, ren,ainO, i, ',', C '°°' "T " ""■ '"«« W necessarily , 569, and ;d as in (2) >d is 'a,.ij'i ures thus It a cipher 1 the next igure last '• Some* does oot BVOLUnoN J 15 To extract the cube root of a decimal. Rule Begin at the units' place, and proceed both toward the left and right to r,cparufe .nto periods of three figures each, then extract the root as %n u/hole numbers. NoTE.~-The left-haud period in whole numbers may have but one or two figures but m decmals each period must have three figures. Hence, ciphers must be annexed to the right of the decimal to complete the periods, when To extract the cube root of a fraction. Rule Reduce the fraction to its lowest terms, then extract the root of its numerator and denominator, h. ,^°^^?r^'^'° ^^^ ^^"onii^ator is not a perfect cube, the fraction should be reduced to a decimal, and the root of the decimal be found as above Note 2.-A mixed number should be reduced to an improper fraction. SERIES 48 Find the cube root of 1. 4096 2. 32768 3. 74088 4. 493039 S- 250047 6. 614125 7. 14706125 8. 84027672 9. 354894912 10. 673373097125 Find the fourth roots of 21. 531441 22. 4100625 24. Find the sixth root of 4826809. 25 What are the dimensions of a cubical block whose volume IS 35,937 cu. in, ? iz. 12. 13. 14. 15. 16. 17. 18. 19. 20. 122615327232 389.017 .194104539 48228.544 2 14.6 1331 2 80 405^«T 23. 1575.2961 116 i-. : i! INVOLUTION AND EVOLUTION I 26. A bin, whose capacitv i.^ fi7';n • . as it is wide or high. What a'e Us itoension"; " '™" ^ '°"« 2% A pile of wood has thp fr rrr, f feet Jong, ,2, fee. wide, and i te" hii "^ff - »M. <68 ■ - ~;.tird':re::^^^^^^^ - co„.n.s and 36 feet high ? ^^^ ^^^^ ^ong, 48 feet wide, -d 3 ft. 9 in. deep, fed L ZZZl^' °"'' " '' ' '"' ^''^- 30. The cubical base nf ^ ^ How n,any square feerro„: oTI" ^'^^ '''■''' ^ "• corrS ^^L": ofa^i'of^f k"- , ^"^ *^ ^'^^ *™nsions gals. ™'' "' " ^bical tank that will hold 1,000 32. If 160, 103,007 cubical blocks of ,t„„. u -Placed in a cubical p,le, ^^^i^CtZ^Z^Z wice as long ar solid, 168 vould he the be ? 3tal contents is feet wide, •• 2 : 3. If 2 in. wide, .625 cu. ft. dimensions hold 1,000 3ot square, th of each PRACTICAL MENSURATION Mensuration treats of the measurement of lines, angles, surfaces, and soUds. SURFACES A Line is that which has length, but not breadth or thickness. A Straight Line is one that does not change direction. It is the shortest distance between two points. A Curved Line is one that chauges its direction at every point. It is one of which no three consecutive points are in the same direction. Parallel Lines are lines that have the same direction and are equally distant at all points. A Horizontal Line is one that is parallel to the horizon or water level. • A Vertical Line is one that is perpendicular to a horizontal plane. A Surface is that which has length and breadth only. If a straight e^ge laid anywhere upon a surface touches at every point, the surface is a plane surface or a plane. A Right Angle is an angle formed when one straight line meets another so as to make the adjacent angles equal. The lines forming the angles are said to be perpendicular to each other. In the accompanying diagram ABC and A B D axe right angles, and the lines A B and C D are perpendicular to each other. c A Triangle is a plane figure with three plane sides and three plane angles. The side on which the triangle stands is the base, the op- posite corner the vertex, and the shortest distance from the vertex to the base, or the base extended, is the height or altitude of the triangle. ' Tr}»ngte Right Angle Right Anglo ii I'll: Kec tangle 118 PRACTICAL MENSURATION ■«^ is .^l^ZlS^e -.^'^^ "-^'e the t?"'*"'"^"^ is the Side .ha. ,„.„. a righ.' a„g,e witt When a plane figure is bounded bv a curv.^ "unating m the circumferenrp +hn ^- one-half of .he dia™e.er, the^^^f *'"»*'-' _ sidef Po'^S"" i3 a p,a„e figure having „ore .han f„„ ,,,^,, To find tte area of a rectangle or square 4 ri'^r™"-™^' '= "■' -- <" a garden 5 rd. ,„„g ,y 5r(3. Solution Isquarerodx4x5=20sq. rds. Mmpiy the length bv iJ" bread/l n^ri //. 6 oream and the mult will be the area. SURFACES 119 iangle having gled triangle t angle with 3c tangle straighc long by I rds. e area. To find the area of a triangle when the base and altitude are ILLUSTRATION.-Find the area of a triangle whose base and altitude are 6 ft. and 8 ft. respectively. .., ^^°|;""°N— 1° the accompanying diagram assume that the base (C B) is 6 ft. and the altitude {A D) IS 8 ft. It will be seen that the altitude divides the triangle into two right-angled triangles, each of which IS one-half of a rectangle whose sides are 8 ft. and 3 ft. Two triangles, each one-half of a rectangle 8 ft. by 3 ft., are equal to one rectangle 8 ft. by 3 ft. The ntv. of the triangle given is, then, the product of these two dimensions, or 24 sq. ft. Rule Multiply one-half the base by the altitude. To find the area of a triangle when the sides are given. .J'^lT^tlT''!^^' '' '^' ^''^ «^ ^ *"^"gl^ ^hose sides are 12 ft., 16 ft., and 18 ft. ? Solution.— (12 -t- 16 + 18) 4- 2= 23 23 - 18=5 23x 5 X 7 X 11 = 8855 •»<3 — 16=7 23-12=11 >/8855= 94.1 sq. ft. Ans. Rule From half the sum of the three sides subtract each side separately • then muUxpiy the half sum and the three remainders together, and extract the square root of the product. To find the hypotenuse of a right-angled triangle. ILLUSTRATION.-The base of a right-angled 'triangle is 12 ft. and the perpendicular is 9 ft. What is the hypotenuse ? Solution. — 12*= 144 92= 81 144 -t._81 =225 \/225 = 15 Rule To the square of the base add the square of the perpendicular • ihc square root of the sum will equal the hypotenuse. 120 PKACTICAL MENSUBATION To find the base or perpendicular. Solution 258= 625 15*= 225 625-225=400 v/400 =20 Rule Principles. ™^ """^'-^ I. The circumference = the diameter . 3.I4I6 nearly , 2. Tlierefore the diameter . the circumference ^ 3,14!6nearly nea^y.^"' "''' °' ' ** = *^ ^^"-^ »' «>e radius x 3.1416 1 umV^ "!t °* ^ ** = ""= '^''^"niference x half the radius - 3. 1416 times the square of the radius. ^ auTsr:" "*"' °^ ^ ** = ^l"- ™* o' («.e area To find the circumference of a circle. radit:rs"4™T '-™'^' '^ '"^ *-"'"-- 0^ a circle whose Solution 14 ft. X 2 = 28 ft. diameter, 28 ft. X 3^=88 ft. Ans. (Prin. 1.) Rule MuUiply the diameter 6y 3.1416, or 3^. ingled triangle ! base ? SURFACES To find the diameter of a circle. 121 ' the given sidt. i 'de. learly. 3. 1416 nearly. iius X 3.1416 the radius = of (the area of the decimal circle whose Illustration 2.-The circumference of a circle is 352 ft What IS the diameter ? Solution 352 -r 3^=112 ft. Ans. (Prin. 2.) Rule Divide the circumference by 3.1416, or 3|. To find the area of a circle when the diameter is given. Illustration 3.-What is the area of a circle whose diameter IS zo it. r Solution 1 28 ft. -;- 2= 14ft. radius, 14 X 14 X 3^= 616 sq. ft. Ans. (Prin. 3.) Solution 2 28 ft. X 3f = 88 ft. the circumference. (Prin 1 ) 28 ft. -=- 2 = 14 ft. the radius. 88 X :y^= 616 sq.ft. Ans. (Prin. 4.) Rule Multiply the square of the radius by 3. 1416 or 3f. Or Multiply the circumference by J of the diameter, or J the radius. To find the radius, diameter, and circumference when the area IS given. Illustration 4.-The area of a circle is 616 square feet. Find the radius, diameter, and circumference. Solution Radius = v/6r6"T^= 14 ft. (Prin. 5.) 14 ft. X 2 = 28 ft. the diameter. 28 ft. X 3^= 88 ft. the circumference. (Prin. 1.) Rule Divide the area by 3.1416 or 31 and extract the square root of i^ q^ot^ent. Multiply the radius by 2. Multiply the diameter oy 3.1416 or 3|. 122 PRACTICAL MENSURATION • . SOLIDS A Solid is that which has length, breadth, and thickness l/l' Rectangular Solid. Cube. Cylinder. A Pyramid is a solid whose basp i= o t^^i terminate in a point called tie ..S.V '*'^«™ '^^ """"^ ^^es in al^^rit' ^t": '" ^ ** '" "^ "-• -0 —mates f J thets'^tl: Zt^' " ~"' '^ *^ "-"-*-'" distance Pyramid. Cone. Frustrumofapyra^ia. Frustrumofacono. ""'uiacono. to theS:^rotin^-:ri:i':e^-- '^°" *^ -•» souos 123 ickness. octangular sides s called a cube. ter whose ends Cylinder. i whose sides d terminates liar distance Q of a cone, the vertex 3 left after betwet^lltdr' ^ ^^^^^""^ '' ^^^ P-P-^^"^- ^^-ance The Slant Height of a frustrum of a pyramid is the distance between che middle points of twoparallel ^des of on of its faces! A Sphere or Globe is a solid terminated by a curve surface' every part of which is equally distant from a ' point within, jcalled the centre. The Diameter of a sphere is a straight line drawn through its centre and terminated at both ends by the surface. A Hemisphere is one-half a sphere. Epliere or Globe. The Radius of a sphere is a straight line drawn from its centre to any point in its surface. ^ To find the solid contents of a rectangular solid. ILLUSTRATION.-What is the volume of a solid 6 ft. long 4 ft high, and 3ft. wide ? ^' "• ^ti. ft. ® 1 cu. ft. Solution.— 1 cu. ft. x 3 x 4 x 6 = 72 cu. ft. Rule u,i^fT^ f-l ^"^^^^ ^^ ^^' ^''""^^^ ^y ^^' ^^^'^^^^^ ««^ ^he result will be the sohd contents. • t i 104 PRACTICAL MENSURATION To find the solid contents of a cylinder. aeep and 8 ft. m diameter, at 35c per cubic yard. ; Solution Area of base in square feet = (4 x 4 x 3|) cu. ft. Solid contents of well in cu. ft. = (4 x 4 x 31) x 25 Sobd contents of weU in cu. yd. = 4 x 4 x 3f x 25 Cost of digging = 35c. x 4 x 4 x 3J x 25 27 = S16.30 Rule Multiply the area of the base by the height of the cylinder. sidef ' ^'"'^^ ^"'^''' "^ ' '^^''^'' '' '^'' ^"^f^^- of its curved The lateral surface of a cylinder is equal to the surface of a rect angular body, the length and height of which are equal to the circumference A and height of the cylinder. Thus, the lateral surface of the cylinder in the accompanying diagram is the area of ^ the rectangle described hy A B C and D B^^ back of the cyUnder. Hence, To find the area of the lateral surface of a cylinder. Rule Multiply the circumference of the base by the height of the cylinder. MISCELLANEOUS To find the convex surface of a pyramid or cone. Rule I. Multiply the perimeter by one-half the slant height. 2 To find the entire surface add the area of the base to the area of the convex surface. MISCELLANEOUS 125 ind well 25 ft. t. < 25 X 25 .30 Under. of its curved f the cylinder. e to the area To find convex surface of a frustrum of a cone or pyramid. Rule 1. Miiltipiy one-half the sum of the perimeters of the mds bv the slant hetght. ' 2. To find the entire surface, add the areas of the ettds to the area of the convex surface. To find the volume of a cone or pyramid. Rule Multiply area of the base by one-third the altitude. To find the volume of the frustrum of a cone or pyramid Rule {A + a + s/A X a) x h x I where " A " stands for the area of the larger end, "a" for the area of the smaller end, and " h " for the perpendicidar height. To find the surface of a sphere. Multiply the square of the diameter by Z\, To find the volume of a sphere. Multiply the cube of the diameter by 3^ and divide the resvU oy D. To find the number of gallons in a cistern. Find the volume in cubic inches and divide the result by 277 118 Note.— There are 277.1 18 cubic inches in one gallon. To find the number of bushels of wheat in a bin or pile. Find the volume in cubic inches and divide the result by 2150 42 Note.— There are 2150.42 cubic inches in one bushel. To find the mean diameter of a cask (nearly). 3 ff/ VJ"' ^'"^ '^''"'''''' ^' ''' 'f ^^'' ^^«^^^ «^'^ ^"^ liitte cufved, ■s of the difference between the head and bung diameters. To find the volume of the cask in gallons. _ Midtipiy the square of the mean diameter by the length {both in inches), and this product by .0034. 126 PRACTICAL MENSURATION SERIES 49 1. How many square feet are there in a floor 22 yards long and 5 yards wide ? 2. How many acres are there in a field 220 yards long and 40 rods wide ? 3. How many square yards are there in the walls of a room 15 ft. 6 in. long, 12 ft. wide, and 8 ft. 6 in. high ? 4. How many square yards are there in the floor of the room in question 3 ? 5. How many square feet of glass are there in a box containing 72 panes, each 12 in. x 16 in. ? 6. How many bricks 8 in. long and 4 in. wide will pave a yard that is 116 feet long and 46 ft. wide ? 7. What will it cost to pave a roadway 80 ft. Ion? and 15 ft wide at $1.50 per square yard ? 8. A certain rectangular piece of land measures 1,500 links by 200 links. How many acres-does it contain ? 9. A man bought a farm 198 lods long and 150 rods wide at $32 an acre. What did the farm cost ? 10. Which would be the more economical and by how much • to pave a walk 4 ft. wide and 200 ft. long with stone at 22 cents per square yard or with brick at $1.02 per square yard ? 11. How many granite blocks 12 in. by 18 in. will be required to pave a mile of roadway 42 ft. in width ? 12. Find the cost at 16 cents per square yard of making a walk 4 ft. wide around the outside of a lot 10 rods long and 130 ft. wide ? 13. If the walk in the preceding question had been around the mside of the lot, how much would it have cost ? 14. The top of a table 4 ft. 8 in. long contains 1| square yards. How wide is it in inches ? 15. A farm cost $8,250 at $75 an acre. If it is 968 yards lone how many rods wide is it ? 16. How much would it cost to fence a field 40 rods long and 30 rods wide at 9 cents a yard ? MISCELLANEOUS 127 22 yards long ards long and alls of a room )r of the room 30X containing e will pave a *nrr and 15 ft. !s 1,500 links 50 rods wide ' how much : e at 22 cents d? 1 be required of making a ong and 130 been around quare yards. ! yards long, ds long and I 17. Two fields contain 40 acres each. One is in tlie ^orm of a square and the other is 4 times as long as ,t is wide, ^ind the difference m the cost of fencing them at 45 cents per rod. 18 How many square feet in the u])pc..r surface of a board 16 ft. long and 6 m. wide at one end and 14 in. wide at the other ? 19. A field containing 8 acres is 5 times as long as it is wide. i:*ind Its perimeter in yards. 20. Find the cost of paving a road of the uniform breadth of 4 yards around the inside of a rectangular 2-acre lot. 20 rods wide at 24 cents a square yard. ' 21 A rectangular piece of ground is 60 yards long and con- tains J of an acre. It contains a grass plot bordered by a walk b It. wide. Find the area of the plot. 22 A square space containing 256 square yards is to be length- ened by 4 ft. 3 in. in one of its dimensions and shortened by 3 ft 4 in. m the other. What will then be its area ? 23' Find the dimensions of a rectangle containing 1,014 sq ft If Its length is to its width as 2 is to 3. "' 24. An electric light is 18 ft. above the ground. What will be the length of the shadow of a man 6 ft. in height if he stands lb It. from the post on which the light is placed ? 25. A rectangular garden 2^ chains wide contains | of an acre. How many feet long is it ? 26. A rectangular field is 40 rods in length and 30 yards in width. Find in feet the side of a square of equal area. 27. Find the difference between the perimeter of a square field contaming 22^ acres and the perimeter of a rectangular field of equal area, the length of the latter being IJ times its width. 28. A board is 8 in. broad ; what length of board must bt cut off to make 1 square yard of surface (on one side) ? _ 29. The perimeters of a rectangle and a square are each 40 m. Find the difference in their areas, if the sides of the rectangle are in the ratio of 1 to 3. 30. The rent of a square field at $12 an acre is $132.24. Find the cost of putting a fence around it at 35 cents a yard. ;i 128 PRACTICAL MENSURATION 1 ;i ■ih 31. At 10 cents a square foot what will it cost to lay sod on a triangular yard whose sides are 8, 15. and 17 ft. respectively ? 32. The sides of an iron plate are 20. 21. and 29 ft. respectively. VVhat IS It worth at $2.70 a sq. yd. ? ^ 33. The hypotenuse of a right-angled triangle is 50 ft. and he base is 40 ft. What is (a) the perpendicular (b) the area of the triangle ? 34. A ladder 17 feet long was placed so as to just reach the top of a building 15 ft. high. How far from the base of the building was the ladder placed ? ^ 35. A triangular sail whose edges are, respectively. 33 56 Wh ?Jl'\r^ T"^' ""^ '^"''^' *^^' ^°^t ^ ^^"ts a square yard.' What did the sail cost ? 36. What is the distance diagonally across a floor that is 40 ft long and 30 ft. wide ? 37' Two upright poles are respectively 57 ft. and 82 ft. high If the poles are 60 ft. apart, what must be the length of a line that reaches from the top of one to the top of the other ? altitude 6a 9^^'"' °^ ^ ^"'"^'' '"^'''" ^""" '" ^^ ^*- ^ ^"^ ""^ i. rf;«T'' !! ^^' 'T °^ ^ t"^"g"J^^ piece of land whose base IS 15.48 ch. and altitude 9.67 ch. at $60 an acre ? 40. At 40 cents a square yard find the cost of paving a triangular court, its base being i05 ft. and its altitude 21 yds .41. The base of a triangular field, containing 1 acre is 90* yards in length. What is the altitude ? * Finf/h^^" ''^'^°^^ ^"^"^'' ^'^ ^^' ^^' ^"^^ ^5 ft. respectively. Find the perpendicular from the opposite angle on the 14 ft. side. 43. The distance from the centre of the hub of a wheel to the outer edge of the felly is 1 ft. 9 in. How long must the tl^^'p diameier V '' '"" ^'''''''^ ^^" ^^'' °^ ^ ^'''' ^^^* '' ^^s t.- K^' ^l""^;. '"" '"1'^''' *^'' ^'"^^ °^ *^^ Sre^^^'t square stick of timber which can be cut from a tree whose circumference is 9 it *> m. r 46. The radius of a circle is 2 ft. Find the wholr. nprima-.r of Its semicircle. "" x— -i-.v.. 01 htoi! 3 lay sod on es]jcctively ? respectively. 50 ft. and the area of it reach th( the building ?ly, 33, 56, quare yard. tiat is 40 ft. 32 ft. high. h of a line ? . 6 in. and -vhose base paving a 1 yds. :re, is 90J spectively. 14 ft. side, leel to the e tire be ? ^'hat is its ^ stick of ce is 9 it. rimeter of radi MISCELI.ANEOUa 47. rhe whole perimeter of a semicircle 129 is 90 in. Find its 48. What is the diameter of a wheel .;„,„ ., - - ""^^' which turns around 1,000 times m gomg a mile ? ' 49. The difference between the diameter and the circumference of a circle is 12 ft. Find its area. ^uimerence 50. A cow is tethered to a post driven in the centre of a lot 00 ft. square ; the tether is just long enough for her to reach the fence. How much of the surface of the lot is she unable to 51. The diameter of a carriage wheel is 24^ in. Find how many turns the wheel makes in going one mile. ' 52. Find the cost of paving a 10^ ft. drive around the outside of a circular plot 28 yards in diameter, at 65 cents a square yard. 53. Find the difference in feet between the perimeters of a circular and a square fi,>ld. if each contains 2 acres. 54. Find the area of a uniform walk 2 yards wide around a circular pond which contains 15f acres. 55- Find the width of a circular path containing 120 square yards which surrounds a circular pond whose circumference is 220 yards. 56. The radius of the outer boundary of a ring is 14 in and Its area is 462 sq. in. Find the circumference of the inner boundary. 57. A circular pond, which is 4 miles in diameter, has a driveway around it. A man wishing to reach a point directly across the pond from where he stands can drive at the rate of ten miles an hour and row at the rate of 6 miles an hour. How many minutes can he save by going the quicker way ? 58. The radius of a circle is 8 feet. Find the circumference of another circle of | the area. 59. Find the side of a square which is equal in area to a circle whose circumference is 55 inches. 60. How many cubic yards will a box hold if it is 10 ft 6 in long, 4 ft. wide, and 2 ft. 4 in. deep ? 130 PRACTICAL MENSURATION 6i. The ice on a pond, whose area is J an acre, is 10 inches ; 1^1. ^KiT thick. How many tons of ice may be taken from the pond 11 supposing a cubic foot of ice to weigh 56 pounds 62. How many bricks 8 in. long, 4 in. wide, and 2 in. thick can be packed in a box 4 ft. 6 in. long, 3 ft. wide, and 2 feet deep ? 63. A room contains 1,536 cu. ft. of space. If it is 16 ft. long and 12 ft. wide, how high is it ? 64. Rain falling uniformly for 5 hours on a roof, whose horizon- tal dimensions are 10 yds. by 15 ft., fills a tank 6 ft. 3 in. by 3 ft. by 2 ft. 6 in. Find the depth of the rainfall per hour. 63. The side of a square field is 48 rods. Find the length of the side of a square field containing two and a quarter times as much land. 66. A lot 96 ft. long and 60 ft. wide is filled with cordwood piled to a height of 6 ft. How many cords are there in the yard ? 67. A farmer owes a merchant $105. They agree to pay it in cordwood at $5.00 a cord. The yard in which the wood is to be piled is 28 ft. long and 16 ft. wide. How high must the wood be piled so that there may be enough to pay the debt ? 68. If a cubic foot of water weighs 1,000 ozs., and a gallon of water weighs 10 lbs., how many gallons will be required to fill a rectangular tank 12 ft long, 4 ft. wide, and 4 ft. deep ? 69. Find the number of acres in a triangular field whose sides are 1,056 yards, 1,980 yards, and 2,244 yards. 70. One blackboard in a school is 4 ft. wide and 16 ft. long, the other is 3^ ft. wide and 24 ft. long. How many feet must I cut off the length of the larger blackboard so that the remainder will have the same area as the smaller one ? 71. Find the cost of gilding the entire outside surface of a covered box, 3 ft. long, 2 ft. 6 in. wide, and 1 ft. 9 in. deep, at $1.20 per square foot. 72. Find the length of the diagonal of a square field containing dO Ecres. i-^A MISCELLANEOUS 131 ' 10 inches the pond 2 in. thick feet deep ? 16 ft. long 36 horizon- :n. by 3 ft. : length of r times as cordwood the yard ? ) pay it in d is to be 3 wood be [ a gallon quired to hose sides I ft. long, it must I •emainder face of a deep, at ontaining 73. To drain a swamp in Dereham, the Township Council had a ditch dug 1 mile long, 3 ft. deep, 6 ft. wide at the surface, and 4 ft.. wide at the bottom. Find the total cost at 9 cents per cubic yard. 74. How many miles must be travelled by a team in ploughing lengthwise a piece of land 60 rods long and 40 rods wide, if each furrow is 10 in. wide ? 75. The Manufacturers and Liberal Arts Building of the Columbian Fair was in the form of a rectangle and covered an area of 30 acres, 76 sq. rds., 19 sq. yds., 7 sq. ft. The building was 787 feet long. How many feet in length was it ? 76. A load of wood 10 ft. long, 3 ft. 8 in. wide, and 3 ft. high, was sold for $3. {a) What was the price per cord ? (b) At $4 per cord what would the load be worth ? 77. How much will it cost to paint the outside and both floors of a two-storey cottage, 36 ft. long, 33 ft. wide, and 18 ft. high, at 10 cents per square yard, the walls to be 18 in. thick and no allowance to be made for cornices, openings, or partitions ? 78. A gravel-bed whose surface has an area of 4 acres con- tains gravel to an average depth of 6 ft. How many miles of road 11 ft. wide can be covered from the gravel in the bed if it be spread on to a uniform depth of 8 inches ? 79. A cord of wood and one hundred bushels of grain fill equal spaces. A cubic bin whose edge is 12 ft. contains 45,900 lbs. of grain. Find the weight of one bushel of this grain. 80. Find the expense of sodding a plot of ground, which is 40 yards long and 100 ft. wide, with sods each a yard in length and a foot in width, the sods, when laid, costing 75 cents per hundred. 81. The whole surface of a rectangular solid is 1,000 sq. in. ; if its length and breadth are respectively 1 ft. 3 in. and 1 ft. 2 in., find its height. 82. A box is made of plank 2 inches thick and without a lid, Its outside measurements are : depth, 16 in. ; width, 18 in. ; and length, 24 inches. How much will it cost to have it painted, inside and outside, at 9 cents per square foot ? VII— I t i| I ■M\ ft i^^ 132 PRACTICAL MENSURATION 83. How many gallons will a can hold if it is 22 in. in diameter and 3 ft. high ? 84. What is the volume of a triangular prism whose length is 12 ft. and one of the equal sides of its equilateral ends is 3 ft. ? 85. Find the number of cords of wood in a cylindrical stick of timber, the length being 40 ft. and the circumference 22 ft. 86. A garden roller is 3 ft. 7J in. wide and 5 ft. lOf in. in cir- cumference. How much ground does it pass over in making three complete revolutions ? 87. A sphere 8 in. in diameter is placed in a cubical box whose interior dimensions are 8 in. How much water will the box then hold? 88. I have a cyHndrical tank which contains 160 gallons. It is 6 ft. 5 in. in diameter. How deep is it ? 89. How many square inches of surface are there in a stove pipe 22 in. in circumference and 12 ft. long ? 90. How many square yards of canvas will be required to make a conical tent 9 ft. high and having a base of 4 ft. radius, no allowance being made for seams ? 91. A conical tin vessel has a lid ; the diameter of the lid is 24 in. and the depth of the vessel is 18 in. How many square feet of tin does the whole surface present ? 92. How many gallons of water would the vessel in the preceding question hold ? 93. Find the weight of gunpowder required to fill a hollow sphere 9 in. in diameter, supposing that 30 cu. in. of gunpowder weigh one pound ? 94. A locomotive, running at the rate of 35 miles per hour, has a driving wheel which makes 4 revolutions in one second.' Find the diamc ter of the wheel. 95. The driving wheel of a locomotive, of diameter 7 ft., makes li revolutions in 1 second. Find the rate of the locomotive in miles per hour. 96. How many pieces of money, f of an inch in diameter and i of an inch thick, can be coined from material in the form of 3 cube whose edge is 3 inches ? * I diameter ise length is 3 ft. ? ical stick 12 it in. in cir- :ing three ox whose box then gallons. I a stove [uired to :. radius, MISCELLANBOUS 133 97. The height of a cylinder is to the diameter of its base as 3 . 2 ; If Its volume is 320 cubic inches, find its height heift'uin^''i' 1^^'^V ^"- ^' '^"^ ^" "^'""^^ '- ^ <^o-e of height 14 m. Pmd the radius of the base of the cone wate?' ^.f!^^7^/^^"' ^"^^^"-1 diameter 14 in., is filled with water. Its contents are poured into a cj^lindrical vessel whose 10 fL^T r ^".' *'^ '^P*' °'*^^ -*- - ^he cylinder! is 'of; ^^"j* *^V°^""^^ ^"d the area of a cone whose slant height IS xO in. and the diameter of whose base is 6 in loi What will it cost to gild a ball 12 inches in diameter at 10 cents a square inch ? 102. Find the number of cubic feet in a log 30 ft. long and 2 ft. in diameter at the larger and 1 ft. 10 in. at the smaller end. 1 il\ A^'"''^ '^'" '' ® ^"- '"^ ^^^•'"^^^^ ^"d its thickness is 1 m. i<= i^ ^"'idered 5 in wide ; while a board 4} in. wide is considered 4 in. wide meiu™ " """"' '°" '' ^° ""'" ' '""--d feet, toard To find the number of board feet or feet of lumber in a board ^recto. '' """ " """'' f-^'" '^ ''P'''''^ '" ^a^h lOfMoTT""-"?'"'' "" "'""'^^ °' '»^^d fe^t in a plank 10 ft. long, 15 in. wide, and 3 in. thick. Solution 1 ^^Jo the number of board feet in the plank = 10 x U x 3= 37J board Solution 2 _^ont£nts_ofplanlt ContentTof board foot 10Jft)j< 15 (in.) X 3 (in.) 1 (ft.) xn[2irnoirr(i5T "" ^ ^^- ^^ and y ''. ft, and two $1.80 per single 12 ft. high from nts a roll, and long by 16 ft. •oards, allowing J each 3 ft. 6 in. loard foot. It d inch lumber t greater than a fraction less is considered : in. wide, d feet, board er in a board, 3 representing Jated in each - in a plank so the unit is 12 inches wide, ck, so the unit 3 = 37J board 2n\ bd. ft. ' LUMBER 139 Short Method Midlipiy the length in feet by the width and thickness in inches and divide the prodnct by 12, and the result will be the number of board feet of lumber. In charging, or billing lumber, the number of pieces are entered first then the thickness and width in inches, then the feet in length. For example' in recording 6 pieces, 4 in. thick by 6 in. wide and 20 ft. long the form would be thus : 6 pes. 4 in. x 6 in. - 20 ft., and would be called off by the salesman, &fom.by.sixes- 20 ft.." four-bysixes being the name by which he selects and sells stock. Instead of writing " inches " and " feet," lumber billing clerks use (') tTP-\i^^ <'^ ^°^ ^'^^- *^"^' 3 i"- by 4 in.-17 ft. long, is written, When the width of a board tapers uniformly, the average width is found by findmg one-half the sum of the two ends, SERIES 52 1. How many feet of lumber in a floor 15 ft. long, 12 ft wide and 1 in. thick } 2. A bridge 84 ft. long and 20 ft. wide, is covered with oak plank 2^ m. thick. What is it worth at $16 per thousand ? 3. Ho.v much lumber 1 in. thick will be required to cover a walk 5 ft. wide around the outside of a lawn 300 yards long and 200 yards wide ? ^ o 4. What is the number of board feet in a stick of timber 33 ft. long and 18 in. square ? 5. A 2 in. plank, 9 in. wide at one end and 15 in. wide at the other, tapers gradually. How much lumber is there in it the length being 18 ft. ? 6. At $20 per thousand, find the whole cost of 5 scantling 20 ft. long, 4 in. wide, 3 in. thick ; 9 scantling 18 ft. long, 5 in. wide, 4 m. thick ; 6 scanthng 14 ft. long, 6 in. wide, 5 in. thick. 7. At $32.50 per thousand, what will be the cost of 8 scantlings 3" x 4"— 18' ; 12 scantlings V x 5"— 16' j 8 scantlings 5" x 6"— 14'. 8. At $19.50 per thousand, what will be the total cost of 9 boards 1" x 2"— 14' ; 6 boards IJ" x 18"— 16' ; \5 boards 2" x 14"— 20' ; 8 boards 1^" x 12"— 18'.' 140 PRACTICAL MEASUREMENTS ■ 1 9. At S24 per thousand, what will be the cost of the lumber required to inclose a field 40 rods square with a board fence if the boards are 15 ft. long, 5 in. wide, and I in. thick, and the fence five boards high ? 10. At $21.50 per thousand, what will be the cost of the lumber in a line fence 160 rods long, if the boards are 11 ft. long, 7 in. wide, and 1 in. thick, and the fence four boards high ? 11. What will it cost to fence 10 miles of railway, both sides, with six rounds of 6 in. boards at $15 per thousand feet ? 12. What will it cost, at $16 per thousand, to fence a field 40 rods by 60 rods with one round of 12 in. boards and five of 6 in. boards ? 13. What will be the cost per mile to ^ence a railway with six strands of barbed wire, which weighs 1 lb. per rod, at 8 cents a pound ? 14. Find the cost of a quarter- mile of fence, with the posts 8 ft. apart, a 12 in. base, a 2 x 4 rail at top, and five rows of 6 in. boards. The posts cost 10 cents each, and the .umber $12 per thousand. 15. If lumber is $20 per thousand, find the cost of the boards and scantling required for a sidewalk 54 ft. long and 4 ft. wide. The boards are 1 in. thick, and are laid on two rows of scantling 2 in. X 4 in. 16. A contractor undertakes to lay a sidewalk 8 ft. wide, on both sides of a street one-eighth of a mile in length. The plank used is to be 2 in. thick, and the walk is to be supported by three continuous hnes of scantling 4 in. square. Determine the cost of the lumber at $15 per thousand feet board measure. 17. A lot, 60 feet wide and 120 feet long, is to be enclosed on the two sides and the back by a tight board fence 6 ft. high. The posts are to be placed 6 ft. apart, and to cost 15 cents each. There are to be two string pieces of scantling, 2 in. thick and 4 in. wide, from post to post, on which to nail the boards. Lumber is $15 per 1,000 ft. (a) Find the cost of the posts. (b) Find the cost of the boards. (c) Find the cost of the scantlings. ROQ£INa 141 of the lumber )oarcl fence if and the fence of the hmiber ft. long, 7 in. /, both sides, 3et ? fence a field 5 and five of raiivvay with )d, at 8 cents th the posts rows of 6 in. iber $12 per )f the boards d 4 ft. wide. of scantling ft. wide, on The plank ted by three 2 the cost of be enclosed e 6 ft. high. > cents each. ick and 4 in. xmber is $15 m.H^^'.'^ certain sidewalk is 250 yards long, 10 ft. wide, and made of plank 2 m. thick. The planks rest on three contiiuous atXerotLr-- ^ ^ '"• -- - - of the .atenal 20. Find the cost of 720 boards, 14 ft. long, 8 in. wide and H m. thick, at $12 per thousand feet. * 21. At $15 per thousand, board measure, what wUl be fh^ cost of 2 in. plank for a 4 ft. sidewalk, half a mile long ? for 1% H ^^A ^'n ^^""f""^' ""^'^^ ^^" ^ *^^ ^°^t «f 2 in. plank for a 3 ft. sidewalk on the s.reet sides of a rectangular corner lot 55 ft. wide and 108 ft. 8 m. long ? boa"'' ''"''' "' ' "• P^'"'' '^ ^"- "^^^' -" ^-"t-n 48 40 botd'^eel ?' ''' "^''' '' ' ' "' ^^^"'' ^' '^^ ^°"^' ^^'^^^'^ --^-- 26. What is the thickness of a piece of timber. 40 ft lone and i.o in. wide, that contains 400 ft. of lumber ? ' 27. What will be one-half of the cost of r. line fence 40 rods long ho fr.% 7'f *' '' P^^'^^ '^ '^- '-^rart at a cost of $16 p r thousand for lumber and $25 per hundred for posts ? 28. At $18 per thousand for lumber and $22 per hundred a lot 40 X 160 ft. with a picket fence, the oickets being 4 ft. lone 3 m. wideband 1 in. thick, aUowing 3 in. space between picket!' thepostsbeirgplaced8ft. apart, two2 x 4's being used as stringe' and a baseboard 10 in. wide extending below th ' pickets ? ROOFING The unit in measuring for flooring or roofing is the square. A square contains 100 square feet. Shingles are 16 m. long, and average 4 in. in width. They are generally laid 4 in. to the weather. Hence each shingle wl 142 Ptt.\CTICAL MEASUHEMENTS cover 16 square inches, and 9 will be required for each square loot, or 900 for each square of roofing. Allowing for waste, 1,000 shingles, laid 4 in. to the weather, are estimated to cover a square. Shingles are sold by the bunch, each bunch containing 250 shingles ; hence four bunches are required for a square of roofing. Dealers will not sell part of a bunch. i SERIES 53 1. Making no allowance for waste, how many shingles, laid 4J in. to the weather, will be required for a square of rooting ? 2. M king no allowance for waste, how many shingles, laid 5 in. to the weather, will be required for a square of roofing? 3. How many squares of roofing are there in a double roof, 45 ft. long, with 20 ft. rafters ? 4. At SIO per square, what will be the cost of the slate for a double roof 45 ft. long and 28 ft. wide ? 5. How many bunches of shingles are required for a shed roof 40 ft. long and 3 ft. wide ? 6. How many bunches of shingles are required for a double roof, 70 ft. long, with 30 ft. rafters ? 7. Find the cost, at $4.50 per thousand, o' the shingles necessary for a double roof, 56 ft. lorg, with rafters 25 ft. long. 8. Find the cost, at $4.20 per th..usand, of the shingles for the roof of a building, 52 ft. 8 in. long and 32 ft. wide, having a gable 12 ft. high and the rafters having an 18 in. heel. 9. A building, 64 ft. long and 36 ft. wide, has a gable 14 ft. high. In roofing the building the rafters were given an 18 in. heel. Find {a) The number of bunches of shingles required for the roof. (b) The value of the sheeting, at $16 per thousand. (c) The value, at $23 per thousand, of the rafters, if they are 2 in. X 4 in., and are 2 ft. from centre to centre. t-VTillNQ AND PLASTERING 143 square /oot, ic weatlier, taining 250 of roofing. ingles, laid ofing ? ingles, laid ofing? iouble roof, le slate for for a shed >r a double 16 shingles ft. long. gles for the ing a gable fable 14 ft. an 18 in. )r the roof. d. if they are itre. 10. How many shingles. 18 in. long and 4 in. wide, lying one- third to the weather, are required to shingle a double roof 54 ft long, with rafters 22 ft. long, the first row of shingles being double and no allowance being made for waste ? LATHING AND PLASTERING Standard laths are 4 ft. long, 1^ in. wide, and are laid i in. apart. 1,000 laths of standard size will, therefore, cover about 74 square yards. Allowing for waste, however. 1,000 laths are estimated to cover 70 square yards. Laths are put up in bundles of 100 and 50. So a bundle of 100 IS estimated to cover 7 square yards, and a bundle of 50 to cover SJ square yards. But all laths are not of standard size. Some are only 32 in long and some are only IJ in. wide. In reckoning the amount of laths required, calculate the superficial area to be lathed, and deduct the area of all openings In reckoning the cost of laboi lor lathing and plastering it IS customary to deduct only one-half the area of the openings • but there is no set rule to this effect, and it is well to have a distinct understanding with the contractor on this point before the job is commenced. SERIES 54 1. How many bundles of 100 standard laths are required m.! !•"?"' ^""^ ""^"^"^ ""^ ^ '"^'^ 27 ft. long, 18 ft. wide, and aJ u f: containing two doors 7 ft. by 4 ft., and four windows b It. by 4 ft. ? 2. In the preceding quebtion, had the lath been 32 in. lone and put up in bundles of 50 each, how many bundles would have been required ? 3. Making no allowance for waste, how many square yards would ir^OO laths, 32 in. long and IJ in. wide! cover Jl^^ three-eighths of an inch apart ? 4. Find the cost of plastering a room 30 ft. long, 27 ft wide Tu a ■ ■"■ u^ T " ''^''^'^ y**'"^' '* ^^^^^ a^e twD doors each a> It. b in. by 7 ft., and three windows each 3 ft. 4 in. by 6 ft., and mi c 144 PRACTICAL MEASUBBMBNTS the plasterer be allowed pay for one-half the area of the openings for his trouble in plastering around them. 5. A room, 16 ft. long, 14 ft. 6 in. wide, and 10 ft. high, has a skirtmg board 1 ft. high, two doors 7 ft. by 3 ft. 10 in., and two windows 6 ft. by 4 ft. Find the number of bundles of 50 standard laths required to lath it. 6. Find the cost, at 22 cents a square yard, of plastering the wails of a room 23 ft. 6 in. long, 15 ft. wide, and 8 ft. 4 in. high, navmg one door 7 ft. 6 in. by 3 ft. 8 in., three windows 6 ft. 9 in.' by 4 ft. 2 in., and a skirting board 11 in. high, allowing one-half the area of the openings. 7. Find the cost, at 22 cents a square yard, of plastering a room 18 ft. long, 15 ft. 6 in. wide, and 10 ft. 4 in. high, containing two doors 7 ft. 4 in. by 4 ft., two windows 6 ft. by 3 ft. 10 in., one mantel-piece 5 ft. by 3 ft. 6 in., and a 10 in. baseboard (deduct one half the area of the openings). BRICK AND STONE WORK It may be stated at the outset that no set rule can be given for the calculation of either the amount of material required or the amount to be expended in labor in either of these cases. Bricks are of varying dimensions. They are laid according to specifica- tions in varying thicknesses of mortar, and the judgment of the contractor, in facing the particular conditions, so often modifies even his own general plan of figuring, that it would be absurd to say that if certain methods of calculation are followed, we will get results as contractors in Canada or any other place would estimate them. What is true of brick work is just as true of stone work. There are many kinds of stone work and many places where the judg- ment of the contractor is brought into play. The best that we can hope to do in a work of this character is to lay down certain general rules, which at least have the sanction of good authority, in the hope that the student who learns to apply his ability under these rules will have no difficulty in making calculations, no matter what changes he may be told to make, according to the part of the \ \ t I! th In th; th( wa le openings high, has a ., and two standard Jtering the 4 in. high, 6 ft. 9 in. g one-half astering a containing 10 in., one d (deduct BIUCK AKD aTUJN'E WOliK 145 be given ed or the . Bricks specifica- nt of the modifies ibsurd to 3 will get estimate . There he judg- t we can I general ^ in the ler these ter what t of the Stone Work 25 cu. ft. are figged al a ptch iT "'""»' ^** "°' "• '" «"i«-a«„g ,ua,,^a„.s Las j.r td ™ rr,r^^^^^^^^^^ measurement is concerned with the AfrunZTT quarryman's be used. The mason's measurement I '^"^"*'*^ °* "^^^^^^l *<> amount of work to be do^ and ^^ . '°°'''"^^ ^^*^ ^^^ng the In measuring for xnateriaT^^^^^^^ consequent price to be paid for it. That is. all opening ar k n o^ aTd^luT'"'^ °' *'^ "^" ''' "^— ^• buying the stone, ft may be bouSt bt th. rT','''t "'"'"'"^^ ^'°^'^- ^^ sions as a cord of wood namdv 8 fX A ^ "'^ ^' °* *^^ ^^""^ di^e"^- estimated that 4 perches' or 100 ^ ft of "^ V n' 1 ''" ^"^ ''" ^"- ^^^ '' '« "t ::t;:::s£r ^^ "-• -- -- s^^ ^°" " ^^°"^' °"^ -at .:r ^r::s=er :;r i^it rx-- r r-^^ ^--^• for openmgs l.s than 3 by 5 ft., and only half ^ta^t " T;en::;:C Brick Work the w?„M:"^3TJL^e:'™L'T' > ""*°''^- ^" '°*°-- '"- "= wall. There « the 9 i„ch w^ Cl^ " '""'"""^ '"""■ "" ''^"■W* "all. There is the L-i^h ™U ™ l'rT''r """"' "« '"'^' >'"'<^ wan or the double brie, the 2™ Lh waS or" he St'o^ J'"' '"= '*""■ to the thickness of the wall T„ * ''''■ ^""^ ^° °° according no exact rule for the vo W of ^arh'T"" u """'"°^ '"^ '''' °^ bricks! is. therefore, a fail average" '" '^ ''"^"- ^'^ ^°"°-"g --«« 7 bricks to the superficial foot in 4-inch wall. 14 bricks to the superficial foot in 9-inch waU. 21 bricks to the superficial foot in 13-inch wall. It W? T T '"P''^''"^ '°°* ^" '«-i"<=h wall. If fh u lu *° "'" superficial foot in 22-inch wall ^<^::^:^^l^;i::J:^- - -- — al 4, inches in than 2 feet square To^ V ^"'^t^^^'-y *« deduct for opening, less the walls, frortheJVeLTremenr^^^^^^ '" f"^'^^ *'^ ^"P^^'-' -- ° wall and then multiply iy The 1^." ' '™" ''^ ''^^'°^^^ °* *^« 146 PRACTICAL MEASUREMENTS ]l:> i SERIES 55 1. How many cords of stone will be required for the founda- tions of a house 39 ft. by 27 ft., the stonework to be 6 ft. high and 18 in. thick ? ^ 2. In the preceding question, for how many cubic yards would the masons be paid ? 3. How many cords of stone are required for the walls of a house 40 ft. long, 27 ft. wide, and 20 ft. high, the wall to be 1 ft. thick If It is to have four doors 7 ft. 6 in. by 4 ft., and eight windows 5 ft. by 4 ft. ? 4. In the preceding question, for how many cubic yards will the men who do the work be paid ? 5. A house is to be built 35 ft. long, 28 ft. wide, and 22 ft. high, and IS to have ten windows 4| ft. by 6 ft., and five doors 8 ft. by 4 ft. 6 in., the wall to be 9 in. thick. How many bricks will be required ? 6. If the wall in the preceding question were made 13 in. thick, how many bricks would be required ? If ' I 'I PERCENTAGE TERMS USED IN PERCENTAGE CALCULATIONS. The Prime Cost of an article is the first cost. The Gross Cost is the prime cost plus charges of freight, dra yage etc. ' The Selling Price is the price for which an article is sold. The Profit or Gain is the amount by which the sell, .g price exceeds the gross c( t. The Loss .,. amount by which the gross cost exceeds the sellmg price. A Trade Discount is an allowance or deduction made by a dealer or manufacturer from catalogue or list prices. An Agent is one who acts under authority for another. The Principal is the one for whom an agent acts. A Commission Agent is one who buys and sells goods or property, or collects money for his principal. A Broker is an agent who effects purchases or sales in the interests of a buyer or seller. He brings the buyer and seller together, as it were, and is chiefly engaged in the case of stock transactions. Commission is the name applied to the commission agent's charge. ® Brokerage is the name applied to the broker's charge. A Consignment is the property received by a commission agent to be sold for a principal. The Consignor is the person who ships the goods. The Consignee is the commission agent who receives the goods to be sold. A Del Credere Agent is one who guarantees to his principal the payment of sales made on time. 148 PERCENTAGE on tT^ '' "-^ "• -^^^ -'^^ 'or guaranteeing sales ™ade , ■ ded^^:r "'"^ '^ "''^' ^^-^^ ^«- ^" charges have been t.^ether wi.h^he to.a7fn,:™t1,r;„Se' ""' ""^ ^''^^«-' Of rais.„g relue and^pro^ hlT ^ J:!;™' "" *= '^"''- of .he"g''llt"'' '^ " ""^™ P^"™'^^' °' '"c -'-' COS. yard' s^™:o':"i:;:snr™ai: t- ^™ - '-■ both kinds of duties are levS "P°" '='='■'="" e^^s thelmt'' " ' "^' °' ^°°<'^' ^'^ «>^ -'- of duties imposed on The Free List includes goods that are exempt from duty on tof ;r' er^I^L^rr^Thr '"r™™' *""'-<' Great Britain or Briti-h ' "'™"- ^''^- eo°ds imported from in Canada '^'"''''""'' "^ «'^cn a preferential duty from ctS: corntriS "tuV"^" *=• ™^™™' ™P-d <>" Soods subjeet to surtax? ' ^"""^ "''""'^<' '■■<"" Germany are »at,r:S4oVt;^r£ntii re-:^'~^ ^' TERMS USED IN PEftCENTAGE CALCULATIONS l4d Insurance is a contract in which one party to che contract agrees for a certain consideration to make up loss which another party may sustain. It is distinguished as Property Insurance Life Insurance, Accident Insurance, and Health Insurance. The Policy is the name applied to the written form of the WeT ^^^^ ^^*'^'^" *^'^ insurance company and the party A Valued or Closed Policy is one in which the amount insured IS definitely determined when the insurance is effected. Houses and furniture are insured in this way. An Open Policy is one upon which additional insurance may be entered at any time. , ' The Premium is the amount paid for the insurance. Adjustment of Fire Insurance Losses.-Under the ordinary lorm of policy, the insurance company undertakes to pay the full amount of the loss or damage, provided such loss does not exceed the sum mentioned in the policy. The policy, however may contam an average clause, in which case the payment made IS such proportion of the loss as the amount of the insurance bears to the total value of the property. Again, the policy may contain a co-msurance clause." As an example, we quote the following 80% co-msurance clause ; ° the "rll 'Itr^^^^ ^^^ consideration of this policy, and the basis upon which lu^ nfin forw^^h".?'"' f^' *'^ ^"^'^"'^ •^'^^^ "'^-*-" '---- con- hrebv in.nrpH . 1 " P°"'^' ^'^ '^^^ ^"^ ^^^'^ ^^em of the property vl u^thereof .nH .. Vf 'r' °' '* ''''' ''^""'^ ^'^ ^^t" °^ ^he actual cash th extent o'n^ that fa.hng so to do, the insured shall be a co-insurer to in^fr^t!* ^ T '■''"' °' P"™'™ '^'""■Sed when the term of insurance is less than a year 150 'U lit ! t I ' j" ''i k PERCENTAGE Marine Insurance refers to insurance of vessels and thp.v . against the dangers of navigation. '^'^'**' Adjustment of Marine Insurance Losses ^urh i usuallv spttlpH K,7 +K^ • ^"'««'*-e J-osses.— buch losses are Taxes are sums collected by a municipality for the pavm^nt of mumcipal indebtedness. The tax is a sum assessed ^"1 the person, property, or income of an individual. citiat'i^bllTor ""T ^"""J' *'' ^"" ^°"^^*^^' ^^-- -^h male citizen liable to taxation without regard to property or income IS exempt, and above that it is liable to taxation. Interest is the use of money. or u!e of'^whl^ri" the money which is loaned, and for the mterest, or use of which, a certain sum in cash has to be paid. The Amount is the sum of the principal plus the interest. ' A Joint Stock Company is an association of individuals who Canfdf if,°' I""n>orat.».-J„int stock companies are formed in Canada m two ways: (a) By special Act of Parliament, either of the Parliament of Canada or the Legislature of the ProXe m wh,ch busmess is to be conducted ; m by the letter, pa en. i^ed onder the Companies Act. In some of th. Province- r---, takes the place of letters patent. "' >-<=S-lrar,on their cargoes I losses are ly such pro- value of the id in saving lie payment id either on I each male income, 1 is assessed I according the income le interest, est. iuals who t business formed in nt, either Province :nt issued jistration TERMS USED IN PEBCENTAaE CALCULATIONS 151 company. '"^"^' ^ Jomt stock share is worth^foo '""'^'^ ™""°"=<' "> '"e contrary, a charte!^,:Sic?™enlnVtt° '^ *rt^ ""^^ "P™ " "y the .e ..her o, sha^r^h- h 7^ t^:^^^^^^ $90 or for $150. This is .11 ! . . ^c ^^'^ "^^^ ^^" ^^^ company ana the wr;r:^:'HL^s:'- si:;;: r^'"^ °' *^ hastugh'stStd t^ir i"*^' '' ' ""■P^"^ '» 0- "h" the holder is entitkd *' ™'"''^'' "' ^"^^^ '" ""W* any''"/'"'!;' 'tos ?t '^ ^"'"'^^ '° ^ ?«'"»« over ofapriordaimonKain?LTe "?"^ '^''^^ ">^ ^^'I- extend in any olr'X: ^ ^hTa t' Mo'l' "r " ""^ number of the board of director ^ "'" " "'^'"^ Common Stock is the ordinary stock of th. „ to any preference. company not entitled 152 in,! I PERCENTAGE Cumulative Preferred Stock is stock which is preferred in the matter of d.v.dends, and which, further, is entitled to have dt denl which are not pa:d in one year cumulate as a charge a^ns^^rofit in succeeding years. Thus, if the stock were a So/preference 1^^ It means that each year 50/, dividend is to be pdd' K the 50/ t not forthcoming the first year, the dividend to be paid the second year would really be IQo/,. if not paid in the first or t ond Z the dividend for the third year would really be I50/, ' ' set Sde'^vtrV' 'r'^ " P^'* °' *^^ P^^^t^ °'f th« ^omjany set aside by the directors as the amount to be divided amon' the shareholders as a return for the money that they investT^'The div^^e^nd mu^ not be paid unless there is a net 'gain from''which An Assessment is the opposite of a dividend, and is the amount contributed by the shareholders to meet losses or expenses Tthe company It will be noted that once a shareholder has paM fo his stock, he cannot be forced to pay any additional amounts The assessment is, therefore, a voluntary contribution. fhn^ ^f u f." ''''^'' *''"'^ ^y *h' ^°^^d °f directors requesting ertain am f " "'V""^ "°^ ^""^ ^^'^ ^^ ^^- ^^-^ t'o pay a certain amount on such stock. "^ An Instalment is the amount paid m answer to a call. excetd^T pa"; valul ^"^°""' '' ^'^^' ''' "^^^^^* ^^^ °^ ^^-^ than^^T^:ai;:.'^ ^"°^"* '^ ^^^^^ *^^ --^^^ -^- ^^ i- A Bond or Debenture is a written promise to pay a sum of money, with a fixed rate of interest, at or before a s'pedfied tTme ,^nt sto'k ""' ' ''' P"™"°^y "°^^^ '' corporatLs, such ^ joint stock companies, cities, towns, villages, etc. First Mortgage Bonds are bonds which are secured by a first mortgage on the property of the corporation issuing the bonds. In the same way we may have Second Mortgage Bonds rred in the '■e dividends linst profits rence stock : the 5% is the second jcond year, i comj-any amon^ the sted. The rom which lie amount ises of the s paid for mts. The •equesting : to pay a ; of stock Je is less I sum of ied time. such as y a first nds. In BASIS OP CALCULATION 153 Registered Bonds are those issunrl to name is registered in the books of tt "" ''"^'" P'''^"" ^^^^^^ such bonds. The interest wmt ^ ^""^""^ ^^ *^« °^"^r of or his attorney. ""'" ^ ^"^^ ^^'^ ^o the registered owner certmTr ft::^tdir^^^^^^^^ --^-^ - ^etachab. off at the time the interest f^; Z T^^^l"^^^ ^e chpped entitle the holder to the intere";^^^^^^ °" ^^^^ P— ^ed, BASIS OF CALCULATION The term, " Per cent./' usually written 0/ ;, ,, ,, , . . Of -eUt,n words. Per ..... ..^ s^.^^yll^trdrt" forXlettome tt: bu^r" 1 "^ ^^^ ^-- by the hundreds (use o^ mone^t eilmple) '' ^^^"^^^^' °^^^^^ isi^^^^TS:;;;;^ He business done the agent is pa^dTs' '"^''^ ^^^^ ""^'^^ °^ ^%^2rrt":::i-- ^^ - ^^ ..wed only have to pay $95. ^ ^ "" ^^^* ^^ owed he will Insurance.— Property is insurM ,„^ paid. It means that foLverySwnl /'■™'™ °' '% '^ is paid to the insurance compan^ TJ ^'"^"'y »="''d »5 -idn-r^s'tifa?;: ■ issif : ;\;r ,; r f/- -^^-^ '^ «.e^o„e_„ho buys the .jr^lT re^r' "'" ^^^^^ 154 PERCENTAGE Taxes. — A man owns a city lot, and pays a tax rate of 5%. It means that for every SIOO assessed value lie must pay into the city treasury $5 as his contribution to the city expenses. Dividends. — Stock in a certain company yields 5% dividei,-ds. It means that for every $100 worth of st')ck held, a man is entitled to $5 as ..is share of the profits. Duties.— An importer has to pay a duty of 5%. It means that in bringing goods into Canada from some other country the importer must pay to the Canadian Government §5 for every $100 worth of goods imported. Interest. — Money is borrovv^d and interest at the rate of 5% per annum is charged. It means that for every $100 borrowed, $5 must be paid for its use every year. Illustration.— What is 5% of $225 ? $225 Solution.— 5% means 5 per lumdred, or 5 out of every .05 hundred, which is jg 8 or .05. The question becomes a simple one in multiplication of decimals. $11.25 Note.— The circumstance which gives rise to the calculation of the percentage cannot alter the method of finding it. It may be we want to know the interest on $225 at 5%, or we may want to figure the commission on a sale of $225 at 5%, or we may want to find the duty on goods worth $225 at 5%. The process of getting the result is the same for all cases. QUESTIONS OF THE FIRST ASPECT SERIES s6 I. Illustration— What is 36% of $480 ? Solution 100% of it equals $480 1% of it equals $4.80 36% of it equals $4.80 x 36= $172.80 or $480 X .36= $172.80, V 2. What is 24% of 375 yards ? ^3. What is 76% of 793? rate of 5%. ist pay into enses. ^ dividei.'ds. in is entitled . It means country the '<5 for every rate of 5% borrowed, i out of every omes a simple lation of the e we want to le commission 1 goods worth r all cases. QUESTIONS OF THE FIRST ASPECT 155 -- 4. A man, who is worth $75,000, has 35% of his wealth invested in real estate. What is the value of his real estate ? 5. In a certain school there are enrolled 460 pupils, of whom 45% are boys. How many girls are enrolled ? 6. A ranclier, who owned 640 sheep, lost 15% of them in a storm. How many sheep had he remaining ? ^- 7. A merchant bought goods for §458.75, and sold them for 36% more than he paid for them. What did he receive for the goods ? 8. A farmer sold 420 bushels of wheat at $0.97 per bushel, and 20% more oats than wheat at $0.43 per bushel. What did he receive for both. 9. A man invests $17,280 as follows : 25% in real* estate 37 J% in bank stock, and the remainder in city lots. How much did he invest in each ? ID. What will 37i% of 480 bushels of wheat f ost at $1.25 per bushel ? 11. A man, buying a house and lot, paid §1,500 for the lot and 37^% more than that for the house. What did both cost ? 12. A farm contained 320 acres ; 25% of it was sold at §45 per acre, 40% at $37.50 per acre, and the balance at $30 per acre. How much was received for the farm ? 13. A man has a yearly salary of §2,400, and spends 33J% of it the first year, 45% the soeoiid, and 64% the third. How much does he save in the three years ? 14. A man deposited in a bank $1,875; he withdrew 40% of the deposit, and with 9^% of the amount withdrawn purchased a gun. What was the cost of the gun ? 15. A man, having a salary of §3,600, spends 20% of it for board, 12^% for clothing, 10% for books and lecture fees, 5% for incidentals, and deposits the remainder in the bank. How much does he deposit ? 16. I owed a man $1,450, and paid him 40% of it at one time, 20% of the remainder at another time, and 10% of what then remained at another time. How much did I then owe him ? 156 I'EItCENTAaE / f ] I J t If 4 4no'^*,'^.u^"'^'' °''"'^ 2.070 cattle, and sold 33Jo/^ at one time at $36 each ? ^ ''^ ^^^^ remainder i8 A farmer had an orchard containing 225 trees and Hp mey averaged 8} barrels to the tree, and lie sold tliem at SI 20 per barrel, how much did he pay for picking and pacK^ng uL P that ;ftt"J,i"' T^' ^"^' "" ''''''' °^ ^'^''^' ^ith instn.ctions tnat after his widow received her share of 33io/ mo/ " be g.ven .„ his brother, and the remainder wa. to L1i,.^"de'^ eXuv among h.s four children. How much did each chUd r^^eT '^ ^ ^o /o, zv /o, and 10% off. Find the net seUing price. Solution Or 100%-25o/„=75o/^ 100",^ -20% =80% 100%- 10%= 90% .75 X .80 X .90 = .54 $720 X .54 = $388.80 $388.80= Net price. isnofiril'irSof 2lo;1o^^^^ ^">^ -- - considered 10%. and 25o/„. or 10^ 25£' «%' etc!" ^"' ^'^ ''""' ^ °^^ °^ ^^%' Find the net amount of the following bills : ^ 20. S625, less 20% and 10%. •^ 21. S432, less 33Jo/^ and 25%. 22. $327.85, less 50% and 12^%. 23- S45.50, less 60%, 20%, and 2^%. ^ 24. $316.80, less 40%, 250/0, and lOo/^. 25. $421, less 37A%, 5%, and 2|%. 26. $360, less 50%, 20%, and 50/0. $720 180 = 25% of 8720 $540 108 = 20% of $5iO $432 43.20 = 10% of $432 o at one time, of what then the remainder trees, and he eir value. If licm at S1.20 dng them ? li instructions 10% was to vided equally eceive ? th discounts = 75% : 80% 90% ► =.54 1388.80 re considered s one of 20%, gUiiSTlONS OF THE FIRST ASPECT 157 2 7. $324, less 33i%, 20%. and IQO/o. 28. $243.50. less 5%, 21%. and 2^%. 29. $325..'>0. less 25%, 12^%, and loo/^. 30. $348.20. less 20%, 25%, and 10%. 31. $127, less 66|%, 10%, and 5%. 32. $850, less 30%, 20%, and 10% 33' $426.25, less 33J',';„ 10%, and ;^i%. V 34. One merchant offers to sell ne :kties Un 912 a dozen, with d.scounts of 20% 12i% and 10%- .no the, offers the same grade tor $12 a dozen, with discounts oi r?.% and 16§% Which IS the better offer, and how much wouia be saved on 35 dozen neckties ? .^?;n^°"^^* ^^ ""^'^^^ sweepers at $2.40 each, less 25% 20% mo/ L^f '°^^ '^^'''" ^^ *^^ ^^"^^ P"<^^' 1^^^ 20%, 15o^, and 10%. What was my profit ? 25of io^/ ' '!! mfr ^S'' °^ ^'*' ^' ^•^' ■'"•^J^^t *« di^^«""ts of ^3 /o. iw /o, ana 10%. How many hats can be bought for $349.92 ? $1.00 Solution .25=25% of $1.00 $ .75 = Net after first discount. .25=33}o/o of .75 $1.00 .25 Or $1.00 •33J $ .50 = Net after second discount. .05= 10% of .50 $ .75 X .668 X $1.00 -.45= .55 $1.00 .10 .90 =.45 $ ,45 = Net after third discount. $1.00 -.45= .55. or 55%= single discount. What single discounts are equivalent to the foUowmg discount Series ? ^^ !|- ^? II'. I'Jr "" 40. 30O/,, 20%. and 10% "* ^;'n, °'°' 41. 50%, 200/0, and 5%. 39. 33J% and loo/^. ^2. 20%, 25%, and IQo/^. 158 PBRGENTAOK ^ r m V.' Thus 20 + 10-tJ^ of 20 X 10= 30 - 2= 28 ••. the single discount is 28% the ^er two.''^ ''!''°"' '' ^^'''' '°°^'''°^ '' ^*'' ^*^« '^"'^ obtained from By inspection find a single rate of discount equivalent to the toUowing discount series : :A3- 30o/o and ib^/o. 45. iqo/^ and 12^0/0. -• 44. 33^/^ and 60/0. 46. 40%. 20%, and IQCZ. 47. 25%, 8%, and So/^. _^'48. Rice Lewis & Co., Toronto, sold Ingram & Davey. St Thomas, Apr. 2, 1908, on account 30 da., 2% 10 da. : 15 culti- vators listed at $7.50 each, less 20% and 10%; 25 doz. table ^r.o . ff-'"' ''" ''"/- ' ^^^- P°^k^t knives. 3 doz. at $6.50 and 2 doz. at $7.50, less 33J% on each ; | doz. cheese kmves at $9.75, less 16f % Find the net amount due on the bill 9 days after date. 49. John J. Doane, St. Thomas, bought of Heintzman & Co. rrri^' ^l- ^' ^^^^' °" ^^^^^^^ ^ ^^^ 5% 10 da. : 5 pianos at $450 each, 6 pianos at $575 each, 4 pianos at $250 each less a discount of 40 % from each list price ; 10 organs at $125 each, less 25% and 10% from the list price. Find the amount of the bill to render, also the amount to be remitted if the bill is paid April 8, 1908. ^ ^ 50. A grocer bought 10 bbls. of sugar, each weighing 330 lbs at 4|c per pound, and sold them so as to gain 16§%. Find the gain and the selling price. -- ., SI. A stock of goods, consisting of $25,000 worth of groceries was sold at a loss of V^o/^, and I50/0 of the selling price was in uncollectible accounts. What was the total loss si.stained ? 52. A produce dealer paid |^20 for apples, $90 for onions, and $120 for potatoes. He sold the apples at a gain of 25%,* 1 1 QUESTIONS OP THE FIRST ASJPECT 159 equivalent heir product btained from lent to the 10%. Davey, St. : 15 culti- doz. table /es. 3 doz. ioz. cheese lue on the lan & Co., : 5 pianos ' each, less $125 each, unt of the )ill is paid g 330 lbs., Find the groceries, ice was in led? jr onions, I of 25%, the onions at cost, and the potatoes at 95% of their cost. Did he gain or lose, and how much ? —^ 53. A man bought three horses, paying respectively $240, $300, and $530. He sold the first at 125% of its cost, the second at a loss of 10%, and the third at a gain of 15%. Did he gain or lose, and how much ? 54. A dry-goods merchant bought a bill of goods amonndng to $175. He sold 14j% of the bill, and realized a gain equal to 50% of the cost of the whole bill. If the remainder of the stock was sold for $100, what was the gain or loss ? 55. Illustration.— An agent sold goods to the amv^unt of $1,580. Find his commission at 2%. $1580 .02 $31.60 Solution. — The value of the sales is $1,580. The rate is .02. Then, $1,580 x .02= $31.60, the com- mission. 56. Illustration. — What are the net proceeds on a sale of goods aniounting to $200, at 3% commission .' $200 .97 1400 1800 $194.00 Solution.— The sale is $200. The rate is .03. 1 - .03 ■= .97. Then $200 x .97 = $194, the net proceeds. The commission may be found and then deducted from the value of the sales. It will give the same result as the method just explained. -. 57. A real estate agent sold a farm of 90 acres at $125 per acre on a commission of 2%. What was the amount of his com- mission ? How much did he turn over to his principal ? 58. An agent sold 450 barrels of flour at $6.25 per barrel on a commission of 3^%. What was his commission ? '--59. A collector succeeded in collecting 80% of a doubtful account of $1,500. If he charged 7^% commission, how much did he turn over to his principal ? 60. My Montreal agent buys for me 4,500 bushels of wheat at 83Jc per bushel. How much should I remit him to cover the cost of the wheat and his commission of 5% ? 160 PERCENTAGE 61. Illustration.— An agent purchased goods for $750 at a commission of 3J%. What was the principal's entire cost, the other expenses being $25.75 ? . $750 1.031 2250 750 250 $775.00 25.75 $800.75 Solution.— The purchase price is $750. The rate is .03J. 1 + .03J= 1.03i. $750 x 1.03J= $775. Then $775 + $25.75 = $800.75. the entire cost. The commission may be found and then added to the value of the goods purchased. '62- ' ACCOUNT PURCHASE Toronto, May 24, 1906. Purchased by C. A. Norman. For account and risk of C. D. Jones. 30 12 40 12 Bags Bran $o.50 Bu. Clover Seed $7.50 Timothy Seed $2.25 " Flax " .^ .90 Charges. Drayage Commission, 1 1% Charge your acct *** ** 25 >i* *** ** *• 63. In accordance with the above form, prepare an Account Purchase of 4 mats Java Coffee, 266 lbs. @ 21ic; 4 half-chests Y. H. Tea. 220 lbs. @ 42c ; 3 half-chests Oolong Tea, 130 lbs. @ 20c ; 1 hhd. N. O. Molasses, 63 gal. @ 46c. Charges as follows : Drayage. $2.25; Commission, 1^%. Commission Merchants,* Student & Co. ; bought for Teacher & Co. ; present data and place. •i! r $750 at e cost, the The rate is 75. Then. Q added to 1906. ONES. *** *** *Mf ** Account alf-chests 130 lbs. '. follows : erchants, data and QUESTIONS OF THE FIRST ASPECT 161 ■^" 1 64. Rule a piece of paper, copy the following Account Sales, and make the necessary extensions, footings, etc. : Toronto, Aug. 3, 1908. Sold for Account of S. L. Bowling. By Edward Hess & Co. 1896 July Aug. July 221% of $49:..= $11.03.' (0) $10+ $11.03= $21.03 lotal duty. SoLUfioN.~The sp.-5cific duty n simply 20c on each gal.N.n, or $10 on 50 gallons. The ad valorem duty IS a percentage of the coi.t. 'Ii.5 cost of 50 gallons at 97c is ;S18.5jX As the value for duty is always given to the nearest dollar, we add another dollar if the cents are 50 or mc,re, and drop the cents if they ure les.s than 50. $48.50 thus becomes $49. 22p/o of $49 is $11.03. The whole duty is $10 + $1 1 03 or $21.03. ■ ' . ^^i ' of ^ 'P'"^' "^"^y "P°" a" importation of o'' 3;^t "'^' ^f- "^\^'""' ^°"^'' '^'' '^ ^"*y 25c per sq. yd. ? 08 i 2^r ""''"""^ '°°'^' '''' °^ ^^'y '^ P^^ pound ? 108. i,200 tons guano, rate of duty 75c per ton ? 109. 30 doz. bottles wine, duty $2.50 per doz ? 110. 650 gallons brandy, rate of duty SI.50 per gallon ? >.v " l^u ^'°'' ^°"^''' '^^^ o^ duty 10c per doz. ? > ^; ^^t'' *^^ ^^'y "P°" ^^ importation of 1.500 yards flannel weighing 350 lbs. net. and valued at 60 cent yer yard the^ra^e^of duty thereon being 24 cents per pound a:dT5orad ^nYfniZ^'ft ^'^"^ '^' ^""^'^ ^'^''' ^'240 bushels of corn o?l * I ?T ^^^' ^"^°^'^d ^* ^9.50 per ton. What amount of duties had I to pay at 15c per bushel on the corn and 200/;^! A2^6 sSinVL 27%r ^" ^" ™^ °^ ^^^^ ^^^^^"^ *« IIS. What is the duty on l.OOC' -ds of Brussels carpet, 2;- ^v 4 QUESTIONS OP THE FIRST ASPECT 165 discount is rtation of te of duty cific iuty i", 1, or $10 nn lorem d.'ity cofct. 'J.h-i : is 5t8.50. is always ar, we add s are 50 or if they are IS becomes 1.03. + $11.03. sq. yd. ? pound ? P yards er yard, 35% ad of corn amount 3 on the ting to , 2.' in. 4 ii6 An invoice of woollen cloth, imported from England was valued at ^956 6s. If its weight was 684 lbs., how much was the duty at 50c per pound specific, and 35o/, ad valorem ? at 4% ^'-'-'^'^^^"^^-Find the interest on $650 iov 2 years $650 Principal .04 $26.00 Int. for 1 yr. 2 SoLUTiON.—Interest for i year is 4% of the principal. $650= $650 x .04= $26.00, and the interest for two years is twice the interest for 1 year, or $26.00 x 2 = $52.00. $52.00 Int. for 2 yi^. Find the interest on the following : 128. $320 for 3 yr. at 6%. — . „^, ^,^^ ^^ ^ii8. $75 for 2 yr. at 10% Nil 1 9. $80 for 3 yr. at 12J%, 120. $120 for 4 yr. at 5%. 121. $240. for 2 yr. at 8^%, 122. $72 for 5 yr. at 6%. 123. $84 for 3 yr. at 5%. 124. $150 for 2 yr. at 6%. 125. $240 for 3 yr. at 10%. 126. $320 for 5 yr. at 4%. 127. $325 for 5 yr. at 4%. 129. $620 for 2 yr. at 10%. 130. $800 for 2 yr. at 7J%. 131. $120 for 4 yr. at 5%. 132. $314 for 2 yr. at 10%. 133. S215 for 3 >T. at 8%. 134. $32 for 1 yr. at 5%. 135. $60 for 2 yr. at 6^%. 136. $75 for 1 yr. at 6%. 137. $1,200 for 2 yr. at 9%. 138. ILLUSTRATION.-Find the interest on $850 for 62 days at 5 ^. $850 ■05 $42.50 Int. for 1 yr. 62 365)2635:60($7.21 + .-' ' or $7.22. Compute the interest on the following ■^139. $840 for 63 days at 5%. -^ 140. $960 for 75 days at 6%. 141. $320 for 96 davs at 7%. 142. $1,260 for 123 days at 8%. 143. $2,480 for 85 days at 9%. Solution.— Sixty-two days is ^^^ of 1 year. The interest for 62 days is, therefore, ^%^ of the interest for 1 year, and this may be found by multiplying the interest for 1 year ($42.50) by 62 and dividing the result by 365. 166 « / * 'ii! PERCENTAGE ^44' $1,244 for 54 days at 10"/ 145. $2,360 for 59 days at Uo/" 146. $9,200 for 36 days at 12%' 147. Illustration.— Find the interest nn «q ocn , 16th, ,889, .0 June ,8th, ,89,, aU^^^ZT'^ '""" ^'"' (Fro„ April ,6,h, .89. to June ,8.h, .9,. ia 2 y.a„ and 63 day, , Solution 1 ' ' $3250 .06 $195.00 Solution 2 $3250 X ^S. X /A= $ 33.66 Int. for 63 days. «3->o0 X i8, X 2 = $390.00 Int. for 2 yea^ $423.66 $423.66 Int. for 2 years 63 days. Find the interest on : 7i%. "' '**'• '" -"""^ ^' '«92. at 4%. At ^^jSO. 1650 from June ,7, ,892, to Ja.,. 2,, ,894, at 70/, At 6}%.'' ^^'-^^ ''■°'" J""- 2*' '«*■ 'o Jan. I. 1893, at 6%. At - ^2. $940 from June ,5, 189,, to Jan. ,5, 1894, at 6Jo/„, At QUESTIONS OF THE SECOND ASPECT SERIES 57 SO. - -— W^^f ^^^^^ -. • -^^t^"""" '— '2^ '^ iiS. or i. of 480 and since 480 is 100o/„ of itself. 120. which is J of 480, must be i of lOOo/o. or 25"/o Or 10/ ^S'LT "-,7^"'' ''' ^^ ''"""/o'ci itself. 1 /o of 480 would be ^J, part of it. or 4 80 Since 4 80 is 1 o/^ of 480, 120 would be as many Pe7";t^ o? -fd-d fsif '' --'^ -' -^ - -- - - What (1) ioi 100%= 25% (2) 120 -f 4.80=25 25 times 1%= 25% 1/ I !■ I ' from April Jays.) 1 days. 2ars. 1 ! irs 63 days. , 1 %■ At 7%. 6%. At i%. At QUESTIONS OP THE SECOND ASPECT F v.'heat, 480 and h is J of of itself, or 4.80. as many in 120. What 167 ico/^\^,^'^^ P"* "P S'OOO tons of ice. During the summer cent, of the whole amount did he still have > perctnl''" ""'' '' ''•' ' ''' ^'^^^^^^^ ^^ 2.58. What is the S. What per cent, does a man make on his money who rents a house that cost $7,500, for $600 a year ? is54ttirwhatisth"' '"°"^' f P"P'^^- ^^ ^^^ ^t*-dance o^ pupils, what is the per cent, of attendance ? 7- In a battle in which 9,000 men were eneiPoH 9 nnn r^ were killed. What ner c^nt ^f .v u "^'^^'^°' ^.000 men killed? ^ ^ ^^'^ ''''"'^'' ^"gaged was not same are $1,095. What per cent, of his income does he save ? $24 m\VhT ' ^'T "'' ^^^'2^^' ^"^ the liabilities are $24 000 What per cent, of its debts can the firm pay p protit 01 $105. Find the rate per cent, of gain. Cost = $350 !gg of 1000/ = 300/ f n ? K / '"• ^^^' ""^'^^^ ''^ *S5 of '° " /° 350, must be Jje of 100%, or 30% - f i" Vs^'''71' T' °^ ^'*" °^ ^^^'^^ ^h^" the cost is 12 $5m and th' ^' f'-^'^- M50 and the gain is $2.25. il' Um nd t\ T" -^^ 5'- '7- ^^ ^"^ the loss is $4.50. if' S-Tnd th '"J^- '^' ^800 and the gain is $2.00. A' $8Sand hT^'f ''• '9- ^^750andthegainis$750. 15. i&oUU and the loss IS $600 ^n «innn ^ ^u ? .1 ^4 21 Whnt i. +1, ^^ ■3>':>w- 20. $1000 and the loss IS $250. a^i'soTd t. sl20 r^ ^^"•- °' P™«' ™ ^ P-° ^vhich COS. $350 ^/^: ^ f-^""""' *"""«'" ^ ■■''^"^ °f paper at $2.40 per ream and retailed .t at 1 cent pe, 4,cet. What was his per ^."^ '1^ bushel- -annit'" ^'*"' "' ^'•^"* »' »"-' " '« ' ''1^ pe cem ';1 ^2 """ ""^""'^ ">' »^"-'^- What was his 168 PERraNTAQR 25. A drover boug>,i 15 aorses at S125 per head, sold 2 oi them at $127 75 per h.^d. 8 at $140 per head, and the remainder at $150 per head. If his expenses in taking them to market amounted to $5 per licad, what was his per cent, of gain ? 26. Oats purchased at 45^ cents per ' ■ish.n v.^ic sold for 54i cents per bushel. What was the rate per cent, of gain ? 27. A grocer bought 536 gallons of vinegar for $150.08, sold 175 gallons ot 30 cents per gallon, 124 gallons at 35 cents per gallon and the remr.i ider for $91.70. What was his rate per cent of gam ? ^ *o Jnn"^'^'''"^''-~'^" ''^''"^ '"'^'^^^ ^50 commission for selling $2,500 worth of goods. What is his rate of commission ? SOI UTION On $2500, commission is $50 On $1, commission is $50 On 3100, commission is 100 x 2500 50 2500 or $2 The commission is 2%. NoTE.-An agent is paid for what he does. If he buys $500 worth of goods and ships them to Ins principal, liis commission is on $500 Other costs such as freight, may bring the cost to the r ncipal up to. say. $600 but the agent gets his commis^.n on ?,Sn,, Agai an agent may sell good^ for $500. H.s commission is on ...00. The principal may receive only $400 after all expenses arc deducted from the sale money, but the agent is paid on what he sold, $500 worth of goods. What is --^28. The -^29. The 30. Tlie 31. The 32. The $286; -^ 32- The ^35. The the rate per cent, ot commission if sales are $960 and the commissio'^ 15. 60 ? cost is $3,264 and the comm ssion for buying $3.06 ? sales are $3,200 and the cc- s? for selhng $6 ' cost IS $460 and the comm' on buying $23 ? first cost of the purchase is $275 and the gross cr.^t total sale:, are $105 and the net sales $102.90 ? total sales are $380 and the net sales $379.05 ? prime cost is $124 and the gross cost $I2a34 ? QUESTIONS OP TEE SECOND ASPECT 169 ad, sold 2 ol :he remainder m to market gain ? sold for 54| in? $150.08, sold its per gallon, per cent, of Dn for selling >n? $500 worth of $500. Other to, say, $600, may sell goods !ive only $400, jent is paid on ) ? ying $3.06 ? ;lling $6 ? g $23? e gross cr^-t 90? 1.34? 36. My agent sold queensware for me, and, retaining his com- mission, $90, remitlcd me $1,910. What per cent, commission did I allow him ? 37. A commission merchant sold corn for $6,000 ; he charged $80 commission and $135 for guaranteeing payment. What was his per cent, of commission and of guaranty ? 38. The total cost of a church was $12,646.40, which includes the architect's commission, $296.40. Find the per cent, of commission. 39. I sold real estate through an agent lor $12,750 ; I received $765 comnjssion and paid him $573.75. What was the per cent, of commissiOii of each ? 40. My commission for selHng furniture was $591.50; the net proceeds, $16,308.50. What per cent, did I charge for my services '^ 41. I ' 'ight sugar for a grocer: the whole cost, including expenses, 5>w -.45, and commission, $170.50, was $6,439.95. What per cent, comu.ission did I get ? 42. ILLU< xRATiOK -I paid $30 for insuring a house, worth $6,400, at J valuati Wliat was the rate ? Solution f of $6400= $4800, the face of the policy. 130 - 4800 = $.00625. or go/^ ^ the rate of insurance. . 'SJ43. The premium for insuring a house, worth $12,000, at it'? full value, was $80. What was the per cent. ? 4'4- If $125 are paid annually for insuring $24,000, what is the rate per cent. ? 45- A fire insurance company charged $129.60 for insuring a house for $13,500. What was the rate of insurance per $100 ? ^ 46. I paid $175 premium on a schooner worth $25,000, which was msured at | of its value. What was the rate per cent, of insurance ? What was the rate of insurance in cents on the $100 ? 47- A marine insurance company rec ved $484.50 for insuring a vessel < orth $80,000 at f of its v.lue. What was the rate per cent, of msurance if $4.50 was charged for the pohcy and survey ? 170 PRRCKNTAQE lit H 48. Illustration.— A tax n( fli-i 7t;n • x •< Solution $3,750 + SI, 250,000= .003 Therefore, the rate of taxation . .003 on ,,. . 3 ,..,. ,„ ,,, ,,„„. was the tax on a farm assessed at 34,2^7 ' ""^ ''^"' Find the ra.e of taxation in mills on «l if ti, valuation is ''^' '^ *"<^' assessed --^50. 8514,000, and the gross tax <^0'i'i ■ i ,• at 5Uc. ^ ^^ ^'233, including 130 polls ^^^51. S15,(300. and the gross tax $137.25. including 3 polls at -iS2. $15,387,200, and the total property tax $169,259.20. Find the rate of taxation in cents on < 76 dl produce $45.60 interest ? '''^'' 8204, what is the per cent, of the per cent, of of .^-lo/„, or 5%, - Find the rate of interest : Principal. IntertFt. Time ^72. 73- '. 74. 75- 76. 8600 $500 $300 $200 $400 872 860 860 824 816 2 yr. 3 yr. 5 yr. 4 yr. 6 mo. 77- ^78. 79. ^80. Priiici|'n 0+ • , real.ed a profit of ,850, 'pifdle J^.™ L^. «"" "' =»%' ' Solution 20% of cost= $850 I % of cost = $850 20 100% of cost = W of $850= $4,250 a loss of SO/" '^ ^''^' ^^' ^"^^ ^"^ ^13 less than cost, by which a loss of 5o/„ was sustamed. What was the cost of the g^oods ? thanrpSd tT ^^hlt f^'f'""' '-' ^orlSLe — ' lo Whl, ;',, ^ "* ""^ "'"'"n for 'he land ? by sdiinll, a .I'oT.^:?; *^ ^°'' "' ^ ^'"^^ °' «°°^^ » owner. M. By seUinT! l/, /J°; ^T"^ **'" ""« '^an the cost it, I .a Jdi:^ ml: dfd'ftTosfJ f/" '-'"' "■- ' ^^■'' '" FwL^oTXd" '"Z" "^ '^"'""^ «»^''- ^« «Je a yard. Find cost 13. 14. IS Z6. GAIN. $3.00 60c. 37^c. $5.60 GAIN %. 10% m% 40% 17. 18. 19. 20. LOSS. S2.50 $4.80 $1.20 LOSS %. 30% 250/ $3.00 6i^ 7o QUESTIONS OF THE THIRD ASPECT which amount Jse worth ? e month, which -s. How many Ions, which was lions were there I the cask ? omatoes, which selling. How $75.50, which he in the bank lin of 20%, I ost, by which e goods ? $195.60 more id? )ods if owner, an the cost ? an I paid for He a yard. LOSS %. 30% 250/ 173 hous: ? ""™""" ^'' '%' ^^'^^^ -- th^ value'oMh: Solution 1 5% of value = $170 1% of value = $170 100o/„ofvalue.-'^i^^''=«^'^«« 5 Or .05)$170.00 Solution 9 Th„ • • r ^JULUTioN ^. — ihe commission is $17(1 tu^ x « 3.m .05. Then, 8170 * .05 = 83,400 valu '™, ho^s: '"*' "^r tasLf nM™° "'"" '*°''° '"■ ""^"'6 ™™ '« "« at 62c ^1 iiuiL. II nis rate of commission was 2Ao/ ,^i,„f ,„^ ,, net proceeds ? ^''<" ^^"^'^ ^^^.s the ~JaS. A Mobiie factor earnpri ' <" rateofc„mmi3sr„l;:^Lr:.an7,r"<'^ °' '"^ ^^^ " ■''^ .us., ot wHeat wL .otll'tHe'trtli.'^roC;-; sSls P- preiU^pM^'ird th:':'. "r ' ^ "-"^ '"^-'' " ">^ i^axu ib ©/o, and the rate of insurance f % ? Solution 1% of policy = $75 1 % of policy = $75 X # 100% of policy = !00 v 7s .. « __ 6i% 7o Premi Or f = $12,000. um ($75) ~ rate (|%, or .6250,^)= $12,000. H i h ^■' "i ^^^^m ^B ' : ■ m! ■i; ^ '! WMi .j./ ^^H > ■j 1 ^^^B ! ■ ' : I 174 PERCENTAGE """^29. A house is insured at -'o/ „„j +1 For how much is it insu"d f "^' " """'""' "^ ««3-'»- For what sun '--^SO. The cargo of a steamer is insured at ^0/ IS It insured, the premium being Si, 500 ? ' °" .t 'f/o/^w.^f^ °'' f '^"P"^^"^ °^ goods 'to insure | the value at 31%. What was the whole value ? 32. A manufacturing company paid S214.80 premium for r?r00 ' W f '" r ^^ ^^^ '"^^^'"^ -^ .nachmeTy io per k'lOO. What was their cost ? 33. ILLUSTRATION.-Tho tax on a certain property was S9610 and the rate of taxation 7| mills on the dohar' Frhow Ich was the property assessed ? "'^'^^ SpLUTION $0.00775 is the tax on $1 $1 is the tax on -^^^^. $96.10 is the tax on .^5= §12,400 ors^lt2TI'ti V^ f^^f^^d value of a property that pays a tax ot SI 82, at the rate of 3| mills on the dollar ? uJJlu^ *°''" '^^"'/«^*'"g ^'2,250, was built by a tax assessed upon the property of the town. The tax rate was 5 mills on the dollar, and the cost of collection 2%. What was the valuation ? K.^-^' J^^usTRATioN.-What amount of stock must be held to obtam $200 income from a 4% dividend ? Solution $4 income is derived from 1 share. ••. $200 income is derived from 200 -f 4 =: 50 shares. 50 shares = 50 x 100= $5,000 stock. What is the par value of stock if the 37. Dividend is $170.50, and the rate of dividend 51% > 38. Assessment is $1,031.25, and the rate of assessment 8J% > »A39. Premium is $3,293.75, and the rate of premium 191o/ p " ^40. Discount is $1,550.25, and the rate of discount 13Jo/o ' I lium is $93.60. For what sun ■e I the value, premium for hinery, at 60c ty was $96 iO. ""or how much 175 at pays a tax . tax assessed ' mills on the valuation ? t be held to res. ;ment 8J% ? m 19|o/„ ? It 13^0/^ QUiitiTluNS OF TUE THIRD ASPECT at lo'=:' f '^.^;f ^^°^-^h^^ -- -ust be invested in 50/, bonds, at 105, to yield an annual income of $1,250 ? Solution The dividend from 1 share = $5 «1.250-f $5= 250= number 0/ shares. The cost of : share = $105 VI JJ"' '°'* °' "'^ '''"'''= ^'^' ^ 250, or $26,250. Nl 42. What sum must be invested nt Q-^ fn ..^ ^ oi $1,600. the r.f. r.i ^,-,.^.„7u '^5.^.^ ^° P'°d"^<^ an mcome of 1,600, the rate of dividend being 8% 43. How much must be invested in 8% stock at 162 ir. ^ an annual income of $1,280 ? ' ^° ^^^^^ i^-m; rlr^" ™"'"^ ?'^ ^' "' ^^^' ^'^^t sum must be mvested m .. to reahze an annual income of $1,500 ? ^vested invested in it to proVeaniri^n^meTj^^^^^^^^^ "^^^ '^^ 46. ILLUSTRATION.-What principal will vield 3^400 • f . m 2 years at 8% ? ^ f ^m yieia $400 mterest /—- ~ Solution Interest on $100 for 2 yrs. at 8°/ = $i6 J $16 is the interest on $100 ] $1 is the interest on ^'00 ^ 16 8400 is the interest on i^OjiJOO 16 = $2,500 Find the principal : RATE. TIME. INTEREST -J^ 47. 3|<% 1 yr. $45| 48. 5io/^ 1 yr, 49. 4^0/0 J. jT. Nl 50. 3|o/o I yr. 51- 8% INTEREST. $29.75 1 J- $25| $3f RATE. TIME. "^53. 50/0 7 yrs 54- 3J% 4J yrs. $94,50 -^55. 40/0 i| yrs. »%= T^of 1122, or 6. 100%, or the number, = 100 times 6, or 600. Heace. the required result is 600. 2. Illustration.— What number, decreased by 35% of itself equals 2600.? , ^ v./o oi iisen Solution Represent the number by 100%. 35%= the decrease. 65%= the number after decrease. 2600 = the number after decrease. Therefore, 65% of the number = 2600 1%=bV of 2600, or 40. 100%= 100 times 40, or 4000, the required result, -^v 3. 4186 is 15% more than what number ? 4. When gold is worth 12% more than currency, what is the gold value of $725.76 in currency ? \; 5- A foreman, whose salary was increased 11%. receives $1,082.25. How much did he receive before the increase ? ,o^of* "^^ ^^^"* ^"^"^ ^ ^""'"^ ^""^ ^°* ^«' $11,002.50. which was 12i% more than it cost him. What did it cost him ? 7. During the month of December a merchant sold goods to the value of $12,620.02, which was 9% more than his sales in November. What did his sales amount to in November ? 8. Sold a horse for $170, which is 6^0/^ more than it cost me. How much did it cost me ? 1QQ ^* ^*'o S''"'^^'" "^ ^^"^^"ts attending a certain school in 1895 was 357, wnich was 40% more than in 1894. What was the attendance in 1894 ? , what is the QUESTIONS OF THE FOURTH ASPECT 177 10. What number increased by 1^1% of itself equals 6825 ? 11. If llio/o of a number be added to itself, the sum will eaual 2000. What is the number ? ^ "^^12. A shepherd, after losing 35% of his flock, had 325 sheep remaining. How many had he at first ? M13. A dealer in dry goods spent for calico $1,726.80 which was 20% less than the amount spent for mushn. How much did he spend for muslin ? 14. A certain man owns two farms. The first farm contains 290 acres, which is 42% smaller than the second. How manv acres does the second farm contain ? 15. In the const uction of a business block, 40% of the entire cost was paid for the brickwork and stonework, 20% for the carpenter work, 15% for glazing, 10% for the elevator? and the remamder, $510, for the painting. What was the whole cost ? 16. What was the cost of a horse that sold for $136 at a loss ^^o^cL,"^ w^/°'' ""^'^ ^'' ^^' ^''^^' ^^^"^"^^ to his principal $540.96. What sum did he collect .? 18. The pressure on the surface of a steam boiler is 81 lbs since decreasmg it IQo/^. What was the pressure before decreasing it ? 19. ILLUSTRATION.-What must be asked for goods that a discount of 20% and 10% may be allowed, and net $2.88 to the seller ? SOLriTION Let 1000/0= 'sking price. 20% and ;>%:-^a'l wance. 72%:^ asL fr.g prio/j after allowance. 72% of asking price = $ 2.88 1% of ask.ixg price = -^|? 100% of asking price =12L-l2-88 72 ~~ " $4.00 178 PERCENTAGE 10% ■i i At what price must goods be marked ^ao. To net ^72, after allowing a discount of lSo/„ . and W»r? ^ • '"" ^'""""S - discount of 25o/„, 20%, 23. To net ». after allowing a discount of ,0%, ,oo/„, and and'?0%° "^' *"•''• ^""^^ ^'-'"^ ^ ^-— of 40o/„, ,oo/„, net?gi"oT^~rrosr ^-^'^^^ ^^^ -" '- *^- Solution.- 100%= cost. _20%=gain. 120%= sale = $240. 1%= 8240^ 120= $2 ^ 100%= 100 X .82= $200. K the ;et gj^jd 25oi r "" '°^ ''"^■^''- ™'^' "^ '^^ -* wh:f"wtr;ott "" ^ "'^^ '"^ «'^ -'^ s-^h --^cf t^ons to deduct his commission of 2^%" and '^t^lt SS QUESTIONS OF THE FOURTH ASPECT 179 mucli did he invest, and what was his in wheat. How commission ? Solution Represent the actual investment by 100%. 2i%= the charges for buying Zm'' T^='':^%:'^- -^* oi the investment to the principal. 54,100 = the cost of the mvestment to the principal. Therefore, 102jo/o of the cost= $4,100 1%= $40. 100"/oz= $4,000, the actual investment in wheat $4,100- $4,000= $100, the commission for buying. "^35. An agent received $6,180 to buy cotton. After deducting his commission at 3%, how much did he invest in cotton ? -^36. How many yards of mushn at 5 cents a yard can my aeent buy with $609 after deducting his commission at Ijo/^ ? --^37- I bought coffee at I|o/o commission and charged 2i% for guaranteeing payment. What did I pay for the coffee if the whole cost was $1,832.60 ? 38. Having sent a Toronto agent $1,835.46 to be invested in sugar, after allowing 3o/„ on the mvestment for his commission I received 32,400 pounds of s^gar. What price per pound dTd the sugar cost the agent ? 39. An agent in Hamilton received $828 to invest in "prints afer deducting his commission of 3^/,. If he paid y^c per "ard for the prints, how many yards did he buy ? ^ 40. A Stratford fruit dealer sent a Grimsby agent $1 946 70 in s xlr r° T ^'^^"^' ""^ '^^PP^^ *^^ P"^^^^^ '- his principal m SIX car loads of an equal number of barrels. How many barrels did each car contain ? ^ udneis 41. ILLUSTRATION.-What is the amount of sales >vhen the net proceeds are $975 and the commission 2^0/^ ? Solution.— Let 100%= gales. ^i%= commission. Then 97^%= net proceeds. 97*% of sales = $975. 1 % of sales = $10. 100 % of sales— $1,000. 180 PERCENTAGE *^42. The net proceeds of a consignment are «fi7<; ^n ^ .u " rate of commission Sio/ uru * ■ ^°^^"^ ^^^ $b75.50, and the ommission JJ ^ What is the amount of the sale ? cent, of the original deb. of Sao^'remata unpaM f ' ^'' ^^^ 44- A farmer received from his citv a^Pnt «,iq« on hot n any't u f al 2^0 ?' '"T'^ °' '^"'""^ "> P"-''-- how ^uic^zt,:: z sjed^ ™" ""^ '^^" -'"■ --^ pT;nfe;rc.":r;s^,tsr■f^r^^^^^ the principal is $2,71 1.64 ? P™"^"^" '''"' other charges^ """""^ '*°''° ^°™™'^='°n and S263.18 stock ■ sdhnrat™21o7"°" """^ '"^'^ ^^^ <" -^-"erce brokerage i%> '^ ''"""™ "="" •« """Sht for «7,275. SoLUTiON.~l Share at par Premium Market value Brokerage = $100 = 21 = 121 = i Cost to purchaser = I21i $7,275- $121 A z=: 60 There are 60 -shares, or $6,000 par of stock. How many shares may be bought for COST. 48. $13,155 "49. $9,760 SO. $5,610 Si. $13,620 MAR. VAL. 225 121J 140 85 BROK. 4 /O i% -4S3. 54. COST. $1,923 $3,850 $12,025 i% 55' $4,134 MAR. VAL. 80 96 240 86 BROK. i% i% Wo iUESTlONS OF THE ' URTH ASPECT .50, and the sale ? e, and, after . What per as the net 'mmission is ' purchasers, n sold, and uaranteeing roceeds due ds of which ind $263.18 Commerce or $7,275, BROK. i% 56. ILLUSTRATION.-How many shares Bank of Commerce stock at 121 must I sell to realize $7,245, brokerage J% ? Solution. — Market value = $121 Brokerage ::::= i Amount received from one share = $120i $7,245 -r $120f = 60 60 shares are sold. How many shares must be sold to realize N58. 59. 60. s. p. $8,505 $10,245 $4,314 $4,350 MAR. VAL. 121| 85J 90 87i BROK. i% i% i% i% S. P, $19,755 $2,400 $8,336 $10,548 MAR. VAL. 220 96i 130^ no BROK. i% i% i% $508 in "^61. ^62. 63. 65. Illustration.— What principal wiU amount^to 4^ years at 6% ? Solution Let 51 represent the principal. $1.27= the amount of a dollar for 4J yrs. $508 = the amount of a certain principal for 4* yrs $508 -r $1.27=400. Since the given amount is. 400 times the assumed amount, the required principal must be 400 times the assumed principal. 400 times $1 = $400, the required principal. What sum must be put out at interest for "^66. 68. 69. 70. 71. "^72. "^73. 74. 75. 76. 77. ^78, 79. 2 years at 4% to amount to $540.00. 4 years at 6% to amount to $2,480.00. 6 years at 2^% to amount to $2 760.00. 3 years at 3% to amount to $87.20. to amount to $342.00. to amount to $616.00. to amount to $4,441.20. to amount to $2,246.70. to amount to $2,586.50. to amount to S3,31&75. to amount to 10 years at 7% 8 years at 5% 102 days at 5% 318 days at 3% 75 days at 6% 150 days at 2i% 200 days at 6|"% 85 days at 174 days at 3^% to amount to 312 days at 6f% to amount to 5% •^10/ -3 ,0 to amount to S755.00. S5 16.95. $46?.96 'f if* ir I'i i' '^■1 ''^ 182 PERC! .VTAOE REVIEW OF PERCENTAGE SERIES 60 I. A grocer mixes 30 lbs. of tea wnrfh ^5 ^„ < , . 20 lbs worth 35 cents a pound, "it^at t^^^^^l he sell the mixture so as to gain 20o/, on his outky/ 2. A dealer sold an article for S6.75 and lost 10°/ At »J..f selhng price would he have gained IC 0/, ? '^' ^^ '' ^""^ 3. How much bettor is a single discount of 6OO/ fhnn . discount series of 25o/o, 20o/„, and 15% ^ '^ *^^" ^ tax ot ^1 fi'^9'?rr, ""'"' "" '^' ^°"^'" "^"^t b^ levied to raise a tax o S5 632.50. the taxable value of the property beine Si 346 250, If 165 polls are taxed at $1.50 each , ^ ^ ""^ ^^'^'*^'- 5. A man invests $6,000 in 5% stock at 120 • at the end of one year, havmg just received the yearly dividend h^l foul at Ul^. How much better of? is he thin if k. 1 , > ,^^ money at 50/, per annum ? ^" '^ ^' ^'^^ ^"^"^^ ^is 6. A premium of m is paid to insure a house for S2 SOO f.r 3 years. What is the 3 eady rate ? °^ 7. A retail deal-r sold a suit of clothes for <59q An , • a profit of 20 per cm. li the cloth .n7\ ^ ^' "'''^'"^ 11. A machinist sold two seed-HHJlc f^,- ^ 1 He gained 25o/„ „„ .he one LTlJtVZnZ T' "L™"^^' loss was $9.m. Find the cost of Ih drill ' "" '"'^ 12. Sold stock at a discount of 1910/ j my money. At what tate of rcount 2fZ\ "^'^ '^«% ™ 13. Assessed valuation of real propertv SSmnnn property $500,700, and there being 250 poll SSfe'd^', ,T'°f collecon charges 5o/„, ta. reaIized%95,3S:rd ttf of taT ' ' 60% than a tor $2,500 for REVIEW OF PERCENTAGE jgg 14. An agent received a consignment of wheat which l,e sn.rt on a commission of 2l%- the amount ser.t to hi empty r v^ equivalent to 81]- cents a bushel. What was h,s coZ!!;; 15. A grocer gamed 200/^ by selling 20 lbs. sugar for SI After wardhemcreasedhispnce,givmgonry ,8 lbs. fo^r $1 pLm^h per cent, did he make at the increased price => 16. What per cent, is made by investing in 4J% s .,t 75 ? t8 1? , .y° ^""^ P"^' '^"*- profit di^ Ji^^ "lake ? 18. Find the per cent, of commission on a purchase if fhp gross cost ,s S2,048.51, the commission .S87.30, t^ca ge ^20 and other charges Si. 21. ^^n-agt, $zu, 19. A merchant failed with liabilities amounting to SSOOOO- his assets m merchandise are S20/XJ0 ; in real estje S8 wS^ ' 20. A merchant has a stock of goods valued it ^i 9m .„ 1 store building valued it ''"" °' *^ """^"' ^' 24. A man's salary is Si 700 nnri Kic ,,„+ • • ^ „r, -^ 'i^ii/uv^, ana nis net income is <5l fi7^ qc after paymg income tax on all over .S400. What is th^ rat'f 25. At what price must I mark cloth which cost me :5 v: / Phofe)graphic Sdences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. MS80 (716) 872-4503 m V N> % V ^ ,^* K^^ ^J^ IL \\n 184 PERCENTAGE 28. Having received a stock dividend of So/ t ^„^ t ""TmLT Tr "^^ --' ^^^^^ -- t^^t r ., 4^: ^ ,f % ad valorem, the duty on 1.580 yards of silk was $1,070 What was the invoice price per yard, and for what nric^ per yard must the importer sell it to gain 20% ? ^ 30. A merchant buys $10.50 worth of sugar. He uses a nound Fmf liigir "° '''' -' ^""-'^ ''' ^-'^ - ^ p-s :f^5t $26'?fin TfR "". 'tna i^ 5S1A000. His assets amounted to ieff^ H ' P' ''^'^ '''^^^'^^^ ""^ *h^ ^^P^"^«^ for settling are $1,360, what per cent, of their claim will A. C, and D received rJ^) \l ?'lf '"^ ^ ^°^''' '^' ^°^* ^f the material was to the cost of the labor as 3 is tn 9 u^a co/ r 100/ i,e. r , u u ^^ ^% more for material and Whtts"st P^" '-''' ''' ''^'' -^^'' ^-- -- ^^'^^0. Droc^oH^nf'T '""'^^^^^V'^"' ^^' ''^y "^^-* «490 as the net proce d. of a shipment of butter. If the agent's commission is 3 /o, cl hvery charges $6.80. and 50/, charge is made for guaranty of quality to purchasers, how many pounds, at 27c pef pound must have been sold, and how much commission was allowedT 34. A man bought 400 sheep at a certain price per head He sold t of them at a gain of 20o/„, ,3^ of them at f gain of* 15% How mucr.T. "' : ^°" '' ^'°/«' ^^'"'"^ - *h^ -hole $217: How much did he pay for the sheep per head ? 35. A broker invests $6,450.75 in stock at 68i on I 0/ commission. What are his charges ? * ^° 36. A city hall costing $36,750 was built by a special tax upon the property of the city. The rate of taxation being 5 n. 11= on the dollar and the cost of collection 2%. find the tTt^" assessment. ^° ^"'•^ 38. Bought oranges at the rate of 10 cents per dozen and sold them at the rate of 5 oranges (or i 1 cents. FinS my"™' "r cent I nnd I am now own at first ? 'aids of silk was d for what price He uses a pound a profit of 15%. )wed A $4,500, ts amounted to nses for settling and D receive ? :rial was to the Jr material and re cost $44,550. 490 as the net ' commission is le for guaranty 27c per pound, s allowed ? per head. He a gain of 15%, le whole $217. m on \o/^ a special tax 1 being 5 mills find the total igars, invoiced $3 per lb. and ozen, and sold gain per cent. REVIEW OP PERCENTAGE JgS fh/f/^^' net profits of a business for two years were $6,400 he second year s profit being 66|o/, greater than the profi s o the first year. What were the profits each year > 40, Find the cost of a draft on Wmnipeg for $1,397.60 bought when exchange was ^%. ^ gaimng 33J% on the rye and 12^/0 on the wheat. He received 20% more for the wheat than for the rye. What was his Ital li/o. and 40% of the remainder at !|o/„. What rate did the company receive on the amount of nsk it earned ? 43. Fmd the alteration in income occasioned by shiftine $4 500 stock from the 5 per cents at 1 1'U t.^ ^k q . ^ ^%^W c v» pel cenis. at 11^ to the 3 per cents, at 91i th- brokerage bemg i% on each transaction. *' 44. A person buys a lot of land at $37.50 ar acre and bv selhng ,t m allotments finds the value increased thrif'd so It" rhtbu^ ^"' "^'"^ ^ '''-' '- '"''-'- «^- -^^y remtfndt^l LrtUTha7lef[ ^sTV"' '''^ '' ''' had I at first ? ' """ ""* ™°"<=y h "**' Is^:?'"'™ ''°''*™ '"soI™* ; the schedule showed that he cwed A Um. B S3,500, C $6,000, and D $4,500 Mhe asset m real estate amounted to $5,000, in accounts re eivable StI^ and m bills receivable «9ono if 4.u " -p^jOou, were m<^n h^ uL^' *^^ expenses of bankruptcy were $650 how much did D receive in settlement of his claim / lfitl\ ''"''"''^'"^" ^e^kons his percentages on his turnover If the turnover is $36,729.28, wages $15,387.20 salaries $8 756 J^ gross profit $26,239.50, and net%rofit $13,729 20 clu^^^^^^^^^^ percentage of wages, salaries, gross profit, and net profit 48. A gentleman owns | of a steamboat, which is insured for ::;at*5%adt,o:e:t " '"= ^ ^"^ ''■ ^- ^->' <«^' '^ 186 PLRCENTAGE hi ! ' I . 50. My broker bou,(,'lit R. and O ^fnrL- f mimediately sold sa>ne at 143? rc^.u? "'' "' ^-'*«' '^^^^ How many shares d,d l,c buy ! br L ^ '' "'* P'""^^^ S'>341. on buymg and the s.une on .'ling ? "''" '' ^"^^ '^^'"^ ^^-ved 51. A merchant, in buym- certiin ^nnri i o. too heavy, and. m Mlm" " T,t' "f ' P'""' "^'^'^^ ^>g'^t. Fmd h.s ,an. per cent, i^om his ^.J^r^^' ^ ^ *- 52. Divide .$700 into two parts such fh-,. S ■ en one part for 3 years at 50/ ll ^ *^^* *^^ ^""P^^ interest snnple interest on the o he pat or fi " ""'' '^ ^^"^^ ^« ^he diiol to make a loss per cent. ? ^'' " '^"'^ ^''^" '-■"^tomer's 63. Find the income derived from .S'>L> 831 SO inv.f . • raec o, S960 per year. How ,„uc,. Uas ^l^, "^Zi:^ "' ' "^' o-n/ , ° '"/o. o-oo less 40% and 10"' • ()"/ • f^.. k„i r , ° ^'-'/o. obOO less ,0 i"u -^^/o, the balance of the bill '-{'-{K'^ .r, i i/vn/ IS the net price ? "' ^° '^"'^ '^%- What did he seh it at ? b'^'Jitu / ^.q. wJuit price 67- A man invests SI2 0G0 in V^^ 600 0(K) ■ fK ate o taxation is 17 mills on the dollar; it osts^'^^Z; for collection. Find the net amount received ^L t:l ''' 69. A man sold 2 lots for $445 eainin^ l'>io/ losing 12A% on the other. Find th'e co t ". 1 T. '"' ""^ S5 on the whole transaction. "^ '''^'' '^ ^^''^ gained h. c^mts;::^^^,;;":::^^:" ^^t^' ^"'' ^^^^'- ^^^^--^-^ , . -^"-"i ui /5/0, ana exchange l^r nr. rii-.,«'<. 1 his princioal SS48 7n 'vi, * . ^^^^*' ^^^ remitted i _ f I! ;' 188 I ,1, , ; i' ■; ^^^H ) ; 3. PERCENTAGE 72. My income is $1,900 annually, of which $500 is exempted frona taxation. What mcome tax do I pay if the rate is 1%? What IS my net mcome ? * ^° $1,000 at 6%. Fmd the percentage he receives on the average 74- If the pig iron of Canada is equal to that of foreign countries what must be the invoice price of the latter to compete with l; when our market price is $43 a ton. the specific duty being equal to 13Jo/o ad valorem, and the freight and charges $9 a ton ? wJv' Vh'T' '"'"^ T'^" *^ ^''' ^"'°""* °^ ^-40' ^"d gained soldtr. ' ^ '^^°^°' ^'""^ ''^'* '^^' ^°°^^ ^'""^'l h^^^ 1. /.' "^ ''^"'\'!!L^'^^' ^ *"'''' ^' "'"'^ ^^'^ "^^te"al as for labor ; had he paid 0% more for material and 6o/„ less for labor, hi contract would have cost hmi $3,637.92. What was his contract 77. The 6 per cents, are at 91J and the 7 per cents, at 102. A person has a sum of money to mvest which will, give him $7,000 more of the former stock than of the latter. Find the difference m income he could obtain by investing in these stocks. 78. A merchant had 500 barrels of fiour insured for i of its value at 2Ao/„, p,yi„g §75 ^^^^^.^^^ ^^ ^^^^^ per barrel must he sell to gain 25o/, of cost, as well as premium paid ? 79. What is the difference between a discount of 40% and three discounts of 20, 10, and 10% ? 80. A town requires $23,832.90 to meet expenses for the year • they pay 2j% for collection. What must be the rate if the taxable property of the town is $1,800,000, and an allowance of 3% is made for uncollectible taxes ? 81 Find the gross proceeds of a sale made by an agent charging 2|% for commission, 5% for guaranty, $17.65 for cartage, til 40 for storage, and $3.25 for insurance, if the net proceeds remitted amount to $1,714.10. «= "mea 3 At ^"/"'"'"^"^^ company took a risk at 2J%, and re-insured y ot the risk at 2%. The premium received exceeded the premium pa-d by $42. Find the amount of the risk. I X — a JiiSVIEW OP PERCENTAGE jgD ing to $1 750. What was h.s per cent, of commission if, by ai-rce- ment wUh the princpal, the conamission was to be 50"2^ of'the nei proceeds remitted ? ^° «S6st '^l;fj^'"^'%°^ ^ g'-^^^'-y l^^^in^^^^ for three years were first and dfe'thTr y"'^'"\^""^^^ ^^^ "'«% S'-eater than the fir t and the thud year's prohts were 10% greater than the second. What were the proiits of each year ? fh.ff ^^ Z^^^ ^'"'' "^""'^ ^ ''''''^ fe'"«^^ ^^'"'^•^ <^o^t S16.20 so a profit o"f t7 ' T"!,"' ''"/° "^ "^^'^^'^ J^'-'^^' ''-^ ^^'U "^-ke a profit of 10% on cost, allowmg 10% of sales for bad debts > at l4 7.r ''''''',"^ '"'"'"^ '^^'^ ^' ^^^^-^"d sell 125 shares t^::^:^::;:::^7 " ^''^- "^^^ '^ -^ -^ ^-' ^'^^--^ 87. A man whose income is $2,500, finds that his net income after paying the tax of 18| mills on the dollar, is $2,466.25. Hmv much of his income is exempt from taxation ? fh.!^* Three-quarters of the selling i.rice is equal to 5% less than cost Pind gam per cent, at which goods wctc sold. get $550 rent per annum for the two. I make 7% on the cost id%"r x^^h^. ' '- '-'- - ''- -^^ ^^ ^'^--v str for ^le'ttfn^ Tl' '"'"'''V ''''''" P'^'^'"^^^^^ ''' '''' ^^^^^ ^^^^al theren V ^r"' T"^ "''""''' responsibility for collecting the rent. On a house let at $38 a month for three years, he fails to IS 5M7.24. Find the percentage allowed him. 91. A building is assessed for |- of its value and the rate of axation IS 17 mills on the dollar. What will be the amount of the tax^ It costs $72 to insure the building for . of its value at ^ divid!*nd" ?T,of\ ^'"^' ^'^^^^y ''""'^ P^y^ ^ semi-annual sem'n'gliLril Z X Pefcent.^" ""'"^ ' ^^"^ ^° '°^° ^^ *^^ 190 I'KRCENTAGE 5% of (he »„,„„„, distributed to i™cl-i.ius. ai i jjj. i^is change in income hciim c'jqs <; j . n.uch 5% stock ho had, brokerage J% each way?' ^ ' "'" """ cent! .00/ ",t^'', """"'", ''"y' "''''''■■' "' "«•' «*« 0' lOO for 40 r;he':at b;Sh,-^t'L':^^ "™^- ™'" - -•• wh rh rn i>^^.50, was SI 38, find the invoice price of the goods p of 'Sio^."'"'"'' '^ "f, '"'' '''"" -^''^^ ^^^- taxed for all i„ excess of SoOO, incomes of less than $1,200 are not rated. If the rate REVIEW OP PERCENTAQB jg^ Of taxation is 19| mills, how much better off ,s the man who receives an mcome of $1,195 than one who receives §1,200 ? an'T' ^''"aof";.? ""^^''^ '''^^'" Soods arc sold are: "Net 60 days; 30/ ,o davs." A customer is invoiced on May 2nd with goods to the value of $560.20. and on May 12th pays S^ in cash. He desires to close the transaction by note takinrfuU tur^^for the unpaid balance. What wiii be the amount Tf the 105. The unclaimed dividends on a certain amount of stock which pays 6% per annum, amounted in 3 years to Sl.lS-^ The stock was sold at a discount f 12^°/ ,„ ^^s par value What sum was realized ? ^ "^' 10/0 stock at 125. How much was his yearly income increased ? cjno?^'^ ^T^ ^"^ '°' '""'" ""^''"^ ^^' sale at an advance of 500/0 above their cost ; but the agent sold the house at 20o/„ below the asking price, receiving S500 more than the cost. Wha1 is the owner s per cent. gain, after allowing the agent 2o/o for his services ? e2w'h,T''^''"'7"' ?"' ^°°^^ *° ^ '"^'■^^^^"t at a profit of 62i/o, but the merchant fails and pays 62^c on the dollar. What per cent, will the manufacturer gain or lose ? 109. A grocer by selling 6 lbs. of tea for a certain price, garaed .ri;t" y^7 '' ^"''""'^^ '^' P"^^' g'^^"& 5i lbs. for same price. What per cent, did he gain ? no. How many pounds of tea worth 35 cents a pound must be mixed with 14 lbs. at 40 cents a pound, so that 2bo/o may 4 made by selling the mixture at $4.41 for 10 lbs. ? ^o > "« ./oio/ ^"J"'"'^"^^*^ ag^nt takes a risk of $20,000 on a vessel at Zi /o, and immediately re-insures i of the risk at 2* <>/ What net premium does he receive ? 112. Two brothers receive by bequest $3,600 each. One's money increases at the rate of I20/0 per annum for 5 years, whUe he others increases at the rate of 10% per annum for the same time. How much more has the one than the other .? 192 PKBCENTAQE i I 113. Fred White sold tobacco at 5% commission; with the proceeds ho bought wlieat at 2%(()inini,,sion; his whole commission amounted to $:M5. Find the vahie of the tobacco and wheat. 114. A merchant marked cloth to make a profit, as he supjwsed, of 20 IKT cent., but tile clotli had cost $:i a yard more tiian lie had supposed, and he therefore lost 25%. Wiiat did the cloth cost per yard ? 115. A speculator bought stock at' a discount of 7J, and sold i at a premium of 3A% and the remainder at par. Allowing broker- age of 1% each way, how many shares did he buy if he netted $6,900? 116. A dealer marked his goods at an advance '^f 25% on cost, and, in selling them, he used yard measure | in. too short. His entire gain wa.s $26.50.. Fiid ost of goods. 117. An agent's commission wa. 4}% of the amount remitted to the consignor of the goods. What was his rate of commission ? 118. A farmer took the following insurance in the Perth Mutual : House, valued at $6,000, for J valuation at 1 J% ; barn, valued at $4,500, for § vtUuation at 1J%; live stock for $5,500 at |%; grain for $3,000 at ^%. What was his total premium? 119. I bought two articles for $150. I sold both, and lost 4% on what one cost me but gained 6% on what the other cost me. I gamed 1 J% on the whole. What was the price of each ? 120. The whole stock of a company is $200,000 ; the net gain is sufficient to pay 4% on the whole amount. The company pays 2% to ordinary shareholders, the bdance giving 7% on the preference stock. What was the amount of the preference stock ? 121. In the purchase of oats, wheat, and barley, a merchant expended equal sums. In the sales he gained 7% on the oats, 9% on the wheat, but on the barley he lost 21%; the total sales' were $2,212.50. What sum did he invest in each kind of grain ? 122. A commission merchant bought 40,000 bushels of wheat at 75 cents per bushel, which he insured at $20,000, taking a policy containing the "average clause." How much does he receive, the wlieat being damaged to the extent of $7,500 ? RBVIKW OK I'LUCENTAQE 193 €s he receive. 123. A township assissor rcimrfvc .,c f 11 n i« taxed on J vuluat.on, and r itiT ;,n ^^'1 '"'r'^ arc 364 polls taxed $i.75 each tl,e 1 ! '^'^^"^^*'"" = <»"••« $100. Find amount of t-fxr "^ ''''^'"' «'■'-* i>^'^ 124. An agent sold a eonsiLMiuieat of ^nrr.r 1 • coin.nission. II.- i„v.sted ,nrt . ^"i ' ''''^'■^'"^' 2^% of Hour at $6 50 per b.n.l ^le proceeds in 200 barrels cK'cluct.ng Si i:fL ; r^'JtheM;^ ^% ^"'""--» ^ -cl. after to his p.^.ipai t..e bi; ;:;tid':::.';;;s'"'f' >"' '^ ""'^^^^ he sell the sugar ? ^'^^ '^'" ^'^'"^ ^n^^h did -»vai,io, „„.i s5^o„;.,.t;ric„u:tr r?'.?''^ "■■ ""'^ ti.o .,abili,io.s .0 bo $27000 fATchhn ["-.7 Z"?' ^''""'' would he receive, the exix^nses n( ?!,„ *■?"*'■ ''"" """^'' , uie txiJcnscs, of the assignment being $500 ? a 1h;,'^,'J'"°„"'"''''™' ""'"•■' » eallons of „i„e worth SI 12) a' S, a ,^1 J' ;td ht S'^rle;!"- '""' ^'^ '"^ -'«"- sa"litg:Ta';::LT25V°r,"" r^ r^ «*■«»• * »' »- of goods'^ "He'„?" ^T " ' '■' *^""' '<"• -"^h. sold $235 worth eheC„ee"^r :,rdThfbo^r^ "^ -^' ^^ ^"o''- dollar on dl 'o^^ssSiT '"■"""''' "" '"'""^ '^'^ "' '« ^"^ "" ""e in^'metilVrLnnT,: ""??"' °' '■•^ ''-■ "' '-. ™.h dedueted" is colr,f„„l%rl f T"* '" ''°"^' '"''""^ of commission for Ju ng s W and T 'r"'"^"™'' The rate the t.a at 41 cent /'^'/^ '^ ''">""S 21%. He sells Pin^ i » , f"™''' """l ''"ys 'he flour at $4 a barrel Fmd h,s total commission and the amount of flour bought 194 I^ERCENTAQB 131. A commission merchant has goods consigned to him to sell, and, after deducting 2% for l)oth selling and investing, he finds that his commission for selling exceeds his conunission for buying by $6. Find the value of the goods remitted to him. 132. A person invested in 3% stock, and receivfid 5j% clear on his investment, after paying an income tax of 2%. What was the market price of the stock, brokerage i% ? 133. I mix 60 gallons of Madeira wine, costing $(150 a gallon, with 40 gallons of a superior quiUity, and sell the mixture at §4.44 per gallon, thereby gaining 20%. Find the cost per gallon of the superior quality. 134. A merchant bought cloth at $2 per yard, and sold the whole at a profit of $120. Had he sold it at 20% less, he would have lost $96. How many yards did he buy ? 135. A piano dealer instructed his clerk to mark a piano, so that by allowing a discount of 25% he would realize a profit of 33J%. By mistake the clerk marked the piano at $300, thereby producing a loss of 165% on the sale. What was the intended marking price and what was the loss ? 136. Find the total duty on the following at the rate of $7 per ton : 45 Steel angles, 3* x 3" x l", at 4.9 lbs. per foot, 32' long. 29 Steel angles, 2'' x 2" x i", at 3.2 lbs. per foot, 32' long. 30 Steel beams, 4", at 7J lbs. per foot, 38' long. 137. I hold some 3% stock. On receiving my first half-year's dividend, I invest it in the same stock at 93|, and my next half- year's dividend is $1,905. What amount of stock had I at first ? 138. A farm cost 3| times as much as a house. By selling the house at 10% loss and the farm at 7|% gain, $3,993.30 is received. Find the cost of each. 139. A merchant bought sugar at $3.75 per cwt., and paid for freight and other charges J of a cent, per pound. How many pounds can he sell for a dollar to make a clear gain of 25% ? REVIKW OP PERCRNTAOE 195 le rate of $7 in !he%ulf ^tTo/"^' *'•'»'• 7'-l' ^-"^ '"^"'O'i at J valuation in the bun at 1 J% ,,„ annum fur 3 years. The house was l„l ,IIv tZZy?" "''■ ™"' "" "" "^'' '"" "'-' «- "- '- °' 'he MI. \Vl.en milk is sold at the rate of 16 quarts for Jl there 142. A person invested $8,341 in 8o/„ ctock on the 7th day of Jaimary, at 109J, and on the I2th day of February of the same rind hKs gam per ce.it. on wliat the stock cost him. h 'il^' ^^ff ""^^^turinfr plant carries insnr.once as follows • On DuiKiiiig S12,000, on machinery $20,000, ind on stock ^K)(W) P^^yng ir/o premium. What is the net loss of 1 intfr'aT^ company ,f they pay the following losses: On machinery To valuation, on building f of valuation, and on .took a totafloss ? 144. A merchant buys a quantity of tea. and sells it again so as to gam l()o/ Had he bought it at lOo/, less and sold iHor tt tea co's t!"" ' ^''"'"^ ^"^"^^ ""^ '"P^'"'^ '"^*' ^^"^ ^^^t ^9n«^' !^ 'T ''"^' '^°'^ ^^ ^* ^"^ '^"^ °"t at 90. thereby losing !h! '-f r l""^''*' '" '*°'^ ^^ ^% P^^'^'"'"' ^"d sells again when It has reached 5o/, premium. With the proceeds he invests mvestment! ^'""^ ""^^ ^'''^^ ^"'"^^ ^^""^ **^^ ^^^^ 2.',f ; \ T'''.^"* ^"^' ^ ^^' 2 ^*- ^^ ^^"^^'-^^ f^^ «I. ^nd sells ^ gal. J qt. for the same sum. What is his gain per cent. ? 147. At what price shall an agent be ordered to buy potatoes at 2/0 commission that, after pajing 7 cents per barrel for transportation, they can be sold at $1.76 per barrel and net IQo/^ 148. A merchant invested $42,500 in dry goods. The first year he gained 20o/,. the second year he gained 12r/^, the third year he lost ie~%, and the fourth year he gained 5% Find the amount mvestcd in business at the end of the fourth year tb^ gam being added or the loss subtracted each year ? ^ ' ■ ' 196 PERCENTAOE ?l ;i:l sr^o/^ t ^'"^^ ^^^^^' ^°"^^* ^" '"^°^^^ °f o'-^nses f^-r $735. sold 20% profit. What was his net loss ? 150. I sold tea at a gain of 250/^; if it had cost 10 cents a pound t-ss, the same seUing price would have realized 50% gain. Find the cost of the tea per pound. /o S'""- 151. A man invested $5,500, a part in the 4 per cents, at 831 and the rest na the 5 per cents, at 102i brokerage J% in each case His totaJ income bemg $266^ find the sum invested in each stock 15^. At what price must goods which cost $66.69 be marked ata;™fit on|%r ''"°""' "' '*°''°' *^^ "^^ ^'"' "^ --^ 153. T. H. Smith, Toronto, buys of C. M. McCoUum & Co Brampton, 10 cases of eggs, 30 doz. each, at 14 cents per doz.'.' ^m\ T^^?- ^'""''- -^'^^"""^ ^ Co. ship with the eggs 5W lbs. of butter 300 lbs. of the butter sell at 16 cents, and the balance at 15^ cents per pound. The total weight of the shipment is 1.100 lbs., and the freight rate is 14 cents per cwt. IS 50/ m r I''"''- ^™'^'' commission for selling butte; IS 5/0. What are the net proceeds of the entire shipment ? of sit ^r 'fi"^ M°* ^ ^89.75 above cost. I reaHzed a profit ot 5/0. I sold another lot, which cost -.e same, for $1,848.85. What was my gam per cent, on the second sale ? tntlff* 1; ""^"u^'m '''^'*°^ '^'^^'''' '^ ^^^s^ed for $150,000. The trustees have built a school-house costing $1 800 '"^ ^"^ (a) What wiU the school-house cost' a ratepayer whose property is assessed for $4,500 ? (6) What would be the rate of taxation per annum on the whole section if the house were paid for in siVequal annu^ payments, without interest ? ^ 156. I invested in 7% stock at 78^ and, having received a ea hCns^cti^'^^^ ^ '' ''^' ^^^^^ *% '-^-^-n How rch id I i^virr "' "^ ^^"^^ ^^^^^^^^^^ ^^ ^2^2-^- a D?ofVnM n'o/ '''f^'i'^'S^' ^t the rate of 22 lbs. for $1. make. Imts whlf " ' '/?' '' ^"^^^ ^^°^^^ ^^^-25 and contain. -J90 lbs., what per cent, of the weight i : lo-t in retailing ? 50,000. The REVIEW OP PERCENTAGE 197 of its value I navYr 7^ ^ ''^^"'' '"^ ^'^^^^^^'^ ^^ |o/, on f the value of each hot ""' '"""" ^'^" "^^ brothen %J brokerage each way i% ? '" '^'"^' ^" ^"^°"^^' i6o. A sells goods to B at a gain of 12°/ anH R c 11 .u goods to C at a gain of 7Ao/ . c lid ^^ 7«/%,T .? '^"' *^^ '^"^« much did A pay for them .^ ""' *^' ^^°^'- "^^ 161. What rate oer rpnf Ar, - in stock at 83i. wh.^h p!;''/;/, anla" "dS7 "^ '"^^'""^ mc^f th*::!:?^*!!^: r™- '"' " '^^^ -^-^ -« » Find the cost of the goods? ^"^ ^""'- """ ''^™ '«% '»^- worfh'sf ner'n' ''7 "".^ '"^'^ °' '°''^'=»' '^^ch weighing 60 lbs on the tobacco'a'nd TTp<^^aZ^Z7^r """"' r "'^ ad valorem on cigars. '='S"=> ^"'^ 25% .he'ic.t::t:d7'" "' ^ '"/^ ^'-^-^ *•> p^^ "ir. -n f of^histtrktt'thir';' "^t ''°* ^' ^'^% P™**- Ate semng ^he pr^LT^ent. ir vard ;„; " In"' ^""P^'"'™ '° -d- had .tended. ,Z Z'Z'XeTy^rT °"'^ " " ^'^^ "^ deC et;:::: ::tir "%t:Ss vr- ^""r"™ '° «150, gas $125. janitor sTw fn T . f '?*• '■™' "•^'O' '«' numbefed 325 p„ to, S 0% ::^: :/^^; „,^|r :"™-"! 24% missed 5% of the time ni t , '^ ""* """• ^in^ of 5 days each. Wiat wl A', , 't°' '"'"' "'''' f" *> *'=='« missing'20% of trtiml? ■ ° ""* ' P"P"^- ""= <" 'I-™ in 6*^rt"i's" atm ' '^' 7'" "' '*' ^""^ '"^«'^'' '"^ P--* If -^-'^ 198 PERCENTAGE i, van. i68. If the cost of an article had been 10% less, the same selling price would have brought me 12% more. What was the gain per cent. ? 169. A house that cost $15,500 rents for $155 a month It is insured for $10,850 at |% yearly ; the taxes are 15 m^Us on an assessment of $12,450, and $346.45 is spent each year on repairs. What rate of interest does the investment pay ? 170. A retired farmer invested 40% of his capital in 3^% stock at 90, and the remainder in 4% stock at 95. His income was $698 per year. What capital had he invested ? 171. How many pounds of sugar, at 4^ cents per pound, can be bought by an agent for $897.75, after deducting $5 paid for drayage and a purchasing commission of 5% ? 172. A man sold 54 yards at a profit of 10% and 165 yards at a profit of 20%, and found that had he sold it all at a uniform profit of 15%, he would have realized $2.77^ less than he did. What was the cost price of the clot> ? 173- A corporation, having net earnings of $5,665, wishes to declare a dividend after reserving a working fund of $2,000. The corporation organized with a capital stock of 250 shares, but has smce issued 90 shares of preferred stock, secured at 6%. What rate of dividend can they declare ? 174. I bought a case of prints, containing 4,500 yards at 4 cents per yard, less 5%, and by paying cash in 10 days an additional discount of 2% was allowed. I sold at 5 cents per yard ; J of the amount, being in jobbing lots, was discounted at 4%. What per cent, profit did I average on the net cost, after allowing for freight and drayage $12.35, and taking advantage of the additional discourt ? ,r ul^\ 0^°"^^* °^ J- ^- ^a^^^son & Co., wholesale merchants: 15 bbl A Sugar, each 327-36, at 6c ; 10 sk. Rio Coffee, each 155-3 at 12c ; 9 ch. Young Hyson Tea, each 95-8, at 37ic ; 12 ch Japan Tea, each 76-12, at 40c ; 14 bx. Laundry Soap, each 74-14 at 4ic • 12 bbl Kerosene, each 45 gal., at 14c. I am allowed a list discount of 20 ,/ , and a second discount of 5% on the first three items. What is the net amount of the bill ? REVIEW OF PERCENTAGE J 99 176. A firm receives an invoice from EnHanH nc f^n ^ I ■ . • J"™'° '""=''• "'y '""■"« will be $20 less is BUo/r„::sis— ^'°'" '' "■>" "-"■'""■ 184 My agent in Montreal charges 30/0 for buying and 20/ IhtvTf' :fr ^'f T^ ^^""^^^^°" ^° 2% for'^u'ar^nteelt quahty of goods purchased. I make him a shipment of wheat with ins rucuons to sell and invest in a shipment of cotton to Liverpool. What was the selling price of the wheat, and whit was the cos^ of the cotton, his total commission being $1.03 1^? 185. I purchased 12 shares of C.P.R. stock at 112*, and after ece,vmg a semi-annual dividend thereon of 3^0/^, sold aglin a 135 brokerage m each case p/,. What rate per tent, per 'annum fust sirm::th: 7 "^"^-^^^^ ' ^^^ ^^^^- -- ^^ -y po^-^on 186 An agent charged me 5% for selling corn, and 2% for S m : ""T.^'^ ? ^°"°"- "^^ commission' amounted to $280. What was the selling pric3 of the corn ? 187. A cargo, valued at $45,000. was insured for $10,000 in the Contmental Insurance Company, $6,000 in the Liverpool cZrv T?"'' ""^ ^'''"^ ^" *^^ «^"^^-^ I---ce cL'!^nsu^n:er ""^ ^"' ""^^"^ ^^^ ^^^^^^^"^ '^ " ^^^^ .nf9irlT™fi°^"''''^^* '''"^^"^ ^'^ bushels of wheat and 24,000 11^. of beef, with instructions to sell and invest $2,500 of the proceeds in cotton, and remit the balance after deducting the charges. He sold the wheat at 62^ cents per bushel, and the beef TJ^^ r P'"''"'^- "' P^^^ ^^^^ ^°^ ^''^Sht, $24 for drayage. and charged a commission of | cents per bushel on the wheat, 2*0/ on the beef, and 2^% on the cotton. How much did he remit? ii[i , his commission i the following : tal commission. Duying and 2% or guaranteeing ment of wheat, nt of cotton to heat, and what Jing $1,031.25 ? 1 12 J, and, after , sold again at ent. per annum 1 my possession 1, and 2% for 1 amounted to for $10,000 in the Liverpool urg Insurance to the extent ng to " average ihels of wheat invest $2,500 fter deducting ;1, and the beef 4 for drayage, le wheat, 2^% id he remit ? SHORT METHODS SHORT METHODS IN MULTIPLICATION Aliquot Parts .n f?" ^«^^7^^^sho"ld commit to memory the following tables o thoroughly that the aliquot parts can be named without the least hesitation when the fraction is given, and vice versa. 1] = i Aliquot Parts of 10 3i = i 13 _ 1 = T _ 1 - «" 5 = 1 1 6i = 18| = i+ iiof 1 V or 125 =J 166f = I 250 = i 333J = J Aliquot Parts of 100 25 = J 31J = A or i + (i of i) 33J = J 37i .. f or i ■'■ a of Jt) 50 = i Aliquot Parts of 1000 375 = f or i + (i of i) 625 = I or i + (* of i) 62J = f or i+(iof i) 75 = 1 or i + (i of J) 87J = 1 or i + i + i 833J = 1 or h + i 875 = 1 or i + i + i Multiplication by AHquots To multiply any number by 10 annex a cipher. ,oo annex two ciphers. loZ^ '''"''' 1 ''?'''■ ^^^ ^""^^ ^^"r ciphers. 100000 annex five ciphers. IJ annex a cipher and divide by 8. If annex a cipher and divide by 6. 202 SHORT METHODS t '•' 21 annex a ciplier and divide l)y 4. 3J annex a cipher and divide by 3. 6i annex two ciphers and divide hy 16. 8J annex two ciphers and divide by 12. 12 J annex two ciphers and divide by 8. I4f annex two ciphers and divide by 7, 16| annex two ciphers and chvitle by 6. 25 annex two ciphers and divide by 4. 33J annex two ciphers and divide by 3. 50 annex two ciphers and divide by 2. 66f annex two ciphers and subtract ^ of the product 75 annex two ci])hers and deduct J of the product m annex two ciphers and deduct | of the product. m annex two ciphers and take | of tlic product. 62i annex two ciphers and take f of tlie product. I2i annex two ciphers and add J of the product. 125 annex three ciphers and divide by 8 133J annex two ciphers and add J of the product. im annex two ciphers and add f of the product. 50 annex two ciphers and add ^ of the product. f ! annex two ciphers and add f of the product. Ibbf annex three ciphers and divide by 6 175 annex two ciphers and multiply by 2 and deduct i of the product. * 1871 annex two ciphers and multiply by 2 and deduct ^ of the product. ^^ ^ 250 annex three ciphers and divide by 4. SERIES 6i Multiply mentally and add products : I. 480 by \l 2. 375 by If 490 by 2| 144 by 8 J 680 by 12| 660 by I6§ 870 by 3i 732 by 25 512 by Q\ 434 by 14f 3. 432 by 6| 528 by 50 588 by 33J 340 by 2^ 784 by 25 SJIOBT MKTIIODS IN MULTIPLICATION 203 product. roduct. "oduct. luct. uct. let. let. let. let. let. deduct i of the ieduet ^V of the J by 6f J by 50 i by 33J • by 2i : by 25 464 by 125 584 by 1^ 564 by 462 by 240 by 8^ 6f 7. 360 by 7^ 8. 1095 by 33,} 125 by 64 250 by 44 584 by 75 2163 by 3} 240 by 13} 432 by 6^ 440 by 37| 351 by 66| 494 by 12| 381 by 16f 482 by 50 864 by 33} 165 by 3} 840 232 320 360 450 6. 384 by 6i 532 by 14? 326 by 125 498 by 6§ 342 by 111 by 250 TO. 420 by 133} by 62} 544 by 125 by IS:^ 384 by 37} by 87} 468 by llj by 83} 364 by 14? To Multiply by Numbers from 13 to 19 inclusive Illustration.— Multiply 485 by 13. (a) Ordinary Method.— 485 13 1455 485 6305 (b) Short Method,— ^«^ ^ X 5 ^ ,5 ,,„y , IJ 3x8+1 (carried) + 5 = 30 carry 3 — — 3x4+3 (carried) + 8= 23 carry 2 6305 4 +2 (carried) = 6 SERHiS 62 Multiply the following mentally : 1. 346725 by 13 5. 435327 by 17 2. 647386 by 14 6. 210349 by 18 3. 58-630 by 15 7. 536274 by 19 4. 138629 by 16 8. 742976 by 19* '' i ■i, I: *"* SHORT METHODS Multiply the following mentally and total the results ; 9. 347 by 16 lo. 158 by 14 ii. 158 by 16 iz. 329 by 15 392 by 19 376 by 16 431 by 18 176 by 17 157 by 18 457 by 11 287 by 13 384 by 12 469 by 12 386 by 19 415 by 19 910 by 18 To Multiply by the Factors of a Number Illustration.— Multiply 95 by 32. 95 8 760 4 3040 1. 784 X 36 2. 891 X 72 3. 794 X 77 4. 485 X 99 5. 284 X 56 6. 187 X 64 Solution.— The factors of 32 are 8 and 4. First multiply by 8 and then multiply that product by 4. SERIES 63 7. 2956 y. 35 8. 2179 X 44 9. 4754 X 108 10. 2816 X 256 11. 4712 X 324 12. 2175 X 192 13. 21754 X 96 14. 17845 X 420 15. 78941 X 144 16. 29715 X 196 17. 49165 X 98 18. 97142 X 625 To Multiply by means of Cross Multiplication Note -To see the reason for any of the following solutions, work the question by the ordinary method, putting down every Une of the solution. When you do the same work by cross multiplication, you will see that it is simply a matter of carrying in your head the work you ordinarily put on paper. Illustration 1.— Find the product of 74 x 33. S0LUTION.-4 X 3= 12. Write 2 as the first figure of the product and carry 1. 7x3+1 (carried) + 12 (4 x 3)= 34. Write 4 as the second figure of the product and carry 3. 7x3+3 (carried) = 24. Write 24 to the left of the figures already xwittcn in the product, thus completing the multiplication and obtaining a product of 2442. 74 33 2441 suits : 12. 329 by 15 176 by 17 iLLl 124 62 384 by 12 910 by 18 768H sr e 8 and 4. First .t product by 4. ;4 X 96 15 X 420 1 X 144 5 X 196 5 X 98 2 X 625 ition utions, work the of the solution. vill see that it is •ily put on paper. le first figure of I + 12 (4 X 3)= 3d act and carry the left of the completing the 142. 3 4 5. 6. SnOBT METnODS IN DIVISION 205 Illustration 2.— Find the product of 124 x 62 SoLUT.ON.-4 X 2=8. Write 8 as the first figure of the procluct. 2 x 2 + 24 (4 x 6)= 28. Write 8 as the second figure of the product and carry 2. I x 2 + 12 (2 x 6) + 2 (carried) = 16. Write 6 as the third figure of the product and carry 1. , x 6 + 1 (carried) = 7. 'write 7 as the fourth figure of the product, thus completing the m.U- tiphcation and obtaining a product of 7688 Illustration 3.-Find the product of 2146 x 32 SoLUTiON.-e X 2= 12. Write 2 and carry 1. 4 x 2 + 1 (carried) + 18 (6x3)= 27. Write 7 and carry 2. Ix 2 + 2 (earned) + 12 (4 x 3) = 16. Write 6 and carJ-y 1. 2 x SX J'"''"'""'^^"*-^ (1x3)^8. Write 8. 2x3=6 pTSf:ct'o5'68^r'^""« ''-' '""'^P"^^^^^" ^"^ °^^^^"^"« - SERIES 64 ' 26 10. 75 X 35 : 44 II. 175 X 24 27 12. 261 X 73 46 13. 485 X 56 52 14. 697 X 28 75 15. 441 X 56 68 16. 247 X 87 47 17. 478 X 56 54 2146 32 « 68672 1. 74 2. 97 33 48 79 15 18. 19. 20. 7. 27 8. 79 9. 28 278 224 976 21. 7172 22. 1478 4196 2198 5164 ^3 24 25 : 87 : 58 47 26 55 74 57 26 To Divide by the Factors of a Divisor illustration.— Divide 9128 by 126. Solution.— Since the divisor is equal to 3 X 7 X 6, the division of 9128 by 126 may be accomplished by dividing successively by these factors. Dividing 9128 by 3 (or one forty-second of the true divisor, 126) produces 3042 (or 42 times the true quotient) and a remainder of 2. Since this remainder is left from the true dividend, it must be a part of the true remainder. Dividing 3042 (one forty-second of the true quotient) by the second factor, 7, pro- 126=3 X 7 X 6 3)9128 7)3042 + 2 = 6) 434 + 4 X 3 = 12 72+ 2x 3 X 7=42 Quotient, 72/!,% 56 206 ISilORT METHODS ■ M dividing one-thinl of the true divi.U-nd. tins remainder mu8t be one-third of the true remainder (4x3= 12), second part of true remainder D.y.d.ng 434 (one-sixth of the true quotient) by the remaining factor b. produces 72 (the true quotient) and a remainder of 2. Since 2 is the romanuler from dividing 434 (one-third of one-seventh of the true dividend) this remainder must be one-third cf onc-D=vcnth of the true remainder (^ X 3 X 7 = 42), thirtl part of tlie true remainder. Add the several parts of the true remainder, obtaining 56 as the total true remainder. 1. 25380 -r 36 2. 178584 ~ 48 3. 23741 -r 42 4. 43165 -r 64 5. 41765 H- 63 SERIES 6s 6. 31279 -f- 72 7. 43827 -=- 84 8. 19375 -f- 125 9. 41643 ^ 135 10. 17496 ~ 147 11. 43716 4. 168 12. 29373 -r 81 13. 41658 4- 45 14. 23725 -r 96 15. 47916 4- 648 if :i SHORT METHODS IN DECIMALS Approximations Suppose that the exact result of an operation is 27.47186. For ordniary business purposes three places may be sufficient. Reading our result to the nearest figure, and retaining but three places of decimals, it becomes 27.472, which is an approximate value of 27.47186 correct to three places of decimals. Short methods in decimals are, therefore, attempts at getting approximate values to a certain number of places. Addition («) 72.142756 15.2176 42.71594 ('') Solution (a) shows the addition carried out complete. Solution {b) shows the solution correct to three decimal places. This is done by writing each addend, retaining only three places of decimals. The addition is then performed in the usual way. Subtraction may be handled in the same way where an approximation is sufficient. 130.076296 72.143 15.218 42.716 130.077 ling 56 as the total hows the addition an approximation SHORT METHODS IN DECIMALS 207 Multiplication ILLUSTRATION.-Multii.ly 171.2478 by 8.4712. retaining only 4 decimal places. ^ J' (a) 171.2478 8.4712 3424956 1712 478 119873 684991 13699824 46 2 1450,6743 6336 Ans. {f>) 171.24780 21748 136998240 6849912 1198729 17124 3424 1450.67429^ 1450.6743 Solution (a) shows the work carried out in full. Solution {!>) shows the work contracted, so as to give an approxi- mation to four decimal places. Rule Reverse the multiplier, plaa.ii: the tinii's fiirurp /A^v^«/ j- ,, urulerthe decimal tolhich I is .W/ J /o^i^^i'r^ tS should be one place further than an accurate answer is rZired) If the multxpher does not contain a whole number, place tlefmlhhJJe duectly under he next figure to the left of the LimaltXtkhYli^ intended to extend the work. Multiply as ir ordinarv ZZ'2r I- ignoring all figures in the ntultipiicind to th rg^^^^^^^ « used as multiplier. Arrange the several prodZsiVZ Ztes on the extreme right are in line vertically. Add and point off the mnZl of places to which the work is extended. i' '"*^U *«e mmoer SERIES 66 4.3678 retaining 2 decimal pl&ces. 36.275 41.3075 17.0036 .43261 I. 2. 3. 4- 5. 6. 700.375 7. .374825 "" '^^^noo.. retaining 3 decimal Jiaces! ^ "Sfrfo retaining 4 decimal places. .003647 X ■^oioS ""^taming 3 decimal places. noS '■*^*ain'"g 4 decimal places. iooo?^ retainmg 3 decimal places. .b9J847 retaining 5 decimal places. Division forms. "^'litmte™'^' ^^'' ^"°^^'"* ^'^^ *"^' °"^ °^ ^^'^^ different (fl) A whole number, with or without a decimal part. M ^ ^''•"'^ '" "^u -"^t *t' ^''* ^^^^^ ^^ a significant figure ; or (c) A decimal in which there are one or more noughts between tne decimal point and the first significant figure. These three forms may be illustrated thus : i„ ,. ... , ,^ 45.6 or 456; .456; and .00456. in dividmg by the contracted method the fust thincr +,^ k» a^ a ^ • in the quotient, how many figures will there be in tl e 3.^ be decided is. many noughts will there L \o the rlghf'of the Secrmri ^oint ™^''"' °' ^°* X-a 208 SHORT METHODS Pi ' I Thus, in dividincr 3754 26 In. i-iOKA u -n . thus ,„„„ip,;„, .hen^Lrj '. :; ;t ;r°,s,v''t'7' r" "'™"' the quotient. The q„cs,i„„ then become" 3 75 Z\ T'. "'" """' that the quotient take. il„. („,.,. ■ T T . ~ ''• '" "'''"'■ " » seen deoi,na. pi. a^Vt'^:!;^ :°™ '1?^ "'"" " °"° "°"^"' "='""""■" number, but takes the formTn whin f^" ^"°*''"* '°"*^'"' "° ^'>°1« Having decided how many figui-b there will hA i„ +v,^ x- . arrange our divisor to contain the sime numb r o fif "'"""*' "' "'" :t;-t°irt;r:„-r;^^^^^^^^ ot agnres in the aiviso. we wiU add nought, tol": ^^.h^nunr °""*" •avuig adjusted the divisor, the next step is to adjust the dividend £«»:"":*■ „"a Te'd""'""" "" "" '"" '°°"^'> o*"- ■» "■' <"'SS to n, „, .: th ....^l; ""■ "'"'"« "" ""■'"■ ■" ™PP'^'"8 noughts i:"^''- 2 'ii>isted both v.isor and dividend h- vill HH-idP »- : > a- d,visio„. excpt «.«. instead o, bringing aown'a C ^^om^ dtS t there will be isrcKunliiig the in the quotient Its to the right ned in 32, and. rted after it in I the dividend, 1 32498. ber in the quo- point and first tained in 3675. essary to shift J and divisor, wil not affect hich it is seen t between the ivhole number of tlie decimal • in the whole mber, we will be correct the lins no whole n the decimal liber of figures between the k'hole number wint and the ill simply be tiect, ^/e will Uegiiiuing at lesired in the :ient number liber. he dividend, the dividend ing noughts i ill ordinary he dividend SHORT MBTUODS JN DECIMALS 209 each time we divid conUjiuing t^o .o untd t.i: dS^^ a^;- .^Ld'^ ''''' °' ''' ^*^^-' diviso°" ino^i,l:r;:h^::s::;^Li:r'"" *'".'''^""^' p"'"* ^-- <'- ti^c ...iv.,ion what for„urn:oUrn7f:;r; ""',""" ''^'"" commencing rolnt in the quotient in itsCl" place S^''th"","" 'f " ^'^^^ "^•*^'"-' disregarded. ' ' ^ '^'' ^° *'"^ decimal points may be thatX«:s:'r^: ;:!;,;: ,rr ?; "^"' ""^^ ^'^^^ ^^^^^ ^»^- is correct ; since f the Zun T T '^'''^ °' '''" contracted quotient answer co'rrect i^' o^^ .!o::\''7:TlT 'u r *" ^'^'^" ^'^ ^"^^ ^''« contracted quotient. ^° ''''^'■''' *° *''° '^^^ fig"'- ^^ the Illustration.— Divide 714 296'^ hv id'iA-j I'laces of decimals. ^ ^^"^^ """"'^ ^^ ^°^'- SoiUTioN 1.— Ordinary Metiiod H.367)714.2965( 14367)714296.5(49.717SH 57468 Solution 2.~Contracte(l Method U«H;fH0)7 1 42965(497 1 793 5746800 139616 129303 103135 100569 Alls. = 49.7179 1396165 1293030 103135 100569 Ans. = 49.7179 2566 1436 1130 1001 129 126 3 25660 14367 112930 100569 123610 114936 86740 86202 places of d»i„,al,,we S ake it ^,,0 fivTS " '""" ""'" '» "»" Since there are only five figures in fh, ,i,„' ■',; ^ ^ '"° divisor. d.v,.or. So »e p^oceea „iU. o„. div^ion/auLX'::: ^.^JT:^ 210 SHORT METHODS I, ) each time. The quotient obtained is 4971 7Q'1 • -,„/, our quotient 49.7I8O '^ ^ °' '"°'^'' ^' ^°"^^ ^^^^ ^^de Divide SERIES 67 I. 2. 3. 4. 5. 6. 7. 8. 27.3782 by 48724 by 8.47326 by .8487564 by 478.325 by 8972.436 1 4.3267 correct to 3 decimal 1.003675 correct to 2 decimal 75.43 correct to 5 decimal .075637 correct to 3 decimal , - ^^J^-^Sf correct to 3 decimal by 756.3452 correct to 4 decimal by 1.007633 correct to 6 decimal Q«79Q K AAn^U^. wiicuL 10 D aecimal .953728 by 44.73654 correct to 3 decimal To Reduce British Currency to Canadian Currency Commercial Par 4b a case the old Hahfax currency of $4 for /I 20 rpnf« ^1 ^f shUhng, and Igc (^, of 20c) for 1 penny. ^ ^^ °^ ^1 at par calculated in this way gives : $4.00 + ^ of $4, or .80 + T*a of SOc or .06| To find the value of ^15 3s. 7d. we proceed as follows : 3s., at 20c each .... qq 7d., at Igc each [12 places. places. places. places. places. places. places. places. at by taking $1) for 1 _L , . .^r. $60.72 + * of $60.72== 12 14 + A of 12.14= 1.01 $73.87 SERIES 68 Change to Canadian currency : ;^ s. d. 1. 72 5 7 2. 47 15 4 3. 57 12 6 4. 195 17 8 5. 240 6 9 6. 7. 8. zo. £ s. d. 475 18 10 547 8 5 297 19 II 547 JO 1 679 13 3 there are to be )ff from the left ve were to have St figure of the ould have made imal places, imal places, imal places, mal places, mal places, mal places, mal places, mal places. ncy at this by taking i of $1) for 1 SHORT METHODS IN PERCENTAGE equivalent^actions should be'lhorouX ^earned °"°' *'''' "'^' ''''" 212 SHORT METHODS 'I m i : ■■; ■ H . ■ ' I Find 1. 20% profit on 2. 25% loss on SERIES 69 4% 4 5^ 6. 7. 8. 9. 10. II. 12. 13. 14. 15. 16. 17- 1 8. 19- 20. I2r/o m% 37i% 66§% on commission interest on duty on discount on premium on _ advance on 6^% brokerage on 31i% assessment on 87^% dividend on 22|% tax on 28f% rebate on 7t3-% allowance on 75% of the value of of the value of of the value of of the value of of the value of of the value of 90% 31i% 43|% 50% 125% $ 25, 64, 6. 12, 80, 9, 32. 48. 16, 27. 21, 26, 24, 70, 86, 374, i 7.50 25, 36, 75, 96, 36, 72, 32, 27, 64, 80. 72, 45, 35, 39, 32, 110, 475, 228, i 375 45 76 125 160 72 60 48 75 256 144 108 63 56 78 28 40 373 937 2 In addition to the methods sue^sted bv thp fa hi. dividing by 4 to get 25% dividmg bTso gef 3340/ and sT " number of percentages can be rfpid'ly cllS^trt TooI base. In Mhng, the student should cultivate the habit of wridnt he percentage on the paper direct, without carrying the worf to a scratch pad and back to the bill. ^^ ^ Illustrations 1- 10% of $747.25 = $74.73. Thus, to the ^^s:^::':::'^:::^:::^^ "^^"^' ^^^^ ^'^- ^^^^^eth.. 2. 20% of $747.25 = $149.45. See first what 10o/„ would be. 874.72.'; Tokin„ .wicp ^hi. « the nearest cent, .ve have $149.45. ^ ^^ ^^^ ^8^"™ *o 45 76 125 160 72 60 48 75 256 144 [08 63 56 78 28 40 73 37 2 ST e, such as id so on, a the 10% of writing the work 25. If the altogether. figure to SHORT METHODS IN PERCENTAGE 213 3. 30% of $747.25 = $224.18. Again. 10% = $74,725; 30o/o is three times the amount of 1224 18 t:i;^ Sen""'- ^"°''°- '»"■ «»''»■ " '»°''° »' -^ "-i' -y i 4. 2J% of $747.25 = $18.68. As before, 10%= $74,725; 2^ is ^ of 10%, J of $74,725= $18.68 ' In other words, see 10% first and divide by 4 »n..h°''''r^" P^^f "^ *^' '^'■'* ^'^""'^ '^^ " the division, if carried out 5. 3J% of $747.25 = $24.91. See 10% first and divide by 3. 6. What is 36% of $2,500 ? i. nt «-? «nn .OAA Solution.— Since 36 times 25 will give i of $3,600= $900 the same product as 25 times 36, 36o/f of SlfiOrt 9=:o/ • 1 , . «2,500 will give the same result as 25% of result ^^/°''*°^*°"'"b«'^ therefore,iof $3,600, or $900, istherequLd 7. What is 16% of $12,500 ? i o, .,s,ooo = ...000 .a.f;=Z'f.r"L7e ,"lr,at m% is , J o, ,,6,000 . t^!^'^^^^^,"''' °' '"•°°°- 8. What is 24% of $37,500 ? $94 000 X a- Monr. Solution.-24 times 37^ will give the $-4,000 X i _ $9,000 same product as 37J times 24 ; hence. 24% 37i% is I. I Of $24,000 is .^m'^rT.llX^lZu' '''''\'' '''''''' SERIES 70 Calculate the foUowing mentally, giving result correct to nearest cent I. 2. 3. 4- s. 6. 10 % of 10 % of 10 % of 20 % of 30 % of 40 % of o/ 358.78 182.34 526.45 346.28 156.97 358.79 7' 5 % of 342.87 8. 2^% of 1,368.74 9. 3J% of $ 438.73 10. 1|% of 8,326.75 11. 25 % of 3,827.49 12. 3 % of 1,437.52 13. 26 % of 2,500.00 14. 18 % of 12,500.00 IS- i% of 3,742.85 16. 33 jo/^ of 3,284.95 214 SHORT METHODS W> ^ In the foUowing questions calculate discounts mentally • 17. What is $928.65 less 10o/„, iqo/, ^nd 50/, . 18. What is $396.17 less 20<%, 100/^, and 2o/o p 19. What is $432.50 less 150/,, 3^/, and 2W^ p 20. What is $342.16 less 30o/„ 30/^, and ^o/^ p 21. Wliat is $1,754.64 less 33Jo/^. 12^0/^, and I60/ . 22. What is $5,438.79 less 25o/„ 400/,, and 2*0/ p 23. What is $1,927.46 less 2O0/0, 14o/„, and *% ^ 24. What is $398.79 less 30o/o, 6o/„ and ^^ ? 25. What is $1,827.54 less 12^/0, 6^, and ^o/^ ? The Six per Cent Method of Calculating Interest -...percent., and tl:;.-:^^^^^^^ changed to the basis of a 365-day yeTr ^ ^'''' '"^ '^'" Then, the interest for 360 days bein^ fio/ nf +>,«. o, xu • for 60 davs is 1 0/ ^f +h. . ■ "^ *^^ ^""^' ^^^ interest -Ply ^: ti^i^^tr;;^xi^i- ^^ '^' --^ The interest for 60 days is taken as the basis of the operation. ILLUSTRATION.-Find the interest on $540 for 49 davs at fio/ calculated on the basis of 360 days to the year. ^ ^°' The interest for 60 days = $5.40 The interest for 30 days = S2 70 m,u ,. . The interest for 10 days = $0 90 Sn th' T ' ""'' *™' ^^ '^^^^^)- The interest for 6 day = $0 54 oZt'Ju '' '""'^^ "^ '"■■ '' ^^y^)' The interest for 3 days = $027 oZtu "' "'"''' "' '°^ '' ^^^^J' ■fr-r- ; ^^ *y;^7^(One-half as much as for 6 days). The interest for 49 davs — «!4 4I /« T~ y days- $4.41 (Sum of^;^^^;;;;;^^^^^-^^^;^;-^^^^ 6 days, and 3 days). It will be noted that in the illustration above wp -. . - , ^ntally ^? rest om the fact s computed Id be at the nethod, the r, and then the interest 100, which operation. •ys at 6%, 5 halved). 30 days). days). ays). s, 10 days, the interest ng, in each SHORT METHODS IN PERCENTAGE 215 case, a number of days which i„o^t i ^ got the sura of the interest for 20 days (, ot 60 dav„ B H *"' ,? '"""" '■"' and 2 days (J of 6 days). Had it been 57 d!l '' ^?' "" "' "'' "">'*'■ of the interest for 30 days « of TO d^vs. 1, nf' T! T"'" ''"■' S"' "" ""■ (J of 60 days), and so on ^ '' ''*^' " °' ™ "^J")' '"I '2 days have taken 30 days (! of 60 days) STat iTlT^^ f 1"" '"" "" -"iel" or J of 60 days), and 1 day () i 6 day! • I l"'.^ "">" " °' * ■"»" 2a days, 5 days ,, of 20 ZZTixt ^oriti:';;: i:^!^^'- Having got the interest at 6%, the next step is to change it LI ^\T^' '^ ^* '^^ ^^^^" ^^^^- Thus, in^ur illustraC had the rate been 40/0, we would proceed as follows : '"'''^*'°"' Interest a t 6%= $4.41 Interest at~^^-^:^5 (Ms much as at 60/A Interest at lo/„= /735_(j^as much as at 3%). Interest at 4%= 2.94 Interest at 6%= $4.41 Interest at 2%= 1.47 (Sum of interest at 3°/^ and at 1%). Or ^as much as at 6%). Interest at 4./,= 2.94 (Inte-;;Slr6%7to;;;;njl%r days is bniU t, lo'^ SZZT^.toXT"" '" '"^ «'™ """'^- °' of a 365.Ly year. ^^° " '" "'" " "°°''' "^ "» "■= '»«'» X — 3 216 SHORT METHODS $540 X ^U X 3^»a at 3I5 VaTtTtTe ye^ ^ ^^ "^^^ ^'^ ^°"^^^ ^'"°"°* °^ ^'^^--^ -''-^^ «540 X 1J5 X g^»5 •.K^l!!n^**l? ^^P'"^^^^" <=^° '^ got from the former one by multiolvine ;t by Ml The 360 in the numerator will cancel the 360 in the de^oZator throwmg the 365 into the denominator. Thus : aenommator, the bLro7a'36o7ar '""I' V° ''""^^ *'^ ""°""* "* ^"t^^* -^^^^-^d on year we m.L t ^^'^I *° ^^'^ ^'"°""* ^^'^^""^^ °" ^he basis of a 365.day SipT;irbTr" '"°"'^* '^ ^^*= "• ^'^^^'^ ^^ ^^^ ^^"^^ ^^^'^^• the iToi.lt^T^lll:' "^"'^'^^^ ^'^^ ^-°-* 'y ?3 is to subtract ^ of at /^^^'^^^^°N-Fi"d the interest on $397.85 for 223 days stepf rtrsoTulr:" '' °'^^"^' ^^^"^ ^^^ ^-^°'"« ^^^^t there are three ''' "^bas-: if aT6;ir;e:r" '°^ ''' '-'- ^^ '"'^' -^^°-^ - *^« (6) Change the amount of interest to what it would be at the given rate. '' '"r oraT5r;;:r '- ^""^ " -^^ ^ ------ (a) Interest for 60 days at 6%= $ 3.9785 Interest for 180 days at 6°/ — 11 Q-iqc /1 a- x , ,,^ IntPr<^^f for ' __ uoywt^ o _ .1989 + (j^ of amt. for 30 days). Interest for 223 days at 6%= ~l4Jm + (b) Interebt at 6% = 14.7867 + Interes t at 1%= 2.4644^ (j pf amt. at 6% ) Interest at 7o/„= ,7.25!I + (amt. at 60/, + 1;^^:^%^ (c) $17.2511 - ^ot $17.2511= $17.2511 - $.2363 = $17.0148= $17.01. the following :erest reckoned •y multiplying ; denominator, t reckoned on s of a 365 -day 2 same thing, subtract ^ of r 223 days ere are three koned on the le given rate, coned on the 60 days). 60 daysV 30 days). 30 days). SHORT METHODS IN PERCENTAGE 217 auow"troiSi puce?p^t'th"'"^^« ""^'^^^ '° "°* ^-^« --^y. enough to give ^^^tj::;::i:z:-:^::- ""'^^^' - ^^^^ allow30daystotherf.on£':„;t J X^^^^ ^""^ -* ''--• if a month is considered as 30 dayrtt yet^uM t "i^o'da^r""^ ' ""^^• an exaTnumbrr 7^'J^^ '^^ T ^^^^^ >'--- together with deduct ^ from the whdl'amount '' " ''' "'°'^ ^^^"^ °^ y^"' -^ SERIES 71 By the six per cent, method find the interest on Principal. Time in dys. I. $450 920 630 385 875 1,450 1,385 429 1,500 325 1,280 850 338 540 2. 3. 4- s. 6. 7. 8. 9- ID. zz. Z2. 13. 14. 33 48 58 226 152 47 269 88 59 125 143 79 148 329 Rate. 6% 6% 5 4 6 7 6 5 3 /o /o /o /o /o /o 0/ /o 17- z8. 8% 4 % 3 % Prirjcipal. 15- S 385.60 z6. 438.15 926,50 457.29 837.45 187.28 1,368.19 436.73 15.28 187.65 348.27 1,425.36 129.37 19. 20. 2Z. 22. 23. 24. 25. 26. 27. Time in dys, 32 206 111 87 289 156 43 251 117 17 46 325 293 Rate. 8% 6% 4 % 3% 3i% 9 % 5 % 4 % 8% 5 % 3i% sr/o 6i V 28. $650 from May 13, 1907. to Sept. 18, 1907. at 6°/ 29. $3,260 from Jan. 9, 1908, to Aug. I, 1908. at 70/7 30. $346.75 from Sept. 3, 1907, to May 10, 1908 at 40/ 31. $293.26 from April 12. 1907, to May 28 1908 at W 32. $914.68 from July 27, 1906. to AprU 13.' 21 tt SV 33- $536.27 from Nov. 23, 1903, to July 11. 1907 'at 3/^*- 34. $1,368.45 from Dec. 14, 1904. t'o May 25 1^8 a 4% 35. $459.38 from Aug. 17. 1902, to Jan. 3. 1^7 ^ 5 / " 36. $98.67 from Oct. 30. 1^5. to July H.l^a a^ ot " ■If 218 iH.i SHORT METHODS BILLING A Bill or Invoice is a detailed statement of merchandise sold or services rendered. A bill or invoice of goods sold usually gives the following information : Place and date of the sale ; the names of the buyer and the seller; the terms of sale ; the identifying marks If any, of case, package, barrel, etc., in which gooas are shipped the quantity, name, and price of each article ; the extension of each Item ; and the total amount of the whole bill. A bill or invoice is receipted by writing at the bottom the words, Rece.vc.d payment," followed by the signature of the seller of the goods or someone authorized to sign for him. A Credit Note is a bill or invoice used as an offset to a previous bill or invoice. Thus, where goods are once billed and part of the goods are returned, the credit note is intended to show the Items which were returned and for which credit is being given. A Statement of Account is an exhibit of the dates and totals of the bills or invoices for a period, say of a month. A statement may be receipted as a bill or invoice is receipted. The Work of Billing requires good writing and quick and accurate hguring. There is no commoner introduction to the general work of any office than this w.rk of billing. Any young man or woman contemplating engaging in office work should, therefore make certain that the requisites for success are thoroughly mastered The rapid figuring will require not only a thorough knowledge of he simple rules, vulgar and decimal fractions, but also the application of many short rules, which will be found to both quicken and simplify the work. A bill clerk should also see to it that in every case possible extensions are made direct, without the necessity of working the extension on a scratcli pad, and then transferring the result to the bill or invoice. We commend the preceding work on short nUes and business methods to the most earnest attention of all students. %. . . 7 ... 'I V-... ;handise sold usually gives ; the names ifying marks are shipped, ision of each bottom the ture of the m. ) a previous ind part of o show the ig given. and totals L statement id accurate' he general ng man or therefore y mastered knowledge t also the th quicken it that in i necessity ansferring preceding at earnest BILLING A I First quality. Acct Account. J^V ^6^""t- 7'"' Amount, ^Pr April. ^'■'■, Arrived. AssM Assorted. Aug August. IH Balance. §•? Barrel. ^'^^ Bundles. gds Boards. Bp Bags. g.^ts Baskets. gr Black. S'^ Bales. ^°t; Bought. ^rot Brought. S" Bushels. B^s Boxes. ^ Hundred. X°V^^ Cents. ^^gU Charged. ^^ Chest. ^° Company. C.O.D • '• Co'lf^ction n ,,-, ' * tli'livery. ^old Colored. S:°'" Commission. y Creditor. ^^ •;••,•, Cases. Cwt. . Hundredweight. Commercial Abbreviations d.... Dec. Dft. . . Disct. Pence. • . December. ..Draft. ■ • • Discount. Do., ditto, or " I "^"^^ rv I same. ^°2 Dozen. ^'■•••- Debtor. Ds. or da Days 219 Ea Each. li.tvu.ii... j onussions „ ( excepted. E:^oh Exchange. Ex Without. JlP^ February. I'f'"^,:-:. Figured. i .U.B..lTee on Board. K°/; Folio or page. i,^t Freight. ■'*' Foot or feet. ^al Gallon. Sf-orgro Gross. ^uar Guarantee. Hlf. Half. JHlid Hogshead \-^ That is. :" Inches. ^"^ Insurance. Inst. ...Present month. ^'^*^ .Interest. Ja° January. K-of Jun Junior. J-bs Pounds. Ledg Ledger. ^l Thousand. J'jar March. Mdse.,.. Merchandise. Mem... Memorandum. Messrs , I Gentlemen ,, I or Sirs. Jf°--- Month. Mr... Master or Mister. Mrs Mistress. V-. At. ... Account. Cents. • • • . Care of. Check mark. Commercial Characters ,?••.• Dollars. .Ditto, or the same. /o Hundredths. "/v New account. ■tP Number. Net. Without discount. N.B. . I Take parti- AT ■ (cular notice. No. or:j^ ...Number. Nov November ^ct October. Oz Ounces. ....Page. • • . Pages. Payment. P Pp Pay'tor^ Paym't ) Pd Paid. Per. p., or 3ft \ ^y. or D, (by the. ^^Ss Packages. PO Post Office. P"" Pair. Prox Next Month Pf Pieces. Pts Pints. ^5 Quarter Qts Quarts. Rec'd 1 . c Received paym't j . { payment. J^e^t Receipt. I^I^ Railroad |- •■ Shilling. S'l'Pt Shipment. ^^tor Storage. ^*-'' Steamer. Sunds Sundries. Super Superfine. J}:^^ Tierces. L"* Last month. Wt, ■ Weight. Yds. Yr.. .Yards. ..Year. £■ X Old account, • • . I'er, or by the.' . . Pounds sterling. . By.as 7x8 inches. 220 SHORT METHODS Commercial Expressions 7/4 English shillings and pence are often written this way. This character stands for 7 shillings, 4 pence. Tune 14/17. "^^^ nominal due date and the legal due date are often expressed as inaicated. Toronto, 4/11/08. ^ date is shortly expressed ao indi- cated, the illustration meaning April 11, 1908. Some prefer to write it 11/4/08. 6» yds., 72 yds., 8^ yds., respectively mean 6J, 7^, and 8| yards. * 15" bushels means 15 bushels and 10 po.nds. 20* pounds means 20 pounds 6 ounces. 15 doz., -A, ^ 2 bbk $8' $9' $10 240 - 18 250 - 20 or 2 bb,s.f f means 15 doz., 5 doz. at $8 a dozen, 5 doz. at $9 dozen, and 5 doz. at $10 a dozen. means 2 barrels, one of 240 lbs. gross weight, from which 18 lbs. is taken for weight of barrel, and one of 250 lbs., from which is taken 20 lbs. for barrel Terms : 5/30, 3/60, n/90. On an invoice this means that if paid in 30 days 5% is allowed ; if paid in 60 days, 3% is aUowed ; and the bUl must be paid, in any event, with no discount in 90 days. ;e are often icter stands id the legal LS inaicated. sed ao indi- ining April d 8| yards. 58 a dozen, doz. at $10 ) lbs. gross s taken for )f 250 lbs.. for barrel sans that if is allowed ; :ount in 90 r. Miiiut mm» flmai ^ « « «. MUMUnto. .« r«CTOIIVi il >»> II *UIC( ITIICtT Toronto, Ont, SoU to i...*^v,^MM i>9*laa,. W6 ^ C St. , TCRMS 10 OAVS NET, Vi |0 OAVt T«ut nuiT cautnia rnuiTa T«Ui MuiT lUVOKlNa MTKMT* ^JP'iijBo, /pfje. city. •riLf MT Put n THi.n 0>v> »| lutjict'to •UM> Mot V/ITHIN FIVE D*VJ AFTER RECEIPT Of OOODS COMPANY. AU OTHER CLAIMl MUJT ec MAOe 4 1 7 s/ie a/is Oals. Plo«appi« " RMpbcrry * Claret Sof, lat Frapp* " Cherry. Or. " Kupbarry /? - "harry. Whola (1 OMt) lea Creaa Sowaer Sal. Sxt. Tanllla " " iMon !•■■ S03( Specimen Invoice Date Sold to Aooncss VIA _( Ttrmi CANADA CYCLE AND MOTOK CO.. ....22Zy.A,^,^ TORONTO JUNCTION, ONT dJj:v.^ -<^^*« LIW'TEO /S So /3 s /Sltrv F • A. Miles, 536 Dundas Street, Toronto, Ont., sells the following bills of goods : 6. To J. J. Walsh, 45 Kendal Avenue. Toronto. Ont. 30 pr. Sash D. C. R.. at $1.50; 137 pr. 1| Sash, at $1 ; 40 Cellar Sash, at 40c ; 24 Casements, at 50c. 1 2 A 3 5 . 30 days Lace, 11 1 )c. AUover :. Guipure, :. Guipure, c. Veiling, t. Terms, 12 yds., at 14i yds., , 22 yds., , 13| yds., , 23i yds., ,23iyds., 30 days ► yds., at yds., at ., at 75c ; pc. Lace, Mms, net , at 18c ; , at 18c ; at 25c; at 15c ; ., at 9c ; at lOic; he ; 1 pc. following ; 40 BILLING 225 7. To F. Armstrong, 296 Berkeley Street. Toronto. Qnv. ^,7JV " o~'^ ^'"^•' ^' ^'^' '^ P'^- 2 X 6^16 Hem at at m' fo'"'':'~^'^^"-'^^ ^'^' 26PCS.2 x4-16Sem at ^17.60 , 10 8-m. Cedar Posts, at 30c. I'ucs 2 X r'T« r'^ ^""^'^"^ ^"^""^' Toronto, Ont. .f ft,r, o"" "'"'•' ^' ^^'^■^^' ^2 pes. 2 X 4-16 Hem rail i-me at 8c , 16 ft. Bottom-rail Pine, at 5c ; 24 ft 3 x 4 NoTE.-Balusters. Cove, and Parting Stop sold by the hundred. Canada Paint Co., Ltd., 572 William Street, Toronto Ont sell the lollowing bills of goods : -^oronio, unt.. 9. To Messrs. Evans & Co., Oshawa, Ont. 100 lbs. Imp. Green, Lt. Dry, at 9c ; 1 28-lb. box " D^' Ultra- B.B.C. B.B. Ven. Red. 400 lbs., at 3c. j , i l^'hZ'' nT/nl'^I'rT.r <^C°-'Yonge Street, Toronto, Ont. 2 bbL. Boiled 0.1, 468 lbs.-69. 504 lbs,-81, at 60c per gal. Oil is figured at 9 lbs. to the gallon. H. P. Eci:..7.DT & Co., Wholesale Grocers, Cor. bcott Streets, sell the following bills of goods : II. To J. A. Hopkins. Main Street. Front and 2|Cases Raynor Lime Juice. Qts. Ea. 1 dz l|Case Napanee Red Cherries, 2's, not pitted Quan. Price. 90 dys 30 dys. Net. Hf. Cases Monogram Currants, 151-21 Dz. C. & B. Malt Vinegar. Bags Rangoon Rice J>|Cases Corn Flakes 2.Dz. No. 27 Brooms Qts 1 Dz. Victor Bamboo Handle Brooms 2|2.40 2 1.35 1301 .07^ 1.85 .03J 2.85 2.25 3.10 100 226 SHORT METHODS 12. To J. A. Farewell, Cor. Parliament and Carlton Street; 15 10 10 5 8 4 6 2 15 3 5 5 Quan. Price, go dys. 30 ays. N'Si. Lb. Blue Label Ludella Tea, I's. Black Lb. Blue Label Ludella Tea, ^'s. Black Lb. Blue Label Ludella Tea, I's, Mixed Lb. Blue Label Ludella Tea, J's, Mixed Dz. Japanese Stove Pipe Varnish Dz. Swiss Food, 10 cts. size Cases Challenge Milk Kegs Ivory Gloss Starch, Large Crystal . Lb. Roasted Peanuts Pineapple Cases Lyle's Golden Syrup, 2's Bk. Jfonsuch Stove Enamel, No. 1 ... Bk. " " " " 2 . . . 200 48 151 15 .20 .21 .20 .21 1.20 .95 4.05 .07 ■m .40 .70 13. To A. B. Woodley, 296 Avenue Road, Toronto, Ont. Quan. Price, godys. 3odys. Net. 2 Bx. Cowan's Cocoa, 10 cts. size 2 Bags McI. Rolled Oats 30 Lb. White Sago (bag 10 cts.) 15 Bags Natural Figs 3Case Paraffin Candles, 12's 5 Lb. British Navy Tobacco, 10 ct. size . . . 2 Dz. Nestle's Milk 2 Cases Heinz New Style Tomato Soup, size 392 108 med, .90 3.00 .07i .03 J .09i .44 1.25 1.80 14. Lyman Bros. & Co.. Ltd., Wholesale. Toronto. Ont.. sell to James Arbuckle, Graft(m, Ont. iu J !?°x^* 9i°^ J°°*^ Powder, at $3 ; J lb. tr. Connii, at 75c £?Si ^""l' J. In Acid Oxalic, at 20c ; 1 doz. P. D. & Co. Capsules, bO B., at $1.70; 1 doz. Orange Wood Sticks, Hoof, at 60c : i- lb. OU Peppermmt at $4 (bot. 4c) ; ^ doz. R & G. Cosmetic Tubes, J'^'I^'.^xV^^-^' ^^ ^^^- ^otli Balls, at 10c; 1 doz. Lyman's Crushed Violet Talc. Powder, at $2.40; 10 lbs. Alum Powder. H 949 ?f ft%T°^*/^^'fr^' J ^^' ^1^2 ' * ^°^- Hair Brush, No. ^ i ,7^ yl-; 1/1^ -Vyeths, C. T., Blaud, & Manganese Co., 20c ; 1/12 doz. Hot Water Bottle. 3 qt., L. B. & Co.. at $20. BILLING 227 IS; The Corticelli Silk Co., Ltd.. sold to Bews Bros.. Hamilton. Terms, 5% 30 days. ^J'ivS^^^ ^^S^' ^^ °^" ^'T., at $12.50; 1 lb. GUt Edge, 12 ?n' ?-^-J:!i ^} ^^' ^* ^^' ^'^^ Edg^' 16 oz. Sp. Sews, at $13; 10 yds. 2504 Merv., 30", at $2.50; 3 yds. 100 Satin. 21", at $1.05. oo/ ^^n P Gordon, McKay & Co., Ltd., Toronto, Ont. Terms, 3% 30 days. i« ^^l^r^SPe*-' ^i '^^*''' 5 ^^^' ^^^^" at 95c; 5 lbs. G. E. 16 oz SPL SWS, at $13 ; 5 lbs. G.E. 12 oz. B.H.T., at $9 ; 12 doz. Bunch Braid, at 32ic ; 6 gr. 81 Lama, at $1.65; 6 gr. Worsted Skirt Prot., at $3.25 ; 2 gr. 3 Twill Tape, at 60c. 17. To W. Kerns & Co., Burlington, Ont. Terms, 5% 30 Qi.^o*'!' ^^'Vool^^^*?' ^ ^°^- ^o'^t" at $2; IJ gr. Worsted ?^i'^,^^^*" at $3.25; 2i gr. Mohr. Skirt Prot., at $5 25; 2 doz. 7 Twill Tape, at 40c ; 2 doz. 8 Twill Tape, at 42k ; * gr. 3 Dress f £i on '^i? ' i ^' ^^2/4 Braid, at $4.20 ; i gr. M/3 Braid. at $3.20 ; 35| yds. 201 Tamiline, at 34c. / «""• ij'?' The Canada Cycle and Motor Co., West Toronto, Ont.. sold to R J. Young, Fredericton, N.B. Terms, net 30 days. 2% cash in 15 days. "^ '° , i"*"'/ 20|^ Century Gas Lamp, at $3; 1 doz. No. 82 BeUs, at $3; 6 only Winner Covers, 28", at $1.75 ea. ; 1 doz. Foot Sr?^''^fi^''m ^^ ^^.'o^ ' */°" ^^*"^^"g ^"^b^^' at $5; 1 doz. f %, oc^ ?lf '' .^} ?^^- ^ ^°^- ' 12 sets No. 66 Front Axle Sets, s!pS:'R.:aJ Zo' "^'^ '^^"'' ''''-'' ^'- ^""- ^-- ^-^' ^ ^19. To the Canada Cycle and Motor Co., Branch Winnipeg. p f f'^'^^l^'i'^' ^/'*' ^* ^^^5 SO pr. Cranks & Sleeves, fitted ?« ? ^'t>^{\^' ^c,^^' ^^ P^' ^*T- 4" Exp. Pedals, at $1.25; ^^ f AT^f * ^^P- ^^eeves, at 10c; 19 20" Front Locks (C.C.M. S/Tiv^/"^' t^ ^^•^^' 29 Rear Hubs, M/A 70, at $1.25; 10 22* M lo ?^n ^°o?'.S"J^-^-' ^* ^1-^' ^ 23 Tooth Sprockets. M 7n A 'T L^^ ' ^^- ^- ^^^als, Exp., at $1.25; 10 Rear Hubs M/70 A, at $1 ; 600 Rim 1| Reai' Spokes (Racer), at 40c a 228 ll'li m i f'C ■■' ■ SHORT METHODS T A V\' ^^l ^t^i.^ ^°" ^^°-' ^°^°"*°' O'^t-' ^^" to Messrs. J. A. Hopkins, North Dovercourt. Onf „ . , Net frice. 30 dys. Cash. 90 dys 2 kegs Snowflake Baking Soda 5 doz. Corkscrew Can Openers 4 doz. Imperial Pickles. Mixed 4 doz. Shino, 5 cts 2 cs. Toasted Corn Flakes . . . 6 bx. Taylor's Carbolic Soao . King Edward Matches '3. 2.25 .85 1.00 .45 2.85 40 60 .85 2.90 1.30 10 cs. 6 dz. Chloride of Lime, Is 10 cs. Quaker Puffed Rice 2 cs. Cowan's Cocoa, J's . 4 dz. Cow Brand Baking Soda, 5 cts.' .' .' .' ... I ' .45 3 cs. Gold Medal Table Syrup, 2's . ! . . ' 2 25 3 dz. Magic Baking Powder, 5 cts . . . .' . .' . . . .J .75 2 dz. Red Cross Baking Powder, 5 cts . . 45 2 dz. Nonsuch Stove Polish, 10 cts " "\ '90 8 lb. Jumbo Roasted Peanuts " " "15 1 tin 2 50 100 50 50 50 50 50 50 50 50 40 uan. Price. Amt. RusKs Gin. Nuts . . . , Asso. Sand . , Niagara Aby Map. Cream . Rich Traveller Animal App, Bloss. . . Mol. Snap . . . Sodas H 14^ 12 6J «i 5| 8 6 16h 16 11 13 14 10 m 14 13 13i 6i 7 ■4.> Note.— The figures in the spcond column fmo^ ^ t4. added for cost of tin. <=°''""n .^om left represent cents to be to Messrs, Net iasii. go dys BILLING 229 irers, sell ; Streets. ce. Amt. H Its to be cash.^' ^° ^" ^'°"' ^^'■^^^^^- Terms. 3% discount aUowed for 1 tin 2 " 1 - 1 " 1 " 2 •• 1 •• 1 " 2/40 " Quan. Price. Amt. 40 100 50 50 100 50 50 50 80 Sodas, I lbs Fig Drops Map. Creams . . F. G. Bread . , . Rich Traveller. Gin. Nut Sultana Pilot Sodas 2J 17 5| 7| 15| 14 8 33J 48 13} 10 14 11 13} 7 7 23. To W. Turnbull, 540 Main Street, Winnipeg, Man, _Q"an. Price. lo dys. Net Cash. i Cs. Robt. Scotch Marm 1 " SheU Walnuts 10 Lbs, '• Almonds ....".. 1 Hlf, Cs. Curr. 78-9 1 Bbl. Common Salt ' " 1 Cs. E. Army Blkg 10 Lbs. Rape Seed 1 Cs. Def. Syrup, 2's 3 Cs. Magic Bak. Powder, less 5% 2 less 5% .....".'.' 3 Bbls. No. 1 St. L. Gran. Sugar, 346-21 322-19, 342-19, 1010-59 1 Cs. Silent Matches, SOO's 1 " Cr. of Wheat 1 Bag Pot Barley " Prl, <• ''' 1 Bx. G, & S. 70/80 Prunes . , , . . . . . . . . . . ' 5 Cs. Def. Map. Syrup Mxt., Pts 5 5 1 1 1 1 5's H. S. Salmon, }'s . . Gusto . , Q. A. Root King Ed. Matches . Upton's H, M, Blk, C. Jam | 2 4 55 10 6^ 1 3 '0 12 8 951 1 1 100 100 25 5 5 40 1 3 1 1.55 .26 .33 .08 1.40 .75 .08 2.40 .75 1.65 4,50 5.20 5,75 .02} .03} .08 2,50 3.90 1.17} 2.85 .90 3.60 2,00 230 SHORT METHODS 24. To Johnston & Co.. Brandon, Man. Quan. Price. 10 dys. Net Cash. 6 Bags Yellow Sugar . 6 Doz. Def. Marmalade 1 " K. Cust. Powder 1 Box Baker's Cocoa, i's i's I Cs. Rob. Marmalade 1 Doz. •• Barley 1 Box Durham C. Starch . . . 1 " Bens. Corn [ 5 Cs. Quaker Oats, Family . 1 " Comfort Soap 1 " Upt. Marmalade, I's. 2 " Sift Peas, Quaker .... 1 Bbl. Common Salt 1 Cs. Bee Syrup, 5's 1 " " " 2's 1 " Def. Syrup. .. . .' .' ." .' .' 3 " Pearline. I's ^ " " lOO's ....... 1 Doz. CeU. Starch [ 2 Cs. Shred. Wheat 1 ' Gusto 1 Brl. Wind. Salt, lOO's .....* J Cs. King Edward Matches . . 1 Box Reck. Blue 1 Cs. Candles, i2's ' 1 Box Keen's Blue 1 Cs. Olives, Stuffed 1 Box Clay Pipes 1 Cs. Wetley's Mincemeat . . . 600 12 6 4 40 40 2 4 12 36 12 4 4.25 1.15 .90 .43 .43 1.55 2.40 .06f .07^ 4.50 3.85 1.00 1.27JI 1.40 2.75 2.40 2.40 3.80 3.70 1.00 5.15 2.85 2.85 3.60 .16 .08i .16 1.40 .80 1.00 b( C] 5 38 I 30 V- 51i at lo dys. Net Cash. BILLINO 231 ! ti I Altf ;.^T^tT-k ^''°'" ^^^•' ^^"^^^^^^ Confectioners. Calgary. Alta., sell to J. Gibson. Terms. 3% discount for cash. ^ Weight. Price. 1 T. T. Mix 1 Coco. Taffy 2 Valentines 1 Peanut Taffy 1 Ruby Mandarines 1 " Pept 1 Sc. Mints 1 Ell. Almonds 1 •' Crisp . ." 1 Ic. Jujubes 1 Quakers 1 Grab Bags 1 Drum No. 1 Choc. Culls 1 " Cry. Mix 1 Swiss Milk Patties 6 Cameo Bon-bons . . . 5 H 5 5 5 5 5 18 20 .12 .07J .50 .07^ .22 .22 .15 .20 .20 .70 .55 .35 .14 .07^ .50 .35 J. J. McLaughlin Co., Ltd., seH Ont^^VL^S;^^ ^"■"'' ^^ ^'- ^^"^ ^'''''- St. Catharines. Unt. Terms, 30 days net, 2% 10 days. %2m^% ^"T^" ^r^' "' ^'•'^' ^ S^- Le'^o" Syrup, at beV S S15 I m '^"""^A '' f ' '/^' ^^^- Crushed St^raw. r u 5t..^ ' */^^ '^°^- C'^^J^ed Cherry, at $16- 3/lo doz SirLT'f' 1 lY' '"' ^°^- CrLed Pea'ch iVsHi ^ Less 15% ' "' ^'•'^' '' ^'^- ^^"^-^^ Ch-olate ai ^T" ^^.^oof- "'^^^ "^ Robertson. Halifax,' N.S. Terms. 30 days net, 2% 10 days. ^ l/12^df/?t "^r'"'' '* ^^^' ^/^2 doz. Strawberry, at $15- 1 12 doz Chop Suey, at $16; 1/12 doz. Cherry, \Yl,o\e at S 7- at 42c . 1 pt. Fruit Acid, at 50c ; 1 M. Straws, at 50c. Less 5o/„. 232 If?) SHORT METHODS 28 Isaac Pitman & Sons, 2 West 45th Street. New York sell to Copp. Clark & Co., Toronto, Ont. Terms, net cash 588 3 3 3 3 1 144 2 6 6 4 3 6 2 6 12 6 Cumulative Speller .... Bible, roan Prayer Book, roan , German Shorthand cloth Church Service, morocco. Shorthand Gradus Insurance Office Organ I j Office Work In Shorthand " & Key, 1 vol. Church Service, roan Sel. Am. Authors, cloth . . Shorthand Writer Key to Office Worlc, cloth Cumulative Spel., C.S. Ed. , Self-Culture cloth 20% 25% .40 Less 25% 3.50 1.50 .50 .60 4.00 06 50 .40 .50 .60 3.00 .50 1.00 .40 .40 .40 Note.— It is the cu.=^om of this firm to show everv item pt «»<. «„ notwithstanding that so many items have the samelscoun" '""' McKavi^o 'Jf^T"''. "" ?•' ''^™'*°"' ''^^^^t °^ Gordon. McKay&Co., Ltd., Toronto. Terms, 3 mos. 30 ds., 50/^. « 49 « «f 5=^* ^^' ' ^^ P''' B- Check's, 41; 45 40 2' 4^5%** 50 622,60 513 55 fio _. 103^ c' ^^''t V ^ P^^- ^- Cashmere, Aoi ^' i ; ^^u ' ^* ^***^ ' " pes. A. L. Cotton 40 462 cc c, 2 421. 40, at 4c ; 2 pes. G. Flannel 60 65. at 30c ' ' ' R ^u i?^''; MiCKELBORouGH. St. Thomas. bought of W. R Brock & Co., Toronto. Terms, draft 30 ds. o vv. k. 273, 212, 232, 263,'2r24"3 J2^^ 'ar£%''Z'^'''^'f\?i^'- ^' 412 35 302 0= 073 o.^, .A« -J ^.* ^^:^^; 20 pes. B. Sheeting, 1 , ds, ^ , 35, -7^^^=-. 40-. ol. 443, 44i. 40. 372, 32S 323. 46< 492,381.413,382, .1;ii t, New York, t cash. CASH STORAGE BILLS 233 31- J- A. DuGGAN, Stratford, bought of T r m.k • p Co., Montreal. Terms, sight draft. ^' ^'^''""'^ ^ at net figure, of Gordon, '. 50, 55. 60, $1.12J; 10 >1 ^ at 8Jc ; i02, 452, 50, 40,551,52, . Cashmere. 162,55,512. : of W. R. ^5n, 502. 02,62,653. 93,262, 25. >. Sheeting, ^ 323, 463. CASH STORAGE BILLS Stora^ is a charge made for storing goods in a warehouse. tii^L:;^s:itr:tr^^^ ''' - -^^-^^^ ^^ - char^t: a": mad?'"^' ' ^'^ ^^^^^^ ^^ '^^^ ^^ ^^'^^ storage contract' hu!T/i ""'' \' '"'"^'' ^^*^^^" ^^^ P-^ies to the ::::Sttr:frarSor:i^^^^^^^^ '^ '--'- -^ -^^ - ^y principle. appropriate heading, as an application of the average ILLUSTRATION.-At a Warehouse there was received and dehvered merchandise as follows : receivea and Received. May 6, 300 bbls. fiour. " 27, 250' " June 12, 180 " " Delivered. May 23, 200 bbls. flour June 3, 80 " 7, 220 " 25, 230 " << How much must be paid for storage on the above at the rate of 5 cents per barrel for the first 10 days or part thereof and 3 cents per barrel for each Subsequent 10 d'ays or'part the'eoJ ? 234 SHORT METHODS ' Solution Date. Time of Storage. Receipts and Deliveries. Rate. Storage, ^^y ^' received 300 bbl. 23 (17 da., or 2 terms), delivered 200 •■ x 8c. = $t6.00 Bal. of 1st receipt = 100 " June 3 (28''-., or 3 terms). delivered 80 '■ x llc.= 8.80 Bal, of 1st receipt =: 20 " 7 (32 da., or 4 terms), Of 220, deliveied 20 • x 14c. = 2.80 ^^y ^^' receivecr25b " June 7 (11 da., or 2 terms), Of 220, delivered 200 " x 8c. = 16.00 Bal. of 2d receipt 50 ■• 25 (29 da., or 3 terms). Of 230, delivered 50 " xllc.= 5.50 " 12 = received 180 " 25 (13 da., or 2 terms). Of 230, delivered 180 ■■ x 8c. = 14.40 Storage due, $63.50 ,7 /'^^^^^^^"°N-The first delivery of 200 bbl. was made May 23, or 17 days after the date of the first receipt, constituting one term r.f 10 days and part o another or practically 2 storage terms, which, at the given rate 8 cenT'' ^\Tl '" '"' '"" ■" ' '''''' '°' -^-d) ^'^oduces ^00 tim ! 80 hh °' M "'"'T- ""' *^^ ""^""^"^^^ °^ th« fi^^t receipt (100 bbl ) stlutLTT '^'T,ol"" '• " '' '^^^ ^"^^ '""^ ^^^^ °* their're eipt. con- the storal .r ^^f"' ^'^^ °' "°°*'^^^- ^ ^ ^^^-g^ ^--^ ^ hence tLZTJ Z T* ^' '' *™"=^ (5 + 3 + 3=) 11 cents, or $8.80. mhlT^fr 7 ' ?t* '■''^'•P* <2^ ^^'-^ "^^ '"<^l"ded in the delivery of tfmes (5 TiTsi T ^T "'^ '*°"' '^ ^^^^' °^ ' '^^^^' producing 20 times (5 +3+3+3 = ) 14 cents, or $2.80 storage. 22oS^Tf ''7"^' I?^ ^^^-^ ^^ °" ^^y 27, and the next delivery (of leavin^J" 00 Jbl"wh' T '' '"' °' "'''^^ ^*°^^^^ ^^ ^^^^^^ ^cen computed, fncTuded ii the d r''- 7o.V''"'"^ '' ""'''■ °' '''' ^'^'-^ r^^-Pt were or 3 term,M / '7.°^ ^^^ '^^^^ °" J""^ ^S. after being stored 29 days, or 3 terms, producmg 50 times 11 cents, or $5.50 storage. on w'Jwh'''"^* V"?.""'-^ ^'^ °° J"'^^ ''■ ^" °^ "h'^h ™ delivered 13davs or 2^'^"^ '""?'' '" '^' ^''^"^^>^ "' 23G bbl.), afte. being stored tLfil\ I t^'--:^-- P'-"^"'^'"? 180 timus a cents, or $14.40 storage. Hence, the total storage is the sum of the storase on all the deliveries, or $63.50. 'ie. Storage. 8c. = $16.00 lie. = 8.Sf^ 14c. = 2.80 8c. = 16.00 lie. = 5.50 8c. = 14.40 5 due, $63.50 le May 23, or ;rm rf 10 days the given rate uces 200 times ipt (100 bbl.), ir receipt, con- terms ; hence nts, or $8.80. he delivery of , producing 20 ct delivery (of ;sn computed, :ing 200 times I receipt were ored 29 days. t^ere delivered being stored age. Hence, ■ $63.50. CASH STORAGE BILLS Rule 235 160 210 40 95 I. MulUpiy each delivery of the first receipt by the rate of storage for the number of terms ^hich such delivery\as been iZ constdenng any fraction of a term as an entire term recemTn^^' ''?"'' '^' '''''^' ^" ^"'^^ ^'^^'^'y ^f the second ZXl f '" """"'T ''' ''^'^''' ''^'^ ^^'^ ^^^^^'^^uent receipts until the storage on all the deliveries has been found cashstorlgr' '^ '^' '''''^' '" "^^ '^' ^'^''''''' '""'^^ ^' '^ ''^^^^'^ SERIES 73 I. The receipts and deliveries at a certain warehouse were : Ri^CEIVED. TN c . <,- Delivered. Sept. 25, 350 bbls. Oct 11 «<; kki. •■ k S " :: ^' '^0 " Nov. 10. 50 " ■ Nov.l; " 16, " 30, „„ cents Aarre, fortcl.''Lt;l?TdrysCpt' ifc^^ ' part thereof: ^^ ^^'^ ^°' '^^^ subsequent 10 days"^ or Received. -. May ,5. 350 bbls. May 20°™ W 14, 50 '. 28, 210 i cent per busL. fortih s^S^qSt JS t^. Z^U^^^S-. ^' Received. _> T 1 , Dbuvered, J'^y '' I'Z ^^- Jfy 10. 1.000 bu. 6000 " ^^' ^' 1'^^ " ^.400 Sept. 25, 6,700 " it It L.u^ ^ .. ^ _,,.._ ^^ g^,^^ TEREST tiable papers, knowledge of any one who int of either the same for J, " The Bills ing addressed igned by the addressed to time, a sum 1 (the payee) f it purports )r (b) drawn Any other Tnerce' ■7J ■ NEGOTIABLE PAPERS 237 "Accepted. D. Roberts & Co " as thf ir^''' '^'"'^'" ""'"^ '''^''' *° *""^ "^ - "U'"bcr of ways as the foliowmg section will show : ^ ' A bill is payable on demand : W Which i, exp„.cd ,o b. payable „■> d^anC, or o„ pro,o„.a.io„. (i) In which no time (or payment is e;"» "-' « and the bUl is due a'nd payaif ™ the Lfd^yX:':" ' " ■""" "^ '"' ''"• Provided that : day'll r Pr™": TernyTcl'tT ° "^" "-■""' " "™'-'^'-' following, not bein'; a tell h„I,, " " P"'"""'' *"" ">" ''ay »«» »haU be the last day of X '">"-l°""i"' lay i. ,„ch Provinc. aitefslgM'^rt™ o, ™™e„r- T.' " " " »■'"' ^^ " ""« <"" »' *b tL ;i„.e r bi„7or a^dtrr,,%x^':f --S '"" bills must, therefore, show date. '"'P*''"'"- ^^^ acceptance of all such (4) The term " Month " in a biU means the calendar month. becJl^iron^t^^sal^^^^^^^^^^ f I '"°'^^'^ °^ "^^"^'^^ ^^*- ^^^e " payable as the ^:^Z^f::l:^ t^^_ -""! ^" -'^^^h it is made month in which it is made nnv.hi -:'''''-''"'"= ^"^^c is no such day in the aay o, that '^^.^^:>rs^^ i^^^^i^z^:! z:t '"* I 238 APPUCATIONS OF SIMPLE INTEREST If; Cheques A Cheque is a bill of exchasge drawn on a bank, payable demand. on YONGE & COLLEGE BRANCH^ teTnrn • ^ °' ^"*-' ^^^^ ^O, 1907. One HuVd atd^^: ^-T^^^^^^ ^^^^^ or order, , Discounted Jan. 10. 1^, ."4^ """"V:^:^;,, BANK DISCOUNT 247 $537i8-«- 4. «J>^/aVTy Montreal, Que., Feb 29 ^Cioft e «ifiooo vo, aio/o. T. MedCRAFT. 5. liibZTTri7 Aylmer, Ont., Dec. 13 1907 6 ©71; 30 o.'xio/q. G.P.Brown. o. «./Oij^^ Windsor, Ont., Nov 15 too? One month after date I promise to nav to T F ii order, Seventv-five anH 30 nnii '^^ P^y ^^.J- E- Norman, or at foir per cTnrper anJu^ '' "^"^"^ ''''^^'^' ^^^^ ^"^^^^^^ Discounted Nov. 15, 1907 at fio/ t 7 «240«o "^^ JohnGloin. 7. »^4Ut^^ Aylmer, Ont., Oct. 31 1907 Four months after date I promise to oav tn D h p order, Two Hundred and Fortv and 00 rfJi. ,^- •^"''^' °^ -tJf,?nterest at seven percent Pannl^iS.''^"^ "' '"""'"' Discounted Dec. 5, 1907. at 50/,. a. ^^ Lhsub. o. «id4bT^^ Ingersoll, Ont., Dec. 18, 1907 received, with interest at five per 2tpera„nl'^ "'"' ^"^"' Ninp^y^S .. . Toronto, Ont., Mar. 15. 1907. Hun'^drTd^anrSix^^^^^^^^^^^ S^„-^- «/ T. Tanton, One charge to the account of ^^^ ''' a 'tt^'I!^"^' ^"^ To W. W. Austin, Toronto, Ont. ^- ^' ^'^°"- X Z..^ '^' '^^' ^^'^°""*^^ ^^y I' 1907, at 60/,. 10. ^^4Jt^^ Ottawa, Ont.. Aug. 1, 1907 Hun';i^?a rFot-tht^Sy ^^ '^V''' f °^^^^^^^' T^ Charge to the ac ol^^f ^^ ^ ^^hJ^L^r ^Lt^skv^"^ To R. Anger, Toronto. Ont. Dii5counted Aug, I, 1907, at 6%. discounted at 5o/„ ?„"*V 1^6]}^ ''H^wlTh^didt H^ ""'' 248 APPLICATIONS OP SIMPLE INTEREST > 1: f ; ! i I t. * i I 1 ! i 5 : 12. Find the proceeds of a draft for $580 at 60 days, discounted at 6%. 13. A note for 81,500, with interest, dated May 1, 1907. at 3 months, was discounted June 3rd. Find the proo^eds. 14. I bought a lot for vsi,200 cash, and sold it at an advance of 12J%, on a 90-day note, which I immediately discounted at 6%. Find my gain or loss. 15. C. H, Good & Co.'s bank account is overdrawn $7,564.19. They discount at 6% : a 90-day note for $3,975.21, a 60-day note for $1,546.19, and a 20-day note for $2,546.85; proceeds of all to their credit at the bank. What is the condition of their bank account after they receive credit as above ? 16. A dealer bought 100 brls. apples at $4 per brl. for cash. He sold 25 brls. for cash at $5 per brl., 25 brls. at $6 per brl. for a 30-day note without interest; and the remaining 50 brls. at $5.75 per brl. for a 60-day note drawing interest at 5%. He discounted the notes at 6% the same day as drawn, getting cash for the proceeds. How much did he make on the transaction ? 17. A farmer purchases a machine for $62, and gives in settle- ment two notes, one for $31, due 1st October following (1907)> and one for $31, due 1st October one year later. On July 15th the company proposes, and farmer accepts, a proposition to pay off both notes on basis of discount at 6% per annum. What is the net amount paid by the farmer to retire his notes ? Questions of the Second Aspect Illustration Toronto, January 7, 1907. Three months after date. / promise to pay to the Bank of Nova Scotia or order at their office, Toronto, Out TO 5 Dollars for value received. No. Due. J. P. Murray. It is desired to fill in the above note for such a sum that, when discounted at 5%, the note will rcahze $500 in cash. What should be the face value of the note ? lays, discounted ray 1, 1907, at c<;eds. at an advance J discounted at rawn $7,564.19. '5.21, a 60-day S.85 ; proceeds ndition of their r brl. for cash. J6 per brl. for a ) brls. at $5.75 He discounted or the proceeds. gives in settle- llowing (1907), On July 15th )osition to pay n. What is the vy 7, 1907. xise to pay to or order • TO 5 Dollars '. Murray. im that, when What should TRUE DISCOUNT 249 SJOLOTION 1. The due date is April 30th. 2. Assume a value of $1 for the face of the note on AprU 10th. 3. The number of days from Jan. 7th to April 10th is 93 days. 4. The int«««t on fl for 03 days at 5% is $ 012741. 5. The proceeds of a $1 note are $1.00-.or2741. or f.987259. 6. If $.9873 is proceeds at note for ||, $500 Then $500 is proceeds of note for , or $506 4S .987259 The note should have a face value of $506.45. SERIES 76 T,= ^" ^ Sf!; ^"^ l>f>rrow $900 at a bank. For what sum must 1 issue a 90-day note to obtam the amount, discount being at 6% ? int^rlf "°*%dat^d Mar. 15, 1908, payable in 3 months, with interest at 5%, was discounted April 10, 1908, at 6% If the proceeds were $1,342.27, what must the face have been ? 3. The proceeds of a 3-months' note, dated Sept. 20 1907 and discounted on Oct. 15. were $426.89. What was the face of tne note ? 4. A 30-day, 5% interest-bearing note was discounted 10 days after it was drawn up. If the rate of discount was 6% and the bank discount $13.40, what was the face of the note ? .hnnM^^"?K^ f """ f\t' ^ ^^""^ ^™ "^y ^-d^y "Ote. What Sscounted at 70/'? °^ '^' "°'' *° ^'^ ^™ '^' ^^^^* ^'^'' " 6. You have $650.80 to your credit at a bank ; you give your f^:.T!j''' $1,872.40, after which you discount a 30-day note for $850.80, proceeds to your credit at the bank. You then discount a 90-day note, rnade by F. D. White, proceeds to your credit, when you find yourself indebted to the bank $24.74. If discount be at b/o, what must have been the face of the note made by White ? TRUE DISCOUNT The Present Worth of a debt, payable at some time in the future, is its value at the present time, and is such a sum that, if put out at interest, it will amount to the given debt when it becomes due. The True Discount is the difference between the amount of the debt and its present worth. 250 APPLICATIONS OP SIMPLK INTEREST Solution And 1525 paid at tUc e„,l o( .her' " '■"'"'™'°°' *° """ P"" '"> ""y- Smith .ho„M i,rig 'oi * ' " rr*"' '" «•■""' p"" "-""y- «d^e „„„,a „, ,„ .„i„, f„:r;:r a'dir.- '^^rs-i :;^5"^'' andVjeltr '""" ""' '^ """ *"' -■"— "=-- bank discount i>HTZi°Z S'tato tr.° ? °°y'" '" '^^ °™°"' »' '^' The bank „„„,„ cha,:: ima ait„„?:,*5°o;„''A"h'' 7" 'T," "'"''""•"''■ would be ,26.25, and Smith wouir"ecl!l52, .Jfil, ''I'^r''' "'"'='' r^Tdrc-:rarr.-t'^^^^^^^^^^ !:tt\^5^r'"''*"'"--°-"^^^^^^^^^^^ This may be stated generaUy thus • inteS: o?r?.u'; dT«^ ^^-^^ ^^--t -d the true discount is the This may be proved generally as follows • Bank Discount = Interest on the debt True Discount - t1 ! ^ ^ debt -true discount). W Ss^nl -^iTdV^^^^^^^^^^ debt -interest on trul discount. .-. Bank discount is^eatlr tMnV .' °" ''''' ^'^^"""t" true discount. ^ ^^^"^ *'"' '^'^^°"°t by the interest on the The bank -discount = the given per-°nt3r^ f +t, • debt. ^ per... ntage for the given time of the TRUE DISCOIJNT paid at the !■ his money, es to-day in be allowing : the $100 out d of the year. ) paid to-day. D paid to-day. t of the debt, = «25. and the true )ank discount mount of the t discounted. ; note, which 498.75. The debt ; while ebt. :rue discount rue discount ' at the given count is the 251 scount. rest on the ime of the presJnt^wrhtrrdTb;'^ «*"" '-''-'''''' '^' ''^ «>- ^-e of th. But the debt = the present worth of the debt + the true discount or ^et^t^^Z :^tS:r '''-' '^ ^'^ «'- I— go true':i::^:^r:S'^:;,^ it'aT'^ ^^^' °^ ^' °^ ^^^ ^^^^- -^ ^^^ be seen that the numeratrs r ^"^ ^, '°"^'""« *'"^ '^^'^"""^ '* -'" fraction representrngTc true d^^ ^"' ''f """ '^"^"'"'"^t- ^^ the Of the fJt.on repr\::nt;nrtl-:an.*dr:ctn:r°^^ This relation is always true, and may be proved as follows • Suppose, say. the bank discount is ^, of the debt. Bank discount is really the interest on the debt. ••• 816 in the given time at the given rate will gather $3 interest. .-. «16 in the given time at the given rate will amount to $19. ■ •• $19 will have a present worth of $16. Or $19 will have a true discount of $3. And the true discount wiU be-^a^ of the debt. but thJtht^, ^ ^""^ *■ '' ^''" ^' ''''' *^^t t'^^ numerators are the same Dut that the denominator of the fraction ^ i» i . ., same. two terma of the fraction ft. "'' '"" "' "" fh. S,'!!!'"'''' ''^™^ '^'"" "" '""'O" "I"'" "-e true discount is of the debt .he fracLon representing the ba„l< discount can be derived from t Th« ' greaf:rThf;th:ir;L:™.'' ^"'"^ '"=' "■' "- *— ' '^ »-y« ire instituted, ami, as we shall ^ef> l=,f»r fi -^'^.' ^^^'^^ Cumpansons «t. . .ndin, the P^senf IX r^ndrorSr^'StLr 252 APPLICATIONS OP SIMPLE INTEREST SERIES 77 Find the present worth and true discount of 1. $503.36 for 1 year at 4%. 2. $752.40 for 9 months at 6%. 3. $109.89 for 3 months at 7%. 4- $129.01 for 90 days at 4%. 5. $588.80 for 60 days at 5%. 6. $75.85 for 6 months at 5%. 7. $918.50 for 48 days at 5%. 8. $2,585.87 for 63 days at 7%. 9. $1,500 for 90 days at 6%. Find the true discount on 10. $1,317,24 for 18 days at 5%. 11. $1,250 for 7 months at 4%. 12. $800 for 5 months at 7% credit. Which offfri^thlTrf, «^-* per barrel on 6 months' worth 6»I? '*"^' """^ ''•'"' ■"""^h. "oney being wastugtt areTyw^d^^ nJ^'Hn"] 8''°^?™<'>'"«ng to $478.25 which w?uld te bSt ?, to'^^r^^wron tlTmF/ ^^^ ^°/°- 60th, and how much better p'^ " *^'' ""'' '^y °' "^ «>e credi^'nS°£ed\'?^,;l^fhe^^fe^°5*^^r ?» ^^^' Money being worth 60/ fi„^ Xr'en^^.'^/^rrfit^rtS "^**- then told r*1n\SceVyr' 'fi '^'^ '"^ ^ ™"*s, and purchaser a creditlfTlt! r'^i^^fSesHf ^^ '° '^"^ worth 5% per annum, what was my pe. c^nt S^rkt ort^T "^ «i.m, T6TdL''cou':t'for'cl''T"'''''i' '° ^7 P^P^rty worth interest, when mTn' S worthly f "" « ™°"th^' ""e without w^Tay^'si Jrs^,is^s-/„rini^^>s«roL^^^^^^ ^' «%• TBUE DISCOUNT 253 o A?u: ?Zc^''? "^^ ^ S^^" " I borrow money at 8% to oav interest and true 22. What is the difference between the discount on $1,345 for 9 months at 7% ? 23. Sold a bill of goods on 8 months' credit for $387 20 If s worfer^' r ^''f ^"^ *^.^" *^^ ^^°d^ cost.^d-money ienT? ^° ^ ' ^""^ ""^'^ ^^ *^^ ^oss a"d the loss per 24. A merchant bought a bill of goods amonntinff to m-^l 60 on 5 months' credit, and the seUer offered a discou/t of 5 0/ fS Zr;^J\ "^°"\y ^^ ^^^t.*^ ^% per annum, how r^uch would the merchant gam by accepting the seller's offer ? . 25. If the interest is /^ of the principal, what fraction of thp pnncipal is the true discount for th^e sam^e W Id at tL lame sum^'f.* iVt l'",^ ""'"^^^^ ^' JT of the sum. what fraction of the sum IS the bank discount for the same time and at the same rate 1 at SI' It "^f^ %L1 tt IZ. "^^^^"^^ ^°^ *^^ ^^- ^- for Sl^^^^ tS^^^^ i-^.and the true discount the1?iJS "^t^l^ t^^^ ^^^-^ *uA°' ■'J^ ^^"^ discount on a certain sum of money is $30 anH thP^fniJifc *^"^,^sco"nt on $1,378 for 6 months is $53. Find the true discount on the same sum for 9 months. 32- The interest is $3 and the difference between the interP<;t tTe'prindpr""' '" *'^ ""^ '"^^ ^"^ -^^ is 25"cenL"S 90/of &rFiSxim. ' ^'^"^ ^' "°"^^ ^^^ « --^^^ ^t is S^ H^A T"^}^ '"!f ^'* °'' ^ "^^"t^^" ^""1 °f money for 2 years Find^he^L .'ni'^h ^'.'°""* ^°' *^^ ^^"^^ time and rate is^$^5 find the sum and the rate per cent, per annum. ruJh'JL^f '^J^^ *™^ discount on $420 for 6 months how much IS the true discount on the same sum for 12 months ? 51 254 APPLICATIONS OP SIMPLE INTEREST ^^' ^S/'Ji i^^'^'' ^"""^ discount on $110 for 8 months, on what sam would $10 h^ the true discount for 4 months ? vK ?^* ^^^-^^^ '^ *^® interest on $180 for a certain time, what is the true discount on $180 for the same time at the same rate ? 38. If $105 be accepted in present payment of $665 due some hme hence, what should be a proper discount off a bill of S! which has only half the time to run ? ,•<; l^%J^ urh^i" discount on a certain sum for 8 months at 6% IS $3.98. What would be the true discount on the same sum for the same time and rate ? 40. If $11.10 is the true discount on $196.10 for 9 months the ^a^'nTe rTtI ? ^^^"^^ ^-^^^ ^'"'^ "^^'""""^ ^'^ $269.50 at' 41. I have two notes, both drawn for 8 months, together amounting to $112. I have them both discounted at 9%!one k -^^4^ Z'^aT T"^ °T ^V*'^^ ^'"°""*- " the total discount IS $t).4i), nnd the face of each note. 42. The difference between the true and bank discounts on a certain sum of money for 3 years at 8% is $30. Find the sum fin P' ^^^i["® discount on a certain sum of money at 8% for ^ days IS $82.24. What is the bank discount on the same sum for the same time at the same rate ? fn i^iAn^'^a"" '''Tu''^ ""^"^y ^°^"'^ a* ^™PJe interest ^mounts to 3M34.40 in 9 months, and in 7 months more to $345.ru. Find the sum and rate. 45. The present worth of $359.04, due a certain number of number of day! '^^^ ""^ '""^^"^'^ ^"'"^ ^°/°' '' ^^^''^^- ^^"^ ^^^ 46. The present worth of $405.60, due a certain number of months hence, is $390. If the rate of interest is 60/" Sid the number of months. ^° on m':^8L%''T5X '''""" ''^ ''''' ^"' ''^"^ ^^^^-"^^ 93 d?;^T!r ^if'"^*^^ *^^ u^"'°''"* ^^ ^ "°*^ ^hich matures in on it to' i I cent ? ""^ ■''^^" *^^ *'"^ ^"""^ ^^"^ discounts 49. A tradesman marks his goods with two prices, one for cash and one for credit of 6 moSths. What relation shoSd the pnces bear to each other, allowing interest at 7Jo/ ? if the creSt price of an article be $33.20, what is the cash price ? 5T months, on what ,s? lin time, what is he same rate ? >f $665 due some ff a bill of $665, 8 months at 6% a the same sum for 9 months, t on $269.50 at' nonths, together ited at 9%, one le total discount ik discounts on Find the sum. oney at 8% for n the same sum nterest n mounts $345.r>u. Find tain number of 0.40. Find the tain number of 3 6%, find the bank discounts ich matures in bank discounts prices, one for ion should the ' If the credit TRUE DISCOUNT 255 «t foo/^'""^ "'! 'T °i ""^^^y ^h°^^ true discount for one year at lOo/o s greater by $3{',% than the sum of the true discoS of one-half of it at 8o/o and the other half ai 120/, for one year ' remiinder^'^f *, li™ ^?l ^\^'^' P^^^blc one-half cash! the for r2fJ)0 nlih?'"^'? '"^T'^ ^* ^%- I sell immediately lor $1J,000, payable in 3 months, with interest at 40/ wi/t IS my present gain, money being worth 50/0 per annum/" Comparison of Rates of Interest and Discount Illustration l . Toronto, May 30, 1908. Seventy days after date I promise to pay to F. D. White ■ „ , ^ , , or order at the Dank of Montreal. Yonge and Carlton Branch, Toronto One Hundred m Dollars. value received. „, „ W. Benner. Suppose that F. D. White got E. Bowlby to discount the above note at Q% on May 30, what rate of interest would Mr. Bowlbv make on the money he so invested } SoLUtlON The note will be legally due 73 clays after the date of discount. Ihe amount of discount for 73 days at 6% on $100= $1 "0 Mr Bowlby would give Mr. White $98.80 for the note. He would then Banner Tu "'^''' l'^ "°*' "^*""'' ^^'^" ^^ ^^^^ ^^^ «100 f^oL Mr = $L20. interest '''* °' *''"'' '°' '' ''"^' ^'^''""^ «100- $98.80 Interest on $98.80 for 73 days = $1.20. Interest on $98.80 for 1 year would be $1.20 x^^^= $6.00. Interest on $100.00 for 1 year would be $6.00 x--^-^= %Q^, Therefore. Mr. Bowlby would reaUy make 6^o/f ^^t.^.^^ ^^ j^ investment. Illustration 2 Suppose that Mr. Bowlby had wanted to make 6% interest on his money, what rate of discount would he have charged Mr white ? C9 ■ ■ H '■ i i i ii 256 APPLICATIONS OP SIMPLE INTEREST Solution The interest on SlOO for 73 days at 6%= $1.20. Then the amount of $100 for 73 days at 6%=. $101 20 Therefore to make 6o/„ interest on his money, he would have to charge discount at the rate of $1.20 on $101.20 for 73 days. Discount on $101.20 for 73 days= $1.20. Discount on $101.20 for 1 year would be $1 20 x ^^- = «6 73 * • Discount on $100.00 for ! year would be 100 ^ 101.20 = «^'^^5- .,, . 1^'^° ^^ ^°° '"'^'""''^ °" *'^^ '"°"^y '^« i^^ested in discounting the note. Mr. Bowlby would have to charge discount at the rate of 5^7^ SERIES 78 H„. •*' ^f^ '"^^^^^^ '"^^""^^^ ^^ "'^^^ When a note nominallv due in 60 days is discounted at 5% ? ^ 2. A bank discounted a note legally due in 90 days at 8% per annum What was the actual rate of interest made by the bank on the transaction ? ^ 3. At what rate should a note legally maturinr^ in 45 davs be discounted to produce 5o/^ interest pe? annum on the investment^ WK f ^"'P'^^y^^'^'^^^'^^'h'^^ to make 7% on the money he invests Sday' f "' '^'"^^ ^' '^^'^' °^ '""^^^ "°™"^y ^^tur?ng 5. A note of 11700, dated Aug. 12, 1907, and payable 90 days after datevvas discounted Sept. 26, 1907. What was the rate per cent, of discount if the proceeds were ^694.40 ? 6. In question 5, what rate of interest did the purchaser make on his investment ? purcnaser ,-n <;7^*^^^^ ""^i^ °^ '"*^'^'* "^""^ '"^^^ '*^hen a note legally due m 57 days was discounted at 4% ? ^ ^ 8. The true discount on $922.10 for 4G dav=i is to an Tr,„^ of dL^unt?^^ "^^ °' '^"' '^^^"""* woufd ^vTth: sfn^amSint GO/ K^u '?°*^ legally maturing in 85 days Wus di.jr mted at fn^^stlnf.^ ''*' °' '"'""' ^^^ ''' P"^^^^^^^ ^-^'^^ °^ l5s «n#'°" ."^ "?*^'^c^o/^ ^'* January, 1908, at 90 days, for $730, r^vV^^Tntl 5%; ^f discounted at a bank on January 21st advanced ? ' ' '"^''''* ""^^^ ^^ *^'^^"^ °" *^" ^^""^ 1 JO. d have to charge ■d in discounting i rate of 5Sg|o/^ >te nominally ) days at 8% made by the in 45 days be ; investment ? ley he invests, lally maturing j^able 90 days was the rate he purchaser e legally due $9.60. Find samp amount lijr inted at n.i "cc on his ^s, for $730, fanuary 21st 1 the amount PARTIAL PAYMENTS Partial Payments are simply part payments made from time llgagV" "^^--^-b-ring ms.uments, such as noTes ^ drawn with the proviso that the principal is the P^vTStet^^^nt Instalment No;;e On the first day of each consecutively, 1 promise to pay to A. Kilgour Fifteen Dollars, the whole amounting t Stratford, July 2, 1906. month hereafter, for four monlhs or order A < . , . - '" ^'■'^'y Dollars, the first of swh payments to he made on the second day of August ne.t, interest, both ieTore and after maturtty. and until paid, at the rate of si. per cent, per ar^/Z. J. Roberts. Unless thus J specifted that partial payments are to be maH^ if i= -^ at tl^e^option of the creditor as to whether partial pay.ent^s SrbfaL'p^:^ The problem presented, where partial payments are made and accepted, is to find at any given date the amoum .emaining Law of Application of Payments It is a principle of law that, in making a payment on i,, interest-bearins paper, the payment is first to be applied to the reduction of the n rest Z then to the reduction of the principal. If the payment is not sui^.c nt to a least cancel the mterest, .t might better be ^yithheld. as the creditor is simplv getting the use of the money without giving any return for it. AU he can d'o IS to hold such inadequate payments until such time as the sum of them will at least cancel the accrued interest. Then he mav proceed to apply the pay- f^orth 17 °' "" "'""* '' ""''- '' "^'^ '^ -°- tha/sumcient or the reduc ,on of the interest, the balance may be applied to the principal. If this point be kept m .und. the work of partial payments presents a very easy application of simple interesu ^ 258 APPLICATIONS OP SIMPLE INTEREST Illustration 1 Where every paymeiit is large enough to at least cancel the accrued interest. •500 jOg^ Ha:nilto,i, Mai: 24, 1908, Six month;: after date I promise to pay /. /• F::ierson Five ■<".:iiivcij . , valm i'f.uLU/r.d, :vUh inter 'in' at six per cent, per annum. Robert Browning. . . or order ^K'(j Dollars On tiie back of this note there are the following endorsements of partial payments : Back of Note Received on the within note, May 20, 1908. One Hundred and Fijty Dollars ($150). J. E. Emerson. July 15, One Hundred Dollars ($100). J. E. Emerson. What remains to be paid on the due date of the note Sept 27, 1908 ? Solution Face of note Mar. 24, 1908 $500 .00 Interest on $500 from Mar. 24, 1908, to date of first payment. May 20, 1908 \ 4 gg Amount due May 20, 1908 $504 .68 First payment 150. 00 $354.68 Balance Interest on $354.68 from May 20, 1908, to date of second payment, July 15 3 26 Amount due July 15 $357.94 Second payment ., . 100.00 Balance $257.94 Interest on $1^57.94 from July 15 to Sept. 27 , 3. 14 Balance due Sept. 27, 1908 $261.08 east cancel the ^ay. 24, 1908. ,'*' order . . . ji;,"(y Dollars Browning. 5 endorsements Emerson. Emerson. ;he note, Sept. $500.00 lyment, 4.68 $504.68 150.00 $354.68 ayment, 3.26 $357.94 100.00 $257.94 3.14 $261 .08 partial payments Illustration 2 259 ^cc'^ZtZr'' "" "' '" ^' ^-- '"^^ --^'' '0 -ce. »2.750^(f^ tlamilton. Aug. 18, 1908. ly'o years after date I promise to pay to Roderick Bethune Twenty-seven Hundred andFiUy "*" °^^^^ value received. r.ith interest at seven ' p'e'r 'c'eni. ' 'J^^'nuln. "" ''^' ''"""'' George Campbell. On the above note are endorsed the following payments April 9, 1909, $ 75. July 3, 1909, 400. Dec. 5, 1909, 150. What remains to be paid on the due date of the note ? T^ , Solution race of note Interest on $2,750 from Aug." Vs io Apr.' 9* at"?"/' ' Since the first payment is less than thi's intet, interest on $2,750 from Apr. 9th to July 3rd $2,750.00 123.41 44.83 Amount due July 3rd •First and second payments ($75 ' ■ * ■ • • • $2,918.24 + «^00) 475.00 Balance due Interest on $2.44a24"from"juiy3n;;oD;c:'5:::::::::;::;:::;*'''7^;^^ Amount due Dec. 5 . Third payment $2,515.87 150.00 Balance due ~~ Interest on $2.365.87";rom"DVc: '5 Vo due" di;; of' n'o'te'. ! ! ! ! ! ! ! ! ! '^''n7:52 Balance due Aug. 21 1910 260 APPLICATIONS OF SIMPLE INTEREST ;. f Series 79 I. $850.00. Belleville, Ont., April 24, 1908 Six months after date I ]iromise to pay to W. G. Harvvood or ^Jraer Eight Hundred and Fifty ^""^ Dollars, value received, with interest. \v. W. Green The above note has the following payments endorsed upon It: June 17th, $125; Sept. 3rd, $200. Find the value of the note at maturity. 2. $1,200.00. Aylmer (West), Ont., June 6, 1908. One year after date I promise to pay to Elmond Bowlbv. or Order Twelve Hundred jO» Dollars value received, with interest at seven per cent, per annum. J. J. Gould. On the above note were eridorsed these payments : Oct 20th $120 ; January 30th, $10 ; May 1st, $350. Find the maturity value of the note. -^ 3. $900.00. Chatham, Ont., Mar. 3, 1908. Nine months alter date I promise to pay to George House or Order Nine Hundred j>p_ Dollars value received, with interest at four per cent, per annum. George Partlow. T9fh^iQ^«%^^r\f *^*^' follo-.ving payments were made : June 12th, 1908, $150 ; Nov. 9th, 1908. .SIO. Find the amount necessary to pay the note on Mar. 3rd, 1909. ^ 4. $2,500.00. Hahfax, N.S., Jan. 1, 1906. Two years after date I promise to pay to W. W. Ingram ' or Order Twenty-Five Hundred 00 *= DnlinrV • value received, with interest at six per cent, per annum. J. D. Brown. The above note has endorsed upon it the following payments • ^^"nc^^'Vff^ ^^^^ ^^- ^^h' '^07' ^500; Mar.^^th 1S08; $l,UOO. i' '2. 1908. - O^der ., . . i.ou;t"en''J|nL''rSrd*°Fi?tT '" ^''".'o^^J^™^ value received, w th interest it Al^.^l t A Dollars, maturUy,a„dthereaf.erattSsa^^r™Sp'ail"jSuo.r' What remain. iL on rheV„'te'rjun'i,A'Si'p'' '^' «^^ 262 APPLICATIONS OP SIMPLE INTEREST 11. $450.00, Woodstock, Ont., Aug. 20, 1907. One year after date I promise to iy to John J. Doane or Order Four Hundred uud i^iuy ^^^ Dollars valr.e received, with interest at four per cent, per annum until maturity, and thereafter at the rate of six per cent, per annum ""*'! paid. J. D. Todd. The following payments were endorsed on the above note • Doc. 24, 1907. $50; April 10, 1908, $4; Sept. 11, 1908, $100.' What was the balance due on the note on Dec. 15, 1908 ? 12. $1,800.00. London, Ont., July 2, 1908. Six months after date I promise to pay to W. J. Long or Order . . . . Eighteen Hundred "o Dollars', value received, with interest at ten per cent, per annum until maturity, and thereafter at th6 same rate until paid. Tu r II C .AILY. Ihe following payments were made on tht: above note • Tulv 26, 1908, «300; Oct. 11, 1908, $400; Mar. 11, 1909, $500. Find the value of the note on July 9, 1909. , l^: .^^T^^'^'^ *^^ balance due May 1, 1889, on a demand note tor $4,119.82, at 8% from maturity till paid, In tod June 25 1888 on which a payment of $450.25 was made Aug. 1, 1888 and a payment of $21.19 on the 15th of each subsequent month. ' 14. On Oct. 15, 1907, I bor owed a certain sum of monev secured by moi:,' ige a' S% lut, st. The following partial pav- ments have been made : Nov. 24, 1907, $200 ; April 15 190b $300 ; Aug. 18, 1908, $750. On Jan. 31, 1909, 1 still owe $4,099,739' Find the sum borr-n .1. 15. Jones purch.-ises a house from Smith, and gives a (^emand note bearing mterest at 5% on Jan 1, 1901 Subsequertly the following payments were made ai endorsed on the nue ■ Mar 15 $59; July 28, $10; A" 8, .?'57; Jan. 1, $214. On th<^ last-nientioned date a renew, lot s given for tl balance then due, to run for one year, ai/ )ea! terest at 7%. Smith imme- diately discounts this note .c 5 per cent., and realizes $a08 25 Find the purchase price of the house. (In K.koning for last-mentioned note, omit days of grace.) 16. D bought a piano, catalogued at $600, at a reduced price. In payment he gave his note dated Jan. 1, 1894, payable on demand, and bearing interest at 5% per annum. During the year the lollowmg payments were made on the note: Mar. 15, $100; Juiy 31, $7.10; Aug. 8, §206. No payments to be anphed to reducing the debt until their sum is greater than the then due CASH BALANCE 263 ralrd- in?e"if^!nf f^^^^^^^^^ the the new note on Aug^ 8 1895 at the R.nl f t ^^'^ discounted cent, per annum, the' p?ocee?s tintt214 1^^^^^^^^ Percentage was the catalogue price redu'cel'/'fe ..X^s^^ CASH BALANCE The settlement of accounts between debtor and creditor ofte > involves the calculation of simple interest having 7 or 8 or p" "cent L .H '°"''"*' *^ ^^^ '"°^«- Sin>ply .ate.^nt does no'rj "he'rge%tLTL'd%K^7^^^ ^V"T^^ °' .. ntraCd to do so, .ay ..use to p^ ^ e'thaTtHXt::;; T^^^c^ far ofM™' "". ,^° '"°"''* ^''''"''' ^"^J^'^t t° ^"^<^^^st is a matter of the ttolX'^TT "'k k^ "*"• '^^'^^ '"^^^ -^^^^^^'^^^ - practice with hi rnTittr.'""" *° ""'"'■ ''™-- -*:>e ^".'a er:L;„u: r Questions of the First Aspect Illustration 1 May lst.-J Brown & Co.. of Toronto, .ell to R. Young of follols :"''' "'""*' "' '* "P^"'"' '" ^^°"" * ^°'^ ^°oks. would show as 264 il •■I L t 4' APPLICATIONS OF SIMPLE INTEREST According to the terms, Young can pay in 30 day., and earn a 5 per cent, discount. In other words, ho can settle the account for «475]n c^h on any date up to May 31st. «500, md It must be paid in 90 days from May l.t, or on July 30th thP I J'' r"I.r ^"'^ ^'''^' ^"'^ '^'' '"*^"-^^* "°t'<^*' »'^« been duly given the account will bear interest from July 30th until paid. If paid on A^igus 31st. for instance, it will require $500 plus the interest o» ^sbo for 32 la^ or. altogether. $502. 19 in cash to settle the account. The Merchandise or Commercial Balance is the difierence between the debit and credit items— $5(K). The Cash Balance is the sum required to settle the account on a given date-.S475 on May 31st, or $502.19 on August 31st. An Account Current is simply a detailed statement of an open account showmg its cash balance on a given date. The account current rendered by J. Brown & Co., to R. Young on August 31st. will appear as follows : ^' R. Young. t- . „ „ ' , ^ , ^ Toronto. Aug. 31, 1908, Woodstock. Ont. In account with _____^_ J. Brown & Co. May 1 To Mdse. 5/;«) N/90 . . . T. . ...,.,. Interest from July 30 to Aug, 31 ^^'^"^''''"^ $502.19 $500.00 2.19 • ^°Y:r/"*^"'* '''''""°* '''■ co"^POunded in this case. If this account not on'he $502.fa'"* '"''' '"''"' "*""* " ^^"^^^ ^^^'^''"^'^ °" '"^^ ^''^- Illustration 2 trv.?""^ *^^ '''''^ ^'''^^"''^ °^ ^^^ following account on July 15 1908, reckonmg interest at 5 per cent. : =^ I I 1 ^^ I ll' ^f^'/ 6sa (TV en? ^0 /J / 0=- SOD /aw av (TV (TV CASH BALANCE and earn a 5 per It for $475 in cash the full amount of July 30th. s been duly given, If paid on August $500 for 32 davs, > the difierence tie the account Dn August 31st. lent of an open to R. Young, on Aug. 31, 1908. $500.00 2.19 . .. } $502.19 If this account )ned on the $500, t on July 15, ^3^ Sao (;v & fov c^ /CVl? tra Dub Date. D*Yi. Items. Solution iNTERE-r. Due Date. Davs. Items. 205 Interest. 1908. Apr. 9 97 S 650.00 $8.64 " I 105 1,000.00 14.38 July 25 10 1,200.00 3.70 I Apr. 20 86 $ 500.00 $ 5.89 Aug. 14 30 9(10.00 June I 44 1,000.00 G.03 1.64 $2,850.00 $ 26.72 2,850.00 Total Debit. . . $2,876.72 2,413.56 Cash Balance $ 463.10 $2,400.00 $ 13.56 2,400.00 Total Credit.. $2.4 1 3. 56 Explanation The steps in the above solution may be set down as follows : 1. Find due date of each item. Tliis is a general direction that applies to all work on accounts. No figuring is done with any dates but due dates. 2. Find the interest of each item from its due date to the date on which trie cash balance is being found. 3. Add debit interests to debit items in order to get the total debit, and add credit interests to credit items in order to get the total credit. 4 Compare total credit with the total debit, and the difference gives cash balance. ° Note.— There is only one possible point of exception to this general plan. It ,s Illustrated in item 3 on the debit side and item 2 on the credit side. In both these cases the due date is aiter the date on which we are asked to find cash balance. The interest in each case is carried to the reverse side of the account. In thus subtracting, the interest from the item, we do not get the absolutely correct present wor'.h of 'he item, but the result is considered to be near enough for business purposes, and the plan is generally followed in business calculations. Questions of the Second Aspect The student who can find the cash balance of an account should have httle difficulty in solving another question of prime importance in business. f,et us illustrate. The cash balance of the account just dealt with is $463 16 calculated to July 15th. The merchandise balance of this TiTiaai 266 APPLICATIONS OP SIMPLE INTEREST ,1 J I :,i 4 I account — that is, the difference between its debit and credit items —is $450 ($2,850- $2,400). Using these figures, our question may be stated thus : Illustration If $463.16 will settle an account on July 15th, on what date will $450 settle it ? Putting this in the more familiar form of one of our simple interest questions, it may be 3tated thus : In what time will $450 amount to $463.16 simple interest ? Solution $450, to amount to $463.16, must accumulate $13.16 interest. Interest on $450 for 1 year at 5% = $22.50. $22.50 is interest for 1 year, or 365 days. $13.16 is interest for 13.16 of 365 days =213 days. 22.50 If $463.16 will settle an account on July 15th, $450 (a smaller sum of money) will settle it some time before July 15th, because we know that the longer an account runs, the more interest it will accumulate, and the greater will be the amount needed to settle it. This time we have just calculated at 213 days. 213 days before July 15, 1908, gives us Dec. 15, 1907. Therefore, $450 would settle the account on Dec. 15, 1907. Note. — It may be said that there in no sense in speaking of $450 settling this account on Dec. 15.1907, as the first transaction recorded took place on March 10, 1908. It ia quits true that the account cannot actually be settled on Dec. 15, 1907, but that fixes a date from which to reckon interest on the account, whenever the debtor comes forward and wishes to settle. We can illustrate this, and prove our previous work, by finding what would settle the account on July 15, 1908. It would require $450 plus the interest on $450 from Dec. 15, 1907, to July 15, 1908 (213 days), or, altogether $463.16. SERIES 8o I. (a) What is the cash balance of the following account on Mar. 15, 1908, reckoning interest at 6% ? (b) On what date would the commercial balance settle it ? J5p. Vouell & Wrong. Cr. 1908. Jan. Feb. To Mdse.,net 30 dys, " net 30 dys, 250 300 id credit items our question on what date of our simple time will $450 titerest. a smaller sum of ve know that the ;, and the greater re just calculated 3 Dec. 15, 1907. g of $450 settling led took place on ctually be settled >n interest on the ) settle. We can /hat would settle IS the interest on together $463.16. ig account on ? ce settle it ? Cr. CASH BALANCE 267 2. (a) What is the cash balance of the following account on Dec. 3, 1907, reckoning at 5% ? (b) On what date would the commercial balance settle it ? Dr. A. White & Sons. Cr. 1907. Sept. Oct. To Mdse., 30 dys. 30 " 450 310 1907. Oct, By Cash 400 3. {a) What amount would settle the following account on May 10, 1908, interest 5% ? (b) When would the commercial balance of the account be an equitable settlement ? Dr. Ingram & Davey. Cr. 1908. Mar. Apr. 9 To Mdse., 60 dys. 17 " " 30 " 275 340 1908. Apr. May 10 By Cash 1|" 240 300 4. (fl) What is due on settlement of following account, Dec. 20, 1908, interest 7% } {b) When should interest start on the account ? Dr. J. F. Foster & Co. Cv. 1908. Jul> Aug. To Mdse., 2 mos. 30 dys. 560 270 1908. Aug. By Cash , Note, 30 dys. 450 300 S. (a) What sum would be required to pay the following account on Sept. 19, 1908, interest at 5% } {b) Find when the balance of the account should be considered an equitable settlement. Dr. C. Chute. Cr. 1908. May June To Sundries,60 dys " 30 • 90 " 370 145 420 1908. June 20iBy Cash 30 Draft, 60 dys. 450 360 6. Of the following account find : {a) The amount due in settlement Aug. 23, 1908, interest at 7%. (b) When a three months' note given in payment of the account for the commercial balance should be dated so that the note would fall due on the equitable date. Dr. Geo Young. Cr. 1908. Jan. Apr. To Mdse. 46870 392 60 1908. I I Mar. 28'ByCash June 1 7l " 1400 145 '•I 268 APPLICATIONS OP SIMPLE INTEREST 7. («) (b) Dr. What amount would settle- this account on June 20, 1908, interest at 5% ? When would the commercial balance of the account pay It ? W. H. Hayslip. Cr. 1908, Feb. Mar. Apr. ! 1 387125 1908. Mar. 22 il75 Apr. 11 !297 30 June 7 ll By Cash 276 70 i200j Note, 1 mo |185l To Mdse., 60 dys. " 60 *" ! 8. (a) What amount would be necessary to pay the following account on Dec. 2, 1908, reckoning interest at 4% ? (b) When would the balance of the account be accepted in settlement ? • Dr. F. L. Sanders. Cr. 1907. July Sept. Nov. To Mdse., 3 mos. . ..I' 179 30 " '■ 60 dys. ...I210I " 60 " ll 87'20: 1907. Aug. Sept. By Cash . " Draft 150| 162:75 9. (a) What is the cash balance of the following account on ib) Dr. July 3, 1908, interest at 5% o ■ When should a note, at 60 days, for the commercial balance of the account, be dated so that by the prompt payment of same Mr. Boyle would avoid paying interest on the account ? H. J. Boyle. Cr. 1908. Apr. May 10. i| I 11 1908. ro Mdse., 90 dys. . . 327 50 ! May " 30 " ..'169 20 ■' 30 126,35; May I II I ~ 3 By CasJi '268 30 15| " Note, at 15 dys... 2001 3l| " Cash 1 1501 (a) What amount would settle the following account on Jan. 10, 1909, interest at 5% ? {b) On what date should a note, at 3 months, for the balance of the account be dated so as to fall due on the equitable date of payment ? Dr. G. P. Brown. Cr. 1908, I June 10 July 23 Sept. 115 To Mdse., 4 mos. ,850 600. Ii730! 1908. ( I Aug, lO'ByCash Dcpr Oct. .9; 560 470 Note, 10 dys... 11350 June 20, 1908, le account pay Cn 27670 |200i mo |185i ' the following rest at 4% ? be accepted in Cr. 150| 162:75 ag account on niercial balance rompt payment interest on the Cr. 268 30 15 dys... 2001 i,150l ccount on Jan. for the balance in the equitable Cr. 560 470 10 dys... 11350 EQUATION OF PAYMENTS 269 EQUATION OF PAYMENTS AND AVERAGING OF ACCOUNTS can'^be'^Sd VT"' " '" '"' ^'^ ^""'^ ""^ ^^^'^^ ^^e account can be settled by the payment of a sum in cash equal to the k tiy*"'/,'"'"'^ T *'"*«^ °^'^ '"'■ ""^ W"i™t of an account h ,. , , "" ''*"* ""= '™'<='«ndise balance may, with fa rnc" to both debtor and creditor, be proffered in payinc^l. Working Plan Those who have carefully followed the work on cash balance know already how to average an account. The questions of the second aspect under the head of cash balance are all of them questions in averaging accounts. There is just one point to be noted by the student. In asking for the cash balance of an account ' It IS natural that the question should give the date on which it is' required to find the cash balance. In finding the average date of an account, the student may select his own date up to which he will find the cash balance. He may also select his own rate of interest as this work of linding the cash balance is merely a means to an end. There are but two simple steps in the work. /..f '"'l/'TZ^'r'^ *^' '""'^ ^^^'''"'' °* *^^ a^^o""t to any date (preferably the latest due date) and at any rate of interest. NoTE.-This date selected is known as the focal date. Step 2.-Compare the cash balance with the merchandise balance, and find the date on which the mwchandise balance will settle the account. 270 APPLICATIONS OF SIMPLE INTEREST i I a Illustration 1.— Find the average date for the payment of the folio wing account : Dr. Andrew Adams. Cr, "I9O8. ^ May 15 Mdse.@ 30 days $500.00 June 9 " @ 60 " 350.00 July 18 " @ net.... 250.00 Aug. 5 '■ @ 30 days 470.00 $1,570.00 Solution 1st Step : Cash Balance to Sept. 4, at 5%. Dr. Andrew Adams. Cr. Due Dates, June 14. . Aug. 8.. July 18.. Sept. 4 . . Items. $500.00 350.00 250.00 470.00 $1,570.00 Int. $5.62 1.29 1.64 $8.55 1,570.00 $1,578.55 Cash Balance . . 2nd Step: Knowing that $1,578.55 will settle the account on Sept. 4 find when $1,570 will settle it. In other words, find in what time $1,570 ^ill amount to $1,578.55 at 5 per cent. $78.50 is interest on $1,570 for 1 yr., or 365 days. 8 5S 8.55 is interest on $1,570 for 365 days x 73 50 • °^ '*^ ^^y^- If $1,578.55 will settle the account Sept. 4, $1,570, a smaller amount, will settle it 40 days before Sept. 4, or July 26, 1908. Illustration 2.— Find the average date of the following account : Dr. Charles B. Heath. Cy. 1908. May 21 Mdse., 3 mos.. " 28 " 3 " . fune 9 30 days $500.00 250.00 160.00 1908. May 24 Cash $300 .00 June 5 Note, 60 dys 400 .00 July 21 Cash 100.00 AVEBAQING ACCOUNTS 271 Solution 1st Step : Cash Balance to Aug. 28 at 5 per cent. ^^- Charles B. Heath. Due Dates. 1908. Aug. 21.... " 28 July 9.... Cr. Items. $500 250 160 $910 Int. $ 0.48 .00 1.10 $ 1.58 910.00 Due Dates. 1908. May 24 Aug. 7.... July 21.... Items. $300 400 100 $800 $911.58 Int. $ 3.95 1.15 .52 $ 5.62 800.00 Cash Balance. $805.62 105.96 $911.58 2nd Step : If $105.96 will settle the account on Aug. 28 find when $110 (merchandise balance) wUl settle it. In other words, Ind in whaltlme lie interest on $110 will be $4.04 ($110.00 - $105,96). $5.50 is the interest on $110 for 1 year, or 365 days. 4.04 is the interest on $110 for -J^^Jx 365 days, or 268 days. If $105.96 will settle the account on Aug. 28, 1908, $110 which is a g' uuer amount, will settle it 268 days after Aug 28th, or May 23rd, 1909 The Interest v. Product Method of Averaging Accounts We have chosen to make the work in averaging accounts an outgrowth of finding cash balance. This we have done only after mature dehberation, as the result of many years' experience in presenting this subje,: aging accounts. Naturally,, the introsc n^.ethod of handling the work has been followed. Our first rca.on for using this method will be found in the fact that finding cash balance requires the finding of interests and, if we use the cash balance work as a means of averaging accounts, we therefore naturally use the interest method. 'There are several other reasons, however. In the first place, it will be found tha^t^m many offices where there is a great deal of work along the 272 APPLICATIONS OP SIMPLE INTEREST i' ! : 1 '^ Hb; 1 I ^^^^m 'i E i ^^B^K 1. ft ' i i ^Hk :^ ■-.m i m 1 line of averaging accounts to be done, the work is done with the assistance of interest tables. In the next place, we believe that the plan is more satisfactory to those to whom accounts are rendered, as they can appreciate the idea of interest calculations where they might not be able to see the point of the product method calculation. From the teacher's standpoint, we are persuaded that much of the difficulty in presenting the work of averaging will be ov«r. come by following the order we have suggested in the work. How- ever, if it is required to use the product method, "it, again, can be quite easily explained as an outgrowth of the interest method, and this will be especially clear, if, as a rate of interest, we use 3.65 or 36.5 per cent., or even 365 per cent. We submit herewith a second solution of the last illustrative example, in which the product method is explained, and, moreover, developed from the interest method. Illustration.— Find the average date of the Charles B. Heath account, first using the cash balance method, and then developing the product method. Solution by Cash Balance Method 1st Step : Cash Balance to Aug. 28th at 3.65 per cent, interest. ■^''- Charles B. Heath. Cr. Due Dates. 1908. Aug. 21 " 28.... July 9 Items. $500 250 160 $910 Int. $ 0.35 .00 .80 $ 1.15 910.00 $911.15 Due Dates. 1908. May 24 Aug. 7 July 21.... Items. $300 400 100 $800 Cash Balance. Int. $ 2.88 .84 .38 $ 4.10 800.00 $804.10 107.05 1911.15 AVKRAGINO ACCOUNTS 273 w.n^1^^.^?'^lrwr irr^"" - ^"^- ^«' - -hat date «2.95 interest ? °'^'" ^'°" ^""^ ^i" ^^ take «1 10 to accumulate «4.015 is interest on $110 for 1 _year. or 365 days 2.95 is interest on $110 for ~~ -- qrc , 4.015" ^^^^^y'^'Oi- 268 days. If $107.05 will settle fhr. n,.., ■^ '*''^ -^"&- '^««. or on May 23rd. 1909, Solution by Product Method Focal date, Aug. 28, 1908 Charles B. Heath. Items. Heath Gains Use of $1 for $500 3,500 days 250 " 160 8,000 " 11,500 days. Cr. Due Dates. Items 1908. May 24 ... . $30O ^ug- 7.... 400 J^h 21.... 100 Heath Losses Use of $1 for 28,800 days. 8,400 ■' 3,800 •• 41,000 days. Heath loses use of $1 for 41,000 days. Heath gains use of $1 for 11,500 days. Heath's net loss= use of $1 for 29,500 daj-s not otlo\^^t?:Hr ;rn 'Th::^'".^"^" °" *^^* ^^^^ ^^-^^ the n.oney, is a loser by our dat J'"'''^T' '''^'^' ^^'"° ^^ «^« °"^ "wing is wrong, L that it's too earlv In'^.f " " """"■ '"' ''''' ^'^^^ ^^^^ ^ays after Au, 28, 1908, or ^ti^MrrSX^^^t" ^rl^ ^r" ^^ pay. Explanation To understand why Heath 0■>^r,= ;„ *» the other, we haye only^o :otid'ert;rac tl^^^^^^^^^^^^^^^ ^ ^°^^^ ^" accounts in the light of our supposition Bv h / ^^ """ °'"'' ^^ '^' us $500, which is due on Aue 2. r ^ ^'*"^^ ^'"°""t "^^th owes proper date for settling the account TJ A^"' supposition we consider that the 3500 due on Aug. 21sf, .: ^tSl aT, IZ t '^'\^- "^^"' ^^^° ^^^ gaining use of his n^one^- fort!- iT ^^ ^*^ *° P^^ ^'^ account, he is days .3 equal to the u^ of $^';or ToolV 't^" "'^ ^'' °^ ^^^ ^^ ^ employed in all items on the debit side ''""" ''"^""'"g '^^'i be I 1: \ I 274 APPLICATIONS OF SIMPLE INTEREST Coming to the credit side, we find that the account shows that Heath actually paid us $300 on May 24th. Where a man makes any payment on May 24th, and we suppose that Aug. 28th is the correct date for settlement, it is clear that, in paying us $300, Heath has deprived himself of the use of this money from May 24th to Aug. 28th. This means the use of $300 for 96 days, which is equivalent to the use of $1 for 28,800 days. The same line of reasoning may be employed with all items on the credit side. SERIES 8i 1. On Feb. 10, 1908, I bought a bill of goods amounting to $1,200 on the following terms : $300 cash, $500 on a credit of 30 days, and $400 on a credit of 60 days. On what day might I pay the whole bill of $1,200 without gain or loss ? 2. Smith bought goods of Brown as follows : On May 30, $200 ; June 5, $400 ; June 15, $300. No payments having been made by Smith, on what date should he start to pay interest on the whole amount ? 3. Bought goods as follows : Mar. 3, 1908, $350 on 3 months' credit. April 10, 1908, $270 on 2 months' credit. May 15, 1908, $125 on 30 days' credit. What is the average date of payment ? 4. John Brown bought goods as follows : On Jan. 15, 1907, $500 worth at 30 days' credit. On Feb. 25, 1907, $300 worth at 40 days' credit. On Mar. 20. 1907, $800 worth at 15 days' credit. Find the equated date of payment. 5. A bill of goods was purchased on the following terms : i cash, J payable in 10 days, J in 30 days, and the balance in 60 days. Find the average term of credit. 6. A man bought a farm on Mar, 10, and was to pay $1,000 cash, $800 in 3 months, $1,200 in 6 months, and $1,500 in 9 months. Find the average term of credit and the equated time. 7. Find the equated date of payment of the following account : June 3, Mdse. @ 3 mos $1,275.00 " 15, " " 60 days 500.00 July 12, " ■' 3 mos 450.50 ^u^. lo, au uay;j ozO.S/ Sept. 25, " " 3 mos 145.63 11 if I i AVERAGING ACCOUNTS 275 8. A person owes a debt of «i aon a,,^ ■ r> 10. On a debt of $3,000 due in 9 Inonths from Aoril 1 .h. the bl *e*- '"' " "^ ^"""''"^ ^^'» '- 'h^ Payn-ent oi as fl °". ^;^'lTd ' "'.t^^^ "' "^^^^ "^0= P^hase. $725 on 60 d^ and S8 J™",?;" '" ''^' *"'' ™ ^ "^y^. i)*-. 1907. j I Aug. ! l|ToMdse. ... ^7= ii425, Thomas Brown. 125' 13. Average the following account : Dr. J. B. Dunbar. 1908. Mar. i 9ToMdse.. 1 mo ....l|250 Ap^- Ml- '• 60dys..:;|3?2|50 3 mos. l!275l40J i908. Apr. May- June 1 By Cash 175 280 202|90 May ,171 " of the'fo^olg ZZu" *™^ '°^ '-^ P^^™"' »' 'he balance Dr. . _ — A. C. Newcomp. ^ — Cr. 1907. 1 r — ^ ^^.- May |l5;ToMdse.. .•?<» dvs June j 8j" .. SO ••" July I12I •• .. 90 -. ...5001 ..7501 ...1(650.' 1907.~] June 20 -^y Cash .... Aug. lis . Sept. I li ■• Note,3ddys' i «' 276 APPLlrATIONS OP PTMPLF fNTEREST 15. Find the equated date of payment for tlie balance of the following account : Dr. K. D. Sinclair. Cv. 1908. ■ — ■ , Jan. 3 To Mdse. 2 mos Feb. 15 If II 3 " ....1 Apr. 20 «' it Net 1 ! I! 1908. 375 Mar. 450 775 9 Apr. 15 May |24 By Cash . " Draft, eOd'ys .... 250 400 750 16, A ledger contained the following account : when shuulU the balance be paid, that no loss may be incurred ? Dr. H. Pressey. Cv. 1907. Nov. Dec. Dec. To Mdse., 3 mos, . " " 60 dys. 45 " 32.V 475: 6001 1908. Jan Mar. Mar. 5 By Note, 90 dys. 1 " SiincJrii's . . . . 25 " Cash 300 450 350 17. Fiiicl llie equated date for paying the balance of the following : Dr. C. D. Benson. Cr. 1907. \ ; Dec. 10 To Mdse., 30 dys. 475' II 24 30 " 515 tt 31 " Accept 'ce, 30 " !410i 1908. I Jan. I 2 " 31 By Cash l400i " Note, 30 dys ;600i 18. Average the following account : W. H. Hayslip. Dr 1907. Aug. 10 To Mdse., 30 dys . . 25 " Cash Sept. 10 " Mdse., 2 mos. . . Oct. 1 " " Net 1907. 375 Sept. 3 450 " 27 175 Oct. 1 200 By Draft, 30 dys. ' Cash Cr. 250 425 25 19. Find the equated time for settlement of the following account : Dr. James Munro. Cv. 1907. Mar. Apr. May June July Aug. To Balance " Mdse., 2 mos.. .. ., 2 " 30 dys. (I (I 60 30 I ! 1907. I 325 i Mar. |16' By Cash '' 250 62347i May I2O; " " 300 I722I3O July !30 " Note, 30 dys. .. 1000 975!l2 Aug. |31 " Cash 500 ]50j j I6OOI . I )alance of the ilance of the AVERAGING ACCOUNT SA.LES Accounts between principal and agent .- .nt as oerson.] accounts are usually handled. For instance, the agent! in his """*'■ "^'" "^" piiuuipcd bdccountwitn all amounts received from sale., oollectionc. or whatever work he is doing for the principal. He debits the account with all amounts paid on account of charges incurred in handling the principal's business, and aiso with all amounts representing the value of his services, such as commissions and amounts representing the value of conveniences placed at principal's disposal, such as storage or cartage. The difference between the two sides of the account represents a balance due to principal. Where it is a case of selling goods for the principal, the state- ment that is rendered to the principal is spoken of as an Account Sales. Rendering an account sales, like rendering a statement of account, necessitates averaging the account in order that the equated date for the payment of the balance may be found. Averaging an account sales presents no difficulties that have not been handled in averaging accounts. There is only one feature to be noticed. Son.etimes the com- mission is put in at the date of rendering the account sales, some, times at the average date of the ales as made, and sometimes at the average due date of the sales. It all a matter of the custom of the commission house or of agreement between the parties. An inquiry among a number of commission houses reveals the fact that, in many of them averaging is a thing unknown. When the last sale is made a cheque is made out for the proceeds, and, along with the accojint sales, is mailed to the consignor. The transaction is immediately closed. m :i wKml •sif ■m^^K^H''' ^^^ >«►. O^, \^ IMAGE EVALUATrON TEST TARGET {MT-3) 1.0 II I.I 11.25 ■^l^jS |2.5 |50 ■^" ■■■ ^ 1^ 12.2 U 6" 2.0 M. 11.6 Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, NY. 14580 (716) 872-4503 iV iV r<\^ \ A I ..V Ua 278 APPLICATIONS OP SIMPLK INTEREST Illustration . , , Toronto, March 4. 1907. On? T r' ';f ' ''""''' °' "PP'^^ '''^''^'^ ^^°- J- Lt-OVD. Stratford Ont.. to be sold on their account and risk by ^tratlord. RuTHERFORn .S: Marshall. 1907. Mar. 5 J2 27 Mar. Sales. i To A. Brown, at 30 days, 200 1,1,1s. . $1 .50 ' §300 00 To C. Dunn, note at 30 Rn.l- ^rARSHAI.L. §300 . 00 750.00 SOit.OO 81,550.00 $110.00 25.00 31.75 46.50 213.25 i 81,336.75 the proceeds of rage and of the c of the sales. I find average date ^00 '50 iOO 50 _ side and charges just found. KS. si,5r)n.oo 279 avt.:raging account sat.es 3rd Step : Average this account as before directed ^^^-^^ ^-*« ^or balance of account. April 21st. SERIES 82 ailes. """'^''^ ^'^" commission due as per average I. Account Sales of Flour. Montreal. April 3 1908 By C. Pined & Son. Mar. 3-124 bbls. " I 8' 48 " " ,28120 " Apr. 21 60 " Mar. Apr. @ @ 4 Freight 20.\dvertising\ 2'Storage ... . Sales. S6.10 Cash 6.20 •• 5.95 ■■ 6.20 " ; Charges. Com mission, 3"^', 124 50 1825 25,80 2. Account Sales of Apples. By F. Rutherford. Winnipeg. Dec. 12. 1907. For acct. of V. Weisbrod. Aylmer, Ont. Nov. Dec. Nov. Dec. 10 85 bbls. 14; 63 •• 19110 " 231 47 •■ 121115 '■ _ „„ Sales. @ $2.75, 30 days . @ 3.10, 20 '■ @ 2.90, 2 months ^ 3.20, 10 days @ 2.95, cash : SlFreight 13 Cooperage .... 20|Cash, advanced" 12jStorage -MARGES. iCom 6520i 13 300 mission, 4% . . • ■ ■ j 2360jj 280 APPLICATIONS OP SIMPLE INTEREST U< : fi ■ Account Sales of Bacon. Sold for acct. of The Wm. Davies Co. Halifax, N.S., April 3, 1908. By L. Lang & Sons. I i S\LES. Feb. 28 800 lbs. (oj 7*c. cash .Mar. 20 900 " (a), Sjc, 30 clays .. " 27 700 •■ ((f). 74'c, 10 ■• Apr. I 3 600 " u^ 8ic, 20 " Feb. 28 Frcii^ht anil cartage " ,28 [nsuranco Mar. Apr. CiiARr,i;s. 9 Ailvirtising 3 Storage |Coniniission, li\"o Account Sales of Coflee. Sold for acct. of Jose Marquez. Jan. Feb. Jan. Feb. I Sales. 3|47 bgs., 5,380 lbs. w> 11 ^c, 30 days 10;S6 " 6,720 ■■ (ci), ll^c, 20 " 10 38 " 4,320 •■ (5) Hie 1 month 23 3 8 4 Toronto, Feb. 10. 1908. By A. Regan. Charges. ' Freight and cartage 72 Duty lO.Slor'age ICoiuuiission, 4"o 35 89 25 1670 Account Sales of Tea. Sold for acct. of T. Lipton. June July June Tune Montreal, July 3, 1908. By Todd & Hepburn. I hAI.ES. 20: 20 half-chests, 1,210 lbs., @ 65c, 30 days . 30 44 •■ " 2,640 " (a^. 72c, cash 18 130 Freight 7,635 " (cO. 68c, 20 days Charges, l9'Cartage "^'Cash, -.vJvanced lo oinniission, 3" 25 2 25 250; April 3, 1908. L,ANG & Sons, 23 3 8 25 70 eb. 10, 1908. !y A. Regan. 35 8925' 16 70: July 3, 1908. & Hepburn. 25; i 225 i 250; INTERRcr ON PARTNKRr' AflCOUNTR 281 6. Account Sales of Pork. Sol,] for acct. of Hhowm & SMrxM. Toronto, Juno 17, ly08. I^y W. J, Long & Sons. Sales. May I'SIOO hl.U. .7 §17. W), 30 ckus Jun «-2^ fe: 17.50, 2 n.onths '7| M ■■ «,) iS.liS, cash CiiAK(;';s. May 2SFri'ijTht '-'SCartai^o ' ' " June l7Stnr,i},'p ' ' 17 Cash, at!vanc.(i iComtnissiou, 3'> ^ ' 375 i 4350 I 12 50, '2500: I INTEREST ON PARTNERS' ACCOUNTS WluMV jurtnors have „ot tl.e sa.ne anu.unls invested in a l-s,ness. u .s ct,ston.ary for the articles of agreement to contain an uiterost clause. Tl... inl.Tost clause provides for interest to bo alloued to each l«r ..cr ,.„ all invest.ncnts. I, withdrawals are „,ade, a clause ■^ also IxMusertod provi.ling that each partner is to be charged mteiest on -il sums uilhdrawn. Im.s™„,.,..-J. R. Conlan and N. M.Ucr l>.con,e partners ""Ar a«re,.u,ent ,o share gains and losses equally. I, i, also agreed that interest at the rate of ,oo/„ i. ,„ be l.ed on all lowing •-ystn...n(s and .-harged on all withdrawals. From the foil, saernent of tlu> partners' accounts itnd the net credit interest '•'">«<' each at the end of the year : Dr. Cr. J. R. COULAN. 1907. Aiir. 4 Dr. 1907. Mar, i) Oft, 1 WlTIIOHAWALS •• •• §3,000.00 t'^'^^- Investments. S li 86,000.00 ' ^"-P^- '^ 5,000,00 N. Miller. Cr Withdrawals. •••• 81,000.00 •••• 1,200.00 1907. Jan. 1 Oct. 6 Investments. •■• $4,000.00 •'■ 1,500.00 282 APPIilPATlONS OF SIAII'T,K INTEREST Dr. Solution Dr. J. B. (lulI.A.N. Cr. Date. Sums. Days. Int. Date. Sums. Days. Int. 1907. 1907. Apr. 4 . . . $.3,000 272 $223.50 J;in. 1 . . . SrtOOO 3H5 8«oo.no Sept. 19.. . 5,000 104 124.47 $742.47 Total credit interest $742.47 Total debit interest 223.56 Net credit interest. N. MlI-LUR. $518.91 Cr. Date. Sums. Days. - . Int. Date. Sums. Days. Int. 1907. 1907. Mar. 9 . . Oct. 1 . . . $1,000 298 . 1,200 92 S 81.64 30.25 Jan. 1 . , Oct. 6.. . $4,000 . 1 ,500 365 $400.00 87 35.75 $111.89 I Total credit interest $435.75 Total debit interest 1 1 1 .89 $435.75 Net credit interest. $323.86 Note. — Under the af^reeinent J. B. Coulan is entitled to receive from the firm $518.91, and N. Miller to receive $323,86. Tliat is, the firm of Coulan & Miller pays Coulan $518.91 and the same firm pays Miller $323.86. Each partner is, therefore, in the position of receiving money from a firm in which he is a partner. In other words, the payment of these two amounts ($518.91 and $323.8G, or $842.77) is a loss to the business, of which loss each partner is under agreement to share one-half. Dividing $842.77 into two parts, we have $421.38 to l>e charged to Coulan and $421.39 to be charged to Miller. If Coulan is entitled to draw out $518.91, he must understand that he is really paying half of the amount required for this interest settlement, or $421.38. He nets or clears only $518.91 - $421.38. or $97.53. Miller, while he receives from the business $323.86, has a portion of loss to sustain of $421.39. In other words, he owes the business $421.39 - $323.86, in ^P"l » is^'ord nivests $1,000 si,^M, a,K, ■:;:';>! ,,^T'ca,c,'"[\v,^^,-;;'/ 1 ^'\-^^<^^^ that nitcrest at the rate of fi"/ i< <,/r n ^\'^^'- „ " 's agreed and charged on alft ^l^^ L " Fn.f th^'^ tiUHT^"*^ due each at the end of the veir F Vl„ , i ^'^^d't niterest interest privately, how much shonld , ^ '^''"^' ''' ^^^'J"^* ^''^ an equitable settlernt ? ''"' ^^^ ^^^^" ''^'^^''" ''^ "'^ke busints!^"l!!io„'-JS./^^^"";/J'Vtyn & Baker engaged n. 86,000 On Am ,"'^"^\'^ ^'^^^' ,^Iartyn $7,000, and Baker but on Sept I inveft«i S?S(/. ^H .•^'''/^'"^'^'''^^'"^^^ §-'0W. ;nvested s5(K)0 adiS:;:;L,' l^uT o,f S"T'.^^^ invested §2,000 additional, but on Feb. J Sdrew k%J ^J'"' .0 adjust "e^tafe 'eJX-atdy ? " ' ""' "'^ '" "" """^ Brown s investments were • On Tin 1 WfJr^ i^r /^^^^"^ ^• on Oct 2S <{9 (M\a u ' > J'^"', ', ^^'^J^ , on Mar. 10, $2,000 ; o, o^ .• ^'^' c^^'^- I^'own's withdrawals were : On Mav IS the net credit interS due Son",:," "^ ="»""'» withdrawn, fad ■■.diust the interest lluZl^^Z ^J^lSs? """ "'«"' *^^ A i \ —a ^ti-i API'LICATIONS OF islMl'LK INTlfiiilCbT 5. On May 1. 1907, Kent, Todd & Tufford hccanit- part- ners, agreeing to sliare gains and losses in proportion ol ;•,, ;!, and ;•;. Kent invested on May 1 S8,(KK), and on Nov. JO .S3,(KH), but on I'eh. 17 withdrew S4,000. Todd invested on May 1 S6.(HK,, but on Nov. 3 withdrew S500, and on Fil). 20 SI,(MK». Tufford invested on May 1 $4,000, and on (Xt. 25 §2.000, but on Dee. 1 with(hi>w SI, 400, and on Mar. 12 81,2tK). Find the net credit interest due eaeli on May 1, 1908, if tiiey wi'ie to receive interest at tlie rate of 9% on net investments. With what single amount might each partner's account be debited or credited to make the adjustment ? ACCOUNTS WITH BANKS Depositors in banks are of three classes : 1. Depositors on current account, who have the privilege of issuing cheques, but do not, as a rule, receive interest. 2. Depositors in savings banks, who receive interest, but, as a rule, do not issue cheques, except in their own favor. 3. Depositors on deposit receipt, who lend a bank one definite sum, and receive a written promise for the return of the same, and receive interest. The methods adopted by banks for reckoning interest show considerable variety. They may reckon it on the minimum balance the depositor has to his credit each day, each month, each quarter or each half-year. And the interest may be addi'd to the ])rincii)al each quarter or each half-year. In Canada since January, 1909, interest is added half yearly only. However, if the student familiarizes himself with the two illustrations given, he should have no difficulty in making any calculations desired along these lines. Note 1.— Banks do not pay interest on a fraction of a dollar. Note 2.— In reckoning interest on monthly balances, banks allow ^ of the interest for one year. Illustration 1.— Verify the amount of $229.64 appearing in John Smith's bank pass book as the amount which he has to his credit on Dec. 31, 1907, taking his deposits and withdrawals as they appear in the illustration shown. The bank pays interest d iK'Ciimc p.irt- )ii ot ;•,, ;J, and j;. (KM), but on Feb. HK,, but on Nov, ord invested on X'C. 1 withdrew •dit interest due st at the rate of lint might eai h he adjustment ? vc the privilege interest. ■e interest, but, :)\vn favor. id a bank one >r the return of J interest show ininium balance h, each quarter to the jjrincipal January, 1909, with the two in making any I dollar. banks allow j^ of 9.64 appearing diich he has to lid withdrawals k pays interest 28^ ACCOUNTS WITH BANKS 30tl, aiHl Do,-, 31st otoa,!, y",' '" ""■■ •'"'"""'' "" J""'' Date. \.Nc:iis. p- , Sor.UTioN subtJti„r:hrnue:. ^^^""'^ '" ''- "■^'■■^-^^ -'"-■ ^^^^in« deposits an. month. Thus, up to Jan. loTe J '?"'''"''' '''''"'"'^ ^•'^'^■' P-* ^f the to end Of .nonth he had a lllance'of S7 ""t V"^ "^''^ = ^^"'" J""' ^' January was nil. From Feb. 1 to Feb Vul i i ""'"■""'" ''.-tLuic. f„r to Feb. 16, $105 ; from Feb 16 to end nT T ""' ^'' ' ^'"""' J"'"''- ^ balance for February was «75. !nd so 1 "" ' ^''^ '° '" "'"'"^"^ The interest to be credited tn hi. ■. ' . intent on ,75 . sss . S^O r 1 S^r^S)": ^ ^« ^^ °- -nth. The mterest on «660 for 1 month at 3 % - $660 , . , The mmimum monthly balances for lu 7 f ^^'^ "" ''= «^-«5. were $276. $304, $284, $254, $254 and $2.5 "' """"^^^ °' '''' ^^'^^ IZi^l *^" •"'"''""'" "monthly balances Is'$l 597 The mterest on $1,597 for 1 month at 30/ - s, =07 The balance to his credit therefore on rZ~J''ll '" r_^^>^ A = $3.99. ■«l $229.64, if ore on Dec, 31 190 /. >s $225.65 + $3.99 286 APPUCATIUNS 01' HlMI'IiK INTEREST U !'■ Illustration 2.— In tlu' previous case what would Jolui Smith have had to his credit ou Dec :^Ist had the hank allowed interest at 3% |)cr amuun on daily balances and c edited the interest on June 30th and Dec. 31st ? Date. HAl.A.NCliS. Dys 75 1 24 105 13 85 24 135 8 50 ' 46 230 33 200 6 275 17 277 305 285 255 301 226 19 12 19 '• 70 19 : 21 19 35 19 '' 35 19 11 230 51 Products. ISOO 1365 2040 lOSO 6900 7590 1200 4675 26(i50 3324 21350 5985 8925 10535 2486 52605 Solution Fill in the " Days " column in the diagram with the number of days each balance was the amount he had to his crccHt. Thus, $75, was the amount he had to his credit from Jan. 10 to Feb. 3, or 24 days ; §105 was his balance from Feb. 3 to Feb. 16 or 13 days, and so nn He is entitled to interest on $75 for 24 days, which is the same as the interest on $1,800 for 1 day. Enter 1800 in tlie " Products " column. Similarly, the interest on $105 for 13 days is the same as tlie interest on $1,365 for 1 day. Enter 1365 in the " Products" column. Complete the " Products " column by multiplying each balance by the number of days it was the balance. Tlie total of the " Products" column at the end of June will be the number 01 dollars upon which 1 day's interest is to be calculated at 3%, and added fo bis balance. ACCOUNTS WITH BANKg 287 aid J oliii Smith .illovvcd iiitiTi'st the utirtbl on . Dvs Products. 24 IWU) IM 13(i5 24 2040 M lOHO 46 «900 33 7590 6 1200 17 4fi75 12 26(i50 3324 ' 70 21350 21 5985 35 8925 i 3''' 10535 1 11 2486 52605 number of days IS, $75, was the days ; $105 was the same as the ducts " column. 1 the interest <;n Complete the number of days ill be the number 3%, and added The interest on $26,650 for 1 dayat3o/„= |26.650 x ,3o X ,<,= ,2 ,9 Similarly the interest to be credited if ♦!„. ,.r„i . .■ may be found to be $4 32 So hU hli .? °' ^'''^ ''""""^ half-year 14.32= 1230.51. ^^"'' °° ^''=' 3'- '907, is $226.19 + SERIES 84 I. On January I, 1907, my bank balance wis ftd^ n • the y,-ar made the following depositr fan 2? Ifl?" rT"".^ S73, April 3, S37.50- Auril '>^ I't^ l' ^'^^' J""« 5, §300 interest at 4% on dailv hnUnri^ T' .^' -'^ ^^'^ ^^"k allows positors' accoits o"l' '3 ' un^'s^'tept"^ ^* .'"^ *^ ^.^- find the merchant's balance or June^) i'907?*- ' ^''- ^^' «79^' ^u-J^"V^' ^^^' Emerson McTaggert's bank hpbn.« 13 ?'^ subsequent deposits were fan 20 4«>.^^ Z^ $100; April 20, $80; Mav 10 Slio.' t1 ,o'.r?' ^^^' 27, $150; Dec 3^ lif'/ .'uJ ^', J^^^ ^3> $215; Sept. 28 4.V TO «qm T^ ,/^'f withdrawals were: Feb 12 « 7?' -Hciy 10, $300; June 16, $35- Aim 9^; «i^n xt ,« T *^'^J the bank allows interest Jslo/TS. ' ^^^ ' ^°''' ^2. $100. If balances and credits interest £rtn^''""'f" minimum quarterly '^0 nnH n- ''I fi ^ 1? Tr V^"^ *° depositors' acconnts on Tjmp •J and Dc.. ol, find Mr. McTaggert's balance on Dec 31. 1S06 if I- fffi 288 APPLICATIONS OP SIMPLE INTEREST ill ,^ 5* • person made the following deposits in a bank : Ian. 25, 19()7, $200; Mar. 13, $152.75; April 10, $175; June 7. $225 Sept. 17, $130; Oct. 7, $436.28. He witluinnv as follows: April 21, $165; June 11, $215; Aug. 9, $135; Dtr. 10, $240 If the bank allows niterest at 4J% on daily balances and credits interest due to depositor's accounts on June 30 and Dec. 31. find his balance on Dec. 31, 1907. ACCOUNTS WITH STOCK BROKERS The adjustment of accounts with stock brokers gives us a familiar examj^lc of the application of the principles of cash balance. Stock is either bought outright or on margin. Where stock is bought outright, through a broker, it is expected that the buyer shall furnish the broker with sufficient money to boy, at the market price, the stock required. Thus, if it is desired to boy outright 50 shares of C.P.R., selling at 155, the buyer must put into the hands of his broker 50 times $155, or $7,750, plus the broker's charge for his services. Buying on margin is simply a form of speculation. The buyer orders his broker to buy, but does not intend to put up the purchase price. Instead, he puts up a margin or small percentage of the par value of the stock bought. This is usually 10% of the par value, but varies with different brokers. The broker then buys the stock with his own funds. If the stock, after purchase, starts to dechne in value, the broker has the margin amount to protect himself. If the speculator does not keep his margin good, the broker will sell the stock to protect himself. This he will always do before the dechne has become sufficient to wipe out the margin. If the stock starts to go up in value, the broker awaits the speculator's order in the matter of selling, and when the sale is ordered, the speculator expects to get back his margin plus his profits. In theory, this is the idea of buying on margin. In practice, it often degenerates into a pure gai.ible, as the broker never puts up the purchase price, and it becomes simply a case of wager between the broker and the speculator as to whether the stoek v/ill go up or down. i I ACCOUNTS WITH STIK'K BWIKEns 28S rLL«ST«„,„N ,.-0„ January 2„d J. WalUTs d..,«si,od wi.h h,s hro ..,. J,^, ,., ,„,,„„ ,„, ,„^. „„,.^,„^^^, _^, ^^^^^^^^ _^^ ^^ ., R.R. s,odc a. 92J. Tho ..ock was sold January 26.h a. 96| Aib™,« 6% on d.,«si., and c„a.g,„s «% on pu.ha. ..Hc. and i/o brokerage each way. what docs the broker owe Walters ? Solution Broker's Account with J. Walters. ^ Cr. Jan. 2— To 50 shares Halifax H.R., „ ^t ^-i $4,612.50 2— To Brokerage, i°^ /o 26— To Interest on $4,618.75 for 24 (lays at 6% 26— To Brokerage, r/o 26— Balance due J, Walters 6.25 18.22 6.25 696.25 i Jan. 2-ByCash , 500 ^qO I '■ 26-By 50 shares ' Halifax U.li., '^t 9''i/ 4.837.50 26— By Interest on $500 for 24 daysat6o/„.. ,97 $5,339.47 $5,339.47 ,' E.XPLANATION from date „( p„„ha,e to date o sa = /^ h f ^"*''"'' '"' '"" ^' ""^^ .H= S.'rpHn":;!'::^'*" ™*- «- ^--' °" ^ '<.r ^4 da,, and waa?:„*,CrrLrf *°- *= -^ ^-e Cue Walter.. „ ,» 8«25 ho Lived trl ihe Sr Thf T '"? "^ '""*<' »'"> '' ^ lue oroKer. The profit is $196.25. ^^;lo^°',^Te"cust'om"of brokers.™ ''"'"''"" P"'' ^'^^ ''■°'^^^^^^' ^« -re St 290 APPLICATIONS OF SIMPLE INTEREST I ) Illustration 2.— Suppose in the previous question that on Jan. 26th the stock had been quoted at 88, how much would Walters need to deposit to make good his margin ? Solution ^''- J. Walters. Cr. Jan. 2— To 50 shares Jan. 2— By Cash $ 500.00 Halifax R.R., »i 2e.-By 50 shares at 921^ $4,612.50 Halifax R.R., " 2— To Brokerage, at 88 4,400.00 i% 6.25 1* 26— By Interest on 6— To Interest on $500 for 24 $4,618.75 for days at 6% . 1.97 24 days at 6% 18.22 " 26— Balance 265.00 $4,901.97 $4,901.97 Walters would need to deposit $500 - $265, or $235, to make his margin ^ood. Illustration 3.— On July 1 a broker bought for VV. C. McCarter 200 shares Dominion Coal at 43f . 30 days later he sold 100 shares at 41 f and on Aug. 18th he sold 100 share ^ at 39|. Allowing J% brokerage each way and 6% interest, how does the account stand ? Dr. Solution W. C. McCarter. Cr. July 1—200 shares Dom. July 1— Margin $2,000.00 Coal at 43| . . $8,725.00 " 31—100 shares Dom. n 1— Brokerage, J%. 25.00 Coal at 41|... 4,112.50 i< 31— Brokerage, |% Aug. 18— Int., 48 days, on on 100 shares. 12.50 $2,000 15.78 Aug. 18— Brokerage ^% " 18— Int.. 18 days, on on 100 shares 12.50 $4,100 12.13 «« 18— Int., 48 days, on it 18—100 shares Dom. $8,750 66.04 Coal at 39J... 3,975.00 '« !*r annum, «n.1 ) number of years er ct. 4 per ct. Yri iOOOOO ,2 2500 17 1787 '5 2300 '6 8631 12 6533 2 7926 S 0901 8 9735 5 9876 9 6972 6866 9 5606 6 9452 3 4883 9 8601 6 7555 i 8920 5 0132 7 8866 4 3147 5 1158 1 1443 3 2849 2 4498 3 5856 5 6711 17196 3 7798 r9370 )3148 r0759 )4235 3 6033 >9045 !66U 12543 11132 17171 :5972 13381 15799 0202 i4160 15855 14110 18404 8898 6459 268« 9930 1327 0824 3202 4114 1.0100 0000 1.0816 0000 1.1248 6100 1.1698 5856 1.2166 6290 1.2653 1902 1.5159 3178 1.3685 6905 1.4233 1181 1.4802 4428 1.5394 5406 1.6010 3222 1.6650 7351 1.7316 7645 1.8009 4351 1.8729 8125 1.9479 0050 2.0258 1652 2.1068 4918 2.19U 2314 2.2787 6807 2.3699 1879 2.4647 1555 2.6633 0417 2.6658 3633 2.7724 2.8833 2.9S87 3.1186 3.2433 3.3731 3.5080 3.6483 3.7943 3.9460 <.1039 3255 4.2680 8986 4.4388 1345 4.6163 6599 4.8010 2063 6979 6858 0332 5145 9751 3341 5875 8110 1634 4.9930 6145 41 5.1927 8391 42 5.4004 9527 43 5.6165 1508 44 5.8411 7568 45 6.0748 2271 46 6.3178 1502 47 6.5705 2824 48 6.8333 4937 49 7.1066 8335 50 7.3909 5068 51 7.6865 8871 52 7.9940 5226 58 8.3138 1435 54 8.6463 6692 65 1 2 3 4 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 80 Si 82 S3 34 85 36 87 88 30 40 t, win Increase at any rate ' rate per annum, ai ahoun t any rate iicr annum, an.l ! in the table.- the result wiH Of principo/ 6|/ 6 3.4;% 9999 .'<.r.84 0,3619 .■'.74.'i:i 1813 3.913.8 B745 4.0,899 SIOI 4.1-T40 3018 4.4063 6154 4.6673 4781 4.8773 7S)G 5.0968 6019 5.3'>62 I92I 5.56">,8 99(ia 5,8163 6451 6.0781 0091 0.,3,'-il6 i.'-.4a 6.6:i-4 .'i813 6.9,161 2290 7,2482 4,S43 7,5744 1961 7,91,'i2 6*h9 8.2714 ,W,'i7 8.6i;i6 7107 9,0320 3627 9.4391 0490 9,86,38 0463 10. ,3077 rvV,3 10.7715 8677 11.256;) 0S17 1,0500 OO<0 1.1025 000 1.1,576 250 1.2155 063 1.2762 816 1.3400 956 1.4071 0(M 1.4774 554 1.5513 282 1.6288 916 I. 7103 394 1.7958 563 1.8856 491 1.9799 516 2.0789 282 2.1.S2S 746 2. '2920 183 2.4066 192 2. 5269 »2 2.6532 977 2.7859 626 2.9252 607 3.0715 238 j'.22.')0 999 3.3863 549 3.. 5556 727 3.7334 563 5.9201 291 4,1161 356 4,3219 424 4.5380 395 4.7649 415 6.0031 885 5.2533 480 6.5160 154 5.7918 161 6.0814 069 6.. 3854 773 6.7047 512 7.0399 887 7.3919 882 7.7615 876 8.1496 669 8,5571 503 8.9850 078 9,4312 582 9.9059 711 10.4012 697 10.9213 351 11.4673 998 12,0407 698 12.6428 083 13.2749 487 13.93,86 961 14. 6,1,56 309 1.0600 000 1.1236 000 1.1910 160 1.2624 770 1.3382 256 1.4185 191 1.5036 303 1,5938 481 1.6894 790 1.7903 477 1.8982 936 2.0121 965 2.1329 283 2.2609 040 2.3965 582 2.5403 517 2.0927 728 2.8543 392 3.0255 995 3.2071 305 3.3995 636 3.6035 374 3.8197 497 4.0489 316 4.2918 707 4.5493 8oO 4.8223 459 6.1116 807 6.4183 879 5.7434 912 6.0881 006 6.4533 867 6.8405 899 7.2510 253 I. 6360 868 8.1472 520 8.6560 871 9.1542 524 9.7035 075 10.2857 179 10.9028 610 11.5570 327 12.2504 546 12.9854 819 13.7646 108 14.5904 875 15.4659 167 16.39,38 717 17.3775 MO 18.4201 643 19.5253 635 20,6968 853 21.9386 985 23.2550 204 24.6,'i03 210 1.0700 000 1.1449 000 1.2256 430 1.3107 960 1.4025 517 1.5007 304 1.6057 81« 1.7181 862 1.8384 ,592 1.9671 514 2.1048 520 2.2521 916 2.4098 450 2.5785 342 2.7590 315 2.9521 638 3.1588 152 3.3799 32S 3.6165 275 3.8696 815 4.1405 624 4.4304 017 4.7405 299 5.0723 670 6.4274 326 5.8073 529 6.2138 076 d.6488 384 7.il42 571 7.6122 550 8.145i 129 8.7152 708 9.3253 398 9.9781 135 10.6765 815 11.4239 422 12.2236 181 13.0792 714 13.9948 204 14.9744 578 16.0226 699 17.1442 568 18.3443 548 19.6284 596 21.0024 518 22.4726 234 24.0457 070 2S.72S9 065 27.5299 300 29.4570 251 51.5190 168 33.7253 480 36.0861 224 38.6121 509 41.3150 015 1.0800 000 1.1664 000 1.2597 120 1.5604 890 1.4693 281 1.5868 743 1.7138 243 1.8509 302 1.9990 046 2.1589 250 2.3316 390 2.5181 701 2.7196 237 2.9371 936 3.1721 691 3.4259 426 3.7000 181 3.9960 195 4.3157 Oil 4.0609 571 5.03,'>8 337 5.4365 404 5.8714 637 ,6.3411 807 6.8484 752 7.3963 632 7.9880 615 8.6271 064 9.3172 749 10.0626 569 10.8676 694 11.7370 830 12.6760 496 13.6901 336 14.7853 443 15.9681 718 17.2456 256 18.6252 756 20.1152 977 21.7245 215 23.4624 832 25.3394 810 27.3666 404 29.5559 717 81.9204 494 34.4740 853 37.2320 122 40.2105 731 43.4274 190 46.9016 125 50.6537 415 54.7060 408 59.0825 241 63.8091 260 68.9138 561 1.0906 000 1.1881 000 1.2950 290 1.4115 816 1.5386 210 1.6771 001 1.8280 391 1.9925 626 2.1718 933 2.3673 637 2.5J04 264 2.8126 618 3.06.58 W6 3.3417 270 3.6424 825 5.9703 059 4.3276 334 4.7171 204 5.1416 613 6.6044 108 6.1088 077 6.6586 004 7.2578 745 7.9110 832 8.6230 807 9.3991 579 10.2450 821 11.1671 395 12.1721 821 15.2676 785 14.4617 695 15.7633 288 17.1820 284 18.7284 109 20.4139 679 22.2512 250 24.2538 353 26.4366 805 28.8169 817 31.4094 200 34.2562 679 37.3175 320 40.6761 098 44.3369 597 48.3272 861 52.6767 419 67.4176 486 62.5852 370 68.2179 083 74 3575 201 81.0496 969 88.3441 696 96.2951 449 104.9617 079 114.408J 61f '1.1000 000 1.2100 000 1.3310 000 1.4M1 000 1.610S 100 1.7715 610 1.9487 171 2.1436 888 2.3579 477 2.5937 425 2.8531 167 3.1384 2S4 3.4522 712 3.7974 983 4.1772 483 4.5949 730 5.0544 703 5.5599 173 6.1159 390 6.7275 000 7.4002 499 8.1402 749 8.9543 024 9.8497 327 10.8347 059 11.9181 765 13.1099 942 14.4209 936 15.8630 930 17.4494 023 19.1943 425 21.1137 768 23.2251 544 25.5476 699 28.10ai 369 30.9128 805 34.0039 486 37 4043 434 41.1447 778 45.2592 556 49.7851 811 54.7636 992 60.2400 692 66.2640 761 72.8904 837 80.1795 321 88.1974 853 97.0172 338 106.7189 572 117.3908 629 129.1299 382 142.0429 320 156.2472 252 171.8719 477 189.0591 426 1 2 8 4 6 6 7 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22 28 24 26 26 27 28 29 80 81 82 I 88 84 I 86 86 87 88 89 40 41 42 48 44 46 46 47 48 49 60 61 52 68 64 55 ;f the amount of «}?«?« nV,''i™.'"'i""11"'t<"-e»t cent |wr annum, immMe the amount of%r«t 8 per cenTC".!'"'""" , .. y^»»(«.21(»73l'.thatV«4VM°6r5''-???,5'.«."> Sl^;e^^;ie"Zref„''rre::;^3-"\T'';h"""'-''°'" »'- tabla,th.'am'ount*or" ' »>mun,, imv:^\i;;r, „«;':' ?';?r''|C; '' "■^s.ime 'ailb, compoune •• iw«, ai 1 por coDt. per anaum, Interest at - -> years at finer yf" at 2i percent^? 296 COMPOUND INTEREST ! i i SERIES 86 1. Find the compound interest on $7,500 for 3 years at 5% compounded annually. ' «*«■ ^/o. 2. Find the compound interest on $3,700 for 4 years at 70/ compounded annually. ^°' 3. Find the compound interest on $3,250 for 3 years at 6% compounded semi-annually. °' 4. Find the amount of $1,850 for 1 year 6 months at 8% compounded quarterly. ^°' CO/ ?' ^^^* ^^ *^^ compound amount of $1,520 for 5 years at 6. Find the compound interest on $1,415 from Tuly 16 1902 to Dec. 27, 1907, at 3%. * J y > '^^. " " years hai^^r^TToi^rmat^iiis t:f ^^^■^- ^"■^•»™« yea3y,'^%?S,r ^atttheSt ™'^'"' ^-P"™^^" ] 'i . ,...,)Biy 298 COMPOUND INTEnEBT lri I ' QUESTIONS OF THE FOURTH ASPECT (Interest tables to be used.) Illustration.— In what time will $5,000 amount to $6,100.95 if compounded quarterly at 4% per annum. Solution $5,000 amounts to $6,100.95. $1 amounts to $1.22019. Since the given rate is 4% per annum, or 1% per quarter, run the eye down the 1% column until the amount $1.22019 is reached, which will be found to be the amount for 20 years, or, in this instance, 20 quarters. Hence, the required time is 20 quarter , or 5 years. SERIES 89 1. In what time will $1,500 amount to $2,984.68; at 3A%, compounded yearly ? 2. In what time will the compound interest on $800 at 5% per annum, compounded half-yearly, be $720,232 ? 3. In what time will $750 amount to $3,322.80 at 7% per annum, compounded yearly ? 4. In what time will the compound interest on $625 be $463. 13|, if compounded quarterly at 8% ? SERIES 90 Work the following questions with the use of the compound mterest tables : 1. Find the interest on $3,600 for 18 years at 7%, compounded annually. 2. Find the amount of $787.30 for 36 years if compounded annually at 5%. 3. Find the interest on $1,960 for 20 years at 5%, compounded half-yearly. 4. Find the amount of $4,500 for 8 years at 6%, compounded quarterly. 5. Find the compound interest on $1,600 for 28 years at 7% compounded yearly. 6. If $300 be deposited in a savings bank for 16 years, and the mterest be compounded semi-annually at 7%, how much would the amount be at the end of the time ? XV— • QUESTIONS OP THE FOURTH ASPECT >unt to $6,100.95 299 7- What sum will amount to $2Qi9 7i .•« ie compounded semi-annually? »2.9I2.71 m 15 years at 6%, 8. On what sum will the compound interest (or m , at 5% per annum, compounded yearly, be H10531 ? ^^"^ conXLa^LSLX fof iTyerr ' '° ««-«'"^««8 « com'jSuldletrnuTl!; fo^'is^'^^r, *'-^^-'«'^ -'"^ " com'pLidltall'y™ 7%'? ^"^ ''™""' "> »'.5'8.639 « com'ASed"^alV;iariyri{o/!r ^^''^ ^'■''^' »'-«' » at ^, '^J^z^^zs;: bi&^st™- f "' ^ --" wiu'the interS te i^wTmes affumT'"""'^"^ half-yearly, anni'm.tXTdyS^,--" " ^™ ^"""'e itself a. ajo/o per ^'i'^''^^tUt^l:-^Z^:^-^^^^^f yearly, .s is e^uivStfeVr^ralf^^^om^^unS^e-a^fyl ''^'•^-■^' ona'cerTamlt™?4';LT:.'6»/toPm;^"^^^^^^^ Find the sum. ^ ®/°' ""Pounded yearly, is $100. jj'?" ^""^ difference between the interest at ino/ „ added yearly, and that aHHerl hJi. , ""^5^' at 10% per annum, Find the suS. ^"' half-yearly, for two years, is «55.06j: 20. The difference between the interest at ao/ ^^^. ^"^ *- ^0='^'' Oa.f-yeSrlor'6 'yis';^L TS ! 1 . ■i M V\i ANNUITIES An Annuity is a specified sum of money paid annually or at equal periods, half-yearly, quarterly, and so on A Certain Annuity is one which begins and ends at a fixed time Tan'^T ZTh ' \'t.'"'^ °" J'"- '' '^^' *^^*' ^*-ti"g with Jan. 1. 1903. hevvUl be entitled to receive $100 each year for three years This might be called a three-year annuity of $100 and might be presented to the mind thus ; Jan. 1. 1902.... ^ _J!^ ___J}0O__^_jm__ (Jan. 1, 1903. Jan. l,"l9oI Jan. 1. 1905. 1 "/'f cor'*^ '' ^"^ ^ ^'"^'^ *'°"^ ^" investment of money, loaned at 5%, it would require the use of $2,000 for three years to secure the income. The principal amount of $2,000 would need to be put out at interest on Jan. 1. 1902. to have the first $100 ready on Jan. 1. 1903. This explains the law that an annuity begins, not at date of hrst payment, but one annuity interval before. A Perpetual Annuity, or Perpetuity, is one which continues for ever. Thus, $100, if paid each year for ever, would require the perpetual use of $2,000 capital at 5%. An Annuity in Possession, or an Immediate Annuity, is one that begins immediately. A Deferred Annuity, or an Annuity in Revereion, is one that begins at some future time. An Annuity in Arrears, or Forborne, is one on which the payments are not made when due. The Amount, or Final Value, of an annuity is the sum to which all Its payments, with interest on each, will amount at its termination. annually or at not at date of QUESTIONS OF THE FIRST ASPECT »100 plus interest on it for 2 years »100 plus interest on it for 1 year Note that the ^-IntS^trtTi r;!a":^\;r;;f '"T' of years marlcing the duration of the annuity ' "'""'^■' con,^r."ttt:t""^t ratoirs;™*'" '-" °" "^^ «- -^ s.epsineaIe.,,:S;rS^::uTora,rnt"y^' "" '"'"""-- SI .03 1 «' . .03 $1.03 end of 1st year .0309 «1.0609 end of 2nd year J1.03 .03 $ .0309 .031827 $1 .0609 .03 <^092727 end of 3rd year $ .031827 The amount of SI is SI ftQ9797 ^, ^i, ■ of what does this iatest of « 092727 '"''T '"'"^ '' *-«^2727. Now. each year-3c-depos[ted at thf °"'"' ' ^^^^^'^ *^= '^''^'^^ «" « allowed to gather S^^l % p^! J^T™'"' °' ^^^' ''''■ ^"^ ^'^^ bank, and took the interest everv vp^' ^°';"^^^°*=^' ^^ ^^^pt our $1 in one amount we would have In th7 ^ ^. u^""^ ^^"'^ '* ^" ^"°th^^ bank. The the amount of an Zll^ :^:Z%o':^:\^'' T °^ ''' ''-' ^^^'^ ^« compound, added to it. ^^'^ '"*^''^^* ^t the rate of 3%. ANNUITIES * . ', Now, an •uiiiii:«\ deposit is called an annuity, md we see that in finding the amount of <1 /or 3 years at 3%, compound interest, we cannot help finding the amount of an annuity of 3c for 3 years at 3%, compound interest. Knowing, then, the amount of an annuity of 3c to be $.092727, we can easily find the amount of an annuity of $1. Thus : If annuity of 3c amounts to .'. annuity of Ic would amount to And annuity of 100c would amount to 100 x $.092727 > . 092727 3 $.092727 That is, we multiply our figure by 100 and divide it by 3, or, which is the same thing, we divide our figure by .03. From all of which we deduce this useful rule : Rule To find the valm at maturity of an annuity of $1, we find the compound interest of $1 for the ^iven time at the given rate, and divide by the given rate expressed decimally. When we know what an annuity of $1 amounts to. we can easily find by multiplication the amount of any annuity. Now, even in finding the compound interest, we can take a shorter method than that abeady expressed. The amount of $1 for 3 years at 3% can be expressed thus : (1.03^3 To get the interest alone we would subtract our principal of $1 from lais, giving us (1.03)»- 1 and when we dd • -J s this interest by the rate we have (1.03) 8-1 .03 or, putting it general:-,- , / dl cases, thr mount of $1 annuity (1 + rate) "■"« - 1 ~ rate Sm^ '.(! that in finding we cannot help impound interest. J. 092727, we can 092727 092727 3 092727 ~"3 '', or, which is the $1, we find the rate, and divide an easily find by a shorter method rs at 3% can be of %\ from Una, QUESTIONS OP THE FJRST ASPECT 393 Illustration 1. -What is thn or« * c 'or 23 years a, 504 com,„:;,u inf^r? °' ™ """""-^ "' »^'» SotUTION BV KULE EsTABLrSHEU 1400 X { <',T-'} = 1400 X = 1400 (1.05)" .05 , (3.071524)-! 1 .05 ~ (2.071524) T05 " $828.6096 } .05 ■• $16572.19 Solution bea.'t:rrtlrr;lt r,f,rif '^^^"-^-^ °^ ^'^^ ^-^- *^« «- deposit and there will be noXo'sU L th ir/.l' ''Jf u' '"^^ °' " ''"y^" ^"""'^y ^ .et t.e result by findi: 211^ ^ !yrar:;ty ^^ S"' ^'"^ ' -ctsr o^p:^^^^^^^^^^ Ti:-r^ °- --- - "-= - 15-year annuity we can addTh 1^ " h'"' '''"^' *° ''^ ^">°"°* °^ '^- years. '^ *^' compound interest on one payment for 15 rate''or4:ofrrptr"antum."'"'°""'^' semi-annually, is equal to an effective (1.0404)'»=(i.02)»o= 1.81136. Result = 4200 x^'-^2121i*-l . \ $^00 X (^ -Q--^ + , .04041, _ , j^ ,4,78.9, SERIES 9Z at 6o^ ^ani'u^n^rcttou^L-'yel'/;?"''' "' *^ '" '» ^^^ comp™K.eTesU "■"""^ °* ^' ^o™' "> '" «> V^- at 4./„, 1 •I 304 ANNUITIBS 'U §i 4. A man pays $150 yearly for 15 years for an endowment policy of $2,500. Find the accumulated value of payments, reckoning money at 6% per annum. 5. Find the amount of an annuity of $500 for 3 years, reckoning money at 10% per annum, compounded semi-annually. 6. If $500 is deposited at the beginning of each year for 8 years, what amount is due at the end of the time, money being worth 5% per annum, compound interest ? 7. What amount will a man have to his credit who deposits in a savings bank $450 at the beginning of each year for 10 years, if the bank aUows interest at the rate of 5% per annum,* compounded half-yearly ? 8. If a man deposits in a savings bank $100 at the beginning of each year for 3 years, what amount will there be to his credit at the end of the third year if the bank aUows interest in the meanwhile at 3%, compounded half-yearly ? QUESTIONS OF THE SECOND ASPECT Given the amount of the annuity, the time, and the rate, to find the annuity. Illustration 1.— What sum of money deposited at ihe end of each year for the next ten years wiU amount to $800, money beine worth 5% ? ^ ^ Solution A deposit of $1 at the end of each year for ten years wiU amount to $i X (L OS'"-!) .05 $800 will, then, be the amount of an annual deposit of «snn . iliOS^l $800 x .05 _J40 .62889== $63.60. Illustration 2.— The town of Woodstock borrowed $20,000, and agreed to pay 5% compound interest. What sum must be seC apart annually as a sinking fund to pay the debt in 12 years? rs will amount to DiTov/ed $20,000, sum must be s^ QUESTIONS OF THE SECOND ASPECT 305 ,t j^at^^^^^^^^^ question i, to find at 5o/„ compound interest. ' *^^ ^°'°"°t "^ »20.000 for 12 years Amount = $20,000 x (l.OSp = J35,917.12 (i.osp-i 05 Then «35,917.12^ . = $2,256.58 Answer. Illustration 3.— a farmpr k «5,340. principal payable iH 'aJs 'f """'f'^' °" ^^ ^^^"^ oi payable half-yearly at 50/! He h' i'"" '' ^^«' ^"^erest but desires to pJe i„ a saving ba^k'T '' 'Z *'^ '"^-^*' compounded at 40/0 every 6 mo^thi ,f -^"""^^ ^"P^^^* ^^ich. o« themortgageatlhe^nLf 5^ r ' ";^r: ^^ ^"°"^' ^^^^^^ to be made on Jan. 1 1898 .ST\ '' *^^ annual deposit «5.340 at end of 5 year^T' '' '°"' '°"°^^"^ ^^-^^ to have show^^^^^^^^^^^ Of Pi.t Aspect, wil, of at the end-the value of $1 annuity mlth ^'"°'°^ °^ ^'^^ ^^^^^ i°«tead interest on $1 for the full time. Th so^ut on .V""'"''^ '^^ *^^ '=°'°P°"°d «5,340 - |li^*^^) - I , ■ I .0404 + (1.0404)*- 1 j = S946.87 Answer. SERIES 92 I. What annual deposit for 15 years at W amount to $5,000 ? ^ ^^ ^% Per annum will compound interest ? y^^^^' allowing 5% 4. A merchant is mortgagor on a mortgage of $5 000 ^ • 1902. He has provided for interest hnt inf ! . ' ^"^ '" nnf «f J r * '"icicbi, out mtenrJQ t^ r"i" -r--, • i "'It Of pxucceds of four mortgages of «I 9V^'~ V ^ / ^'"'"P^^ holds, ana Which e.p,e o/e ^ .^s^'f^.Ts^:',*^" hI 306 ANNUITIES I ' proposes to invest sufficient of the principal of these at compound interest, 4% half-yearly, to provide for the $5,000 he owes in 1902 How much of each does he invest ? 5. A man pays $240 yearly for 15 years for an endowment policy of $4,000. Reckoning money worth 6o/„ per annum, payable yearly, how much is he paying each year for the life risk ? 6. A corporation obtains a loan of $100,000, to be paid durinR or at the end of 15 years. Show, by finding in each case the annual tax to be collected, which of the following ways is the best, and by how much : "^ (a) Pay the interest annually at 50/0 per annum, and create a sinking fund to meet the debt, to be invested at 40/ per annum, convertible half-yearly. ° (b) Repay loan and interest at 5^% per annum in 15 equal annual instalments. (c) Invest annually an amount bearing interest at 6^°/ per annum which, at the end of 15 years, will repay the loan and interest at 6% per annum. (1,055 ^ " = 2.232479 • 1 065 1 ^ - 2.57184.) ' ■ QUESTIONS OF THE THIRD ASPECT Given the necessary data, to find the present worth of an annuity. Illustration l.-What is the present value of an annuity of $154 for 19 years at 5% compound interest ? Solution Final value of annuity =-^^^^^^^'-1- Amount of $1 for 19 years at 5% compound interest = $(1 .05)" $(1 .05)»» has for its present value $1. $154 (1 .05^»-1) ^ g,54 ,, osio n " 705 has for its present value^^^^^^^— -L^ -f 1.05" _ $154 (1.05»- 1) $3,080 (1.52695) .05 (1.05)>»~= 2752695 = 81,861.14. Illustration 2.-What is the present value of an annuity of $200, aeierreU 5 years and to run 10 years, if money is wortii 5% per annum, payable yearly ? mum in 15 equal c of an annuity QUESTIONS OP THE THIRD ASPECT 307 Solution Final value of annuity - ??^( >• ^^S'" - 1 ) ^ ^~ .05 — Present worth for 15 years (5 years + 10 years) __$200_n. 0510-1) .1 ' .05 TTosi* = $1,210.04. Illustration 3.-A town issues debentures for $I2 orwi k. • mterest at 6o/o, payable yearly and to run sT ^'^•^' ^^ring should they sell, money LnjCiso^^yfaJiy"" "^^^ ^'^^ ^"- i-05« + :os~[r:65)s — =$12,519.54. Illustration 4.-If money is worth 50/ fin^ .u value of a perpetuity of $450. ^°' *^' P'"'""* use !rir'~^^o'^°'"^^ '''' "^'^ ''' ''-' ^°"'^ ^^^"^- ^•^^ P-P--' use of $450 X -5= «9,000. The present value of the perpetuity is, therefore. $9,000. SERIES 93 2. Fmd the present worth of an annuity of $1 000 f. Wng worth 4o/„ per annum. payablTeariy > '" ''""' """^^ S35 to cmttoue 4/ , f ^* 5"^"^' """^ "«' <"her for compounded haif-yeaV""' "' '°''° ™""'™"'' ■"'^-'■ 906 imruiTus !:! ^ I, r ■1 I ■! il ! 'i »d of the eW V«ar, •"^^^^tltZ^irjtlr^^^t'Z'^ %£'. .t fi ■ t^''^' '' '.""^ Rf'^"' ™''"= 0' * perpetual annuity of «2'»1 .0 ru?; /'jl^l *:S:?eV^"5V:VSrr"'' '^'^"^^ ' ''''' '"' payISle\r;fX"hff t-r'SS? JS'r ^'pf% ??^ »— • value, calcu Jed I{6% per°:;nL%a%^i,ai^yel^lyr """"' being worth 5% per annum, payable half-yearly ? ^ interest ^t^fio/^lS""'""* ''^"' °lf mortgage for $10,000, bearing veai to rnn"^ ^ ^"""J''. Payable half-yearly, and haWng thref hS yeiriy ' °"'^ '^"'"^ ^"^'^ ^% per annum, payable Whl?cfn''f ^ff^S"'?^ ^°^°' .P^^i^^" ^"""^"y' ^^^^ 3 years to run. wnat can 1 afford to pay for them so that I shall make 5°/ npr annum on my money as long as it is outstandingT ^ ^^^ P"' ^ve't^t should be paid for a $1,000 coupon bond maturing tlTf S • ^T' ^",? ^'''""S ^% ^"te^est, payable annuaUy so onl'moryT "'^ ""^^^ '^^^ ^^^ annum^Lpound inS IS. What can I afford to pay for a $2,000 bond maturing 5 H't rifl''"^^'^""^ ^"*''''* ^* ^%' P^y^ble annually, so that I shall be makmg 6o/o compound interest on my money ? i6. What can I afford to pay for a debenture for $100, having 3 years to run and bearing interest at 5o/„. payable yearly, so that 1 may realize 4J% per annum on the investment ? 17. What amount will be required to be raised annually at the beginning of each year for 5 years so that there may be sufficient to provide a sinking fund of $25,000 at the end of the 5th year and to pay interest on $25,000 in the meanwhile at 5% per annum' money being worth 4% ? /or, ■Vhat is the value ? )erpetual annuity erred I year and QUESTIONS OP THE THIRD ASPECT 309 fnr \l' ^'""^ fu^ Z'^'^"* ''^"^ °^ ^" ^"""ity Of «200. payable lor 12 years, the first payment to be made at the end of 2 years money at 3% per annum yearly. ^ ' 19. What sum of money, deposited at the end of each year for the next five years, will then be sufficient to purchase a Srj yeariy?""""^'^ °^ ^' "^'^'"'"^ ^ ^'^'"' """"'^ ^"'""^ ''''*^ 20. What sum of money, deposited at the end of each year nf'iS^"!f '/''' f ^''' """^ *^'" ^" ^"^"^"* *° P"^<^h^s« an annuity of $500, deferred 2 years, to run 5 years, money being worth 4^1 per annum, payable yearly ? •' o /o 21. Wliat sum of money deposited at the end of each year for the next five years, will then be sufficient to purchase a perpetual annuity of $100. deferred 2 years, money being worth 50/? 22. Money being worth 60/0 per annum, compound interest. M xm?''* ^"""^^ ^ ^^^ '°'* ^^ ^ ^-y^ar annuity of $4 ^ ? (6) What annuity to run 5 years could be bought for $2 000 ? interest ^eV' '^' T'"' ''f "' '^ " "^°'*^^^^ °^ ^^'«^' bearing mterest at 6%, payable yearly, having 5 years and 6 months to S^ worT sor""'"' "' ''''''''' '^'"^ ^"^ ^" 6 months, money t>eing worth 5% per annum, payable yearly ? half^'v;.^ farm bears a mortgage of $3,000 at 8o/„ interest, payable touMhl^' the mortgage has 5 years to run. What sum paid now would be equivalent to reducing the interest on the mortgage to 5/0. money being worth 4o/„ per annum, payable half-yearly ? 3 year's In^i '^' T''"^ "^"^"^ °^ ^" ^"""^^^ °f «100. deferred J years and to run 4 years, calculated at 5% yearly. ^ I li ■ '■t 1 'M FOREIGN TRADE BILLS OF EXCHANGE Importing goods into Canada makes it necessary that remit- tances of money should be made in payment of these goods to the persons from whom the goods are bought. As in the case of canceling domestic debts, where the creditor hves in a different city in CanMa, we find that the usual custom m making a foreign remittance is to purchase a bill of exchange, which may in turn be remitted in cancellation of the debt. Foreign bills of exchange are usually drawn in sets of three to provide against loss in transmitting. This custom is a long- established one and still obtains, although the reason for the custom m these days of safe and rapid ocean transit is not so apparent The wording of each of the bills in a set of exchange wiU make it clear that the honoring of one practically cancels the other two The /allowing forms will illustrate a set of foreign exchange : Set of Exchange r 1. Exchange for ^500. Toronto. Ont., April 22. 1908. Sixty days after sight of this First of Exchange '. . . {Second and Third of the same tenor and date unpaid), Pay to the order of Messrs. S. E. Hill &■ "o ' Five Hundred Pounds Sterling _" ' Value received, and charge the same to account of To J. S. Morgan & Co., ^, .,^ ^'^'''don. A. E. Amks & Co. No. 149. BILLS OP EJCCHANQE g, , 2. Exchange for /500. ~ f .» H»*.i p»„^, ^,,,4- ^- I'll ^ Co ^o J. ii, Morgan & Co., \T 1.^ London. . ^ ^o. 149. A. E. Ames & Co. ml 22, 1908. IMES & Co. 3. Exchange for /500. 7- , ^ ^tve Hundred Po,mds Sterling ^- "^'^ '^ ^' Value received, and charge the sa^l 'L To T <: M ^ ^ "*"^ *° account of ■' o y. o. Morgan &- Co., \T , ^^ Loiidon. * T^ . ^0- 149 A. E. Ames & Co. herewith will give these values *^^^' ^^ ^PP^^^ f. I. % 312 FOREIGN TRADE 1 > . 1 ■ '■ . i', 1 i m I § i. 55ea S8g " 0) ■-• s 8 S 8 •o G s 8 » 01 :iff ta •B • •'O g : : B o'o'3:3'3'o'5~'o 5 Sao 05 "g -S BILLS OP EXCHANGE Peculiar Methods of Quoting the Rate of Exchange 313 Ordinarily we expect that the rate of exchange would be quoted by giving the value of the monetary unit of any country n'terms of our own currency. ^ be t?^ve'th?vate"oron "' ""f"" ^''^ '''' '°' '"'^'''^^ ^'^^'^-^^ --'^ find th?r. , u ^ P""""^ '" ""'■ currency. Accordingly we mav find that sterling exchange is quoted at $4.88, $4.89, and so on ^ to Z ^a! I ^ reference to the old par of exchange which used he n.r * °": ^"""^ ^*^^'^"^- ^^ ^^'^ ^^ ^elow the fntril c vale 1 zzt wve? Lr;\^ijr °^ ^^"^^- ''- °^^ ^- ^"^^ ^--" been establkhT f ' . """ ^^"^ "P' ^^^° ^^t^^- ^^e new par had old Daf Th . TT^ '*''""^ ^''^'^^"^^ ^t ^ ^^^-t^i^ increase on the fwnr I .''• r "^""^ *^^* ^*^^""^ '^'^^hange is quoted at a premium of iii«<- h,i„„ ^ it P ***• ^h's increase of 91%, by the wav xpress"? tL sterLT °' ''•''^' ^"' ^'^P^^^"^ ^^« sotewhlt queer expression that sterling exchange is at par when it is at a premium of 9*0/ S pr"lVster L'^ '* T P"^^"* ^'' -^^" ^* ^^ ^' ^i% premium ove?t;fe premilonttt/pr^^^^^^^^^ '%T^' '' ''''^ P^'"^-^' ^* -- '«% on this old par! ^^ ""' ""^ ""^ Percentage may be quoted it5;ltTot:d^n^tabte^^^^^^ ^■^ -^^^^ --«-. as be expected to be ^'uoSd ^ ^^^^^^^^^^ 7*' "°"^' "^^"^^"^ Thus, a franc at par is worth^9 " cenl t/ 1 .' """' '" °"' """"^J^' exchange quoted at I9I or 20 or 20^ h. ' °'\ "' '°""^ ^''^'^^^ ever we find thaf +h u *' "leaning would be clear. How- exchange i, a. 5.2,, « LlTharord:^:™^;^^^'^, 03™°'' "^=° The.. «■,.„„ H-utea at idft, or 23J, or 24, the meaning would be clear .hat ,„nr n.ar., ^ »:«" sT^s": T ^r '"^^ " ''' " ™"" 314 POREIQN TRADE 1 • DIRECT EXCHANGE Questions of the First Aspect Illustration 1.— Find the cost in Montreal of a bill of exchange on London, England, for ;f900 when exchange is quoted at $4.87J Solution Cost of bill for £1 = $4.87}, Cost of bill for ;i900= $4.87} x 900= $4,386. Illustration 2.— How much must be paid in Toronto for a draft on Liverpool for ^458 13s. 4d., exchange being quoted at 109i ? Solution ;^458 133. 4d. = ;£4583. Cost of draft for £1 when exchange is at 109J= $4^ x 1.09|. Cost of draft for ;£4583 when exchange is at 109|= $4* x 1.09J x 458? = $2,237. 27}^ or $2,237.27. "" Illustration 3.— Find the cost of a bill of exchange on Berlin for 1,600 marks, when exchange is quoted at 93|. Cost of bill for SOLUTION'. 4 marks = $.93 J Cost of bill for 1,600 marks = $.93| x -7^= $375, SERIES 94 Find the cost of the following London drafts : 1. For £374 7s. 6d., exchange lOSJ. 2. For £193 6s. 8d., exchange 109J. 3. For £836 17s. 6d., exchange 110. 4. For £527 15s., exchange 108|. 5. For £1,638 14s. 7d., exchange 9|% premium. 6. For £947 lis. 9d., exchange 9|% premium. 7. For £385 19s. 5d., exchange 8f% premium. 8. For £593 16s. 4d., exchange $4.86|. 9. For £267 5s. 9d., exchange par. 10. How much must be paid in Winnipeg for a bill of exchange on Paris for 3,048 francs when exchange is quoted at 5.19^ ? Wc ange on Berlin DIRECT ISXCHANQE 315 eXgf ."'qfoldtt 4^ """ ™ ^""^ '- ^.'^S marks when .36^.r.':rHe:tci;^f ;:^^^^^^^^ - ^--- ,0^ 3.65^'f™!fs a t™^' dal'th. ^ ^ °' ^''^"-^^ <»■ <^"eva for draft, exchange beingl^rb^ker'^^jo;? '"^ "--* <=' the 16. What will a sight draft on London for /2«n r?. . • currency ,„ Philadelphia when exchangetViSgS is^^; Questions of the Second Aspect Solution ^ , ^383 12s. 6d. = /3835 Draft for ;^383i cost $1,854. 18| Draft for ,1 -/ /J-S^^^^IS* . 383|= ,4.83J. «4.83J^ $4^= 108|. The rate o, exchange „,a, ^ „ve„ as M.83J, ,08,, or Si% p„^„„. wa/m"4™Fi'„dlt"r' 1 ' f " °" ^"'^ '- ''^ '-CS o^J. l^md the rate of exchange, brokerage |o/^. Solution there had^.een no brokerage, the cost of the draft would have been lool °^ »-62i or «JJ of $500.62i= $500. $500 is cost of draft for 2,605 francs. $1 is cost of draft for -^— <; oi x 500 = ^-21 francs. •'. rate of exchange = 5.21. 316 9'.'' n !' il FOREiaN TRADE SERIES 95 Find the rate of exchange 1. When a draft for ;f9[)0 cost $4,370. 2. When a draft for ;^306 13s. 6d. cost $1,492,441. 3. When a draft for ;f563 12s. 9d. cost $2,724.25. ^^^^4. Wlien a draft for 4.800 marks cost $1,147.43^, brokerage 5. When a draft for 3,576 marks cost $840.36. 6. When a draft for 3,575 guilders cost $1,443.41 7. When a draft for 33,250 francs cost $6,412.72 8. When a draft for 366.20 francs cost $72.09, brokerage 40/ • i^V , nTl °^, ''' ^'" "^^ Bordeaux for 2,746 francs was $538 20. includuig i% brokerage. What was the rate of exchange ? Questions of the Third Aspect Illustration l.-A bill of exchange on London, England cost $2, 104.22 J when exchange was at 109^. What was the face of the bill ? Solution Cost of bill for £1 when exchange is 109J= $4.44| x 1.09i= 14 86» $4,861} will buy a bill ior £1. a » • 3 $2104. 22J will buy a bill for £1 x 2104. 22J -^ 4.86| = ;£')32.375 = £432 73. 6d. <^.ni'■''''^'■''''"°'' ^•~'^''^ '°'* °^ ^ ^'^ °^ exchange on Paris was $600. and exchange was at 5.19. Find the face of the biU. Solution $1 will buy a bill for 5.19 francs $600 will buy a bill for 5.19 francs x 600 = 3,114 francs, face of bill. SERIES 96 1. A draft on London, England, cost $1,194.94 when exchange was at $4.88. Find the face of the draft. 2. Find the face of a bill of exchange on Manchester, England which cost $2,730 when exchange was at 9iJ% premium. 3. An exporter sold through a broker a bill of exchange on Hamburg at 95|, and received $5,953.49 as net proceeds. Wiiat was the face of the bill, brokerage J% ? XVI— 3 , .■<■,* INDIRECT OR CIRCUITOUS EXOHANOK 1.09J= $4.86§ 317 5. What is the face of „ t m^, '™f """"S quoted at 5.17J ? can be bought for »S,807.2S if ex ange" r^'/s" ,,''?' °" ""''" 6. An importer purchased a 60-dav bili L ^ ^' "'''■' '"^^ ' at par for M46.20. What was TfTce fb^ T °" ''""■"" 1^^ ^ 1, mcluduig i /„ brokerage. What was the face of tile ^Ufto l^rtiHer'td^nX- T-. -'-nse was at face of the draft ? ^ $1,489.50 for it. What was the florins i„ Amsterdam by rcmiJtrt'T "f ' ' *" °' ^''^^O was 14.885 ; thence to pJLl ^ . ™'^°" ™''™ ^«'iange a : and thence to Amstr^l th" f"'' ™^ ''•" '™» '- 100 florins. What did he pavlrr T'""'" ""' ^'^ fr"-":^ '°r "m ne pay in Canadian money ? Solution 100 florins =212 francs ••• 27940 florins =-?^<'^ 212^ 100 " iruncs 25.4 francs = n . 27940 X 212 970.^ „ 100 francs = ^ '!!'«^^ ^12 JOO X 25.4 ^lM-^25^'=«^'-^-^^^^«x2i2 100x25.4 » 100x"25:4 =511,391.82 SERIES 97 francs should be given flr^a^nt t^l """^^' "^ --^ Hamb4."ltmITL ' ™*^ '°"— '' 2.^00 marks to to Paris'wheT^eT Lsa^e rrtr^r"'"^^ '^ «•«« ^ «'»'° when 47 franc, are w^th 25 „:r ^vjiat'd' T"' '" "^""'"'S money? ^o marks. What does he pay in Canadian ■H " !''l 318 POBKIGN TRADE ' ■ ■ ':J' I !;i , 3. K £} is worth 12 florins or 25.56 francs, how many francs IS one florin worth ? 4. A merchant in Montreal drew on Amsterdam for 10 000 gmiders at $.415. How much more would he have received if he had ordered remittance through London to Montreal, exchange at Amsterdam on London being llj guilders for £l, and at London on Montreal 9^% premium ? S- If the exchange of London on Hamburg is 14 marks per pound sterling, that of Hamburg on Amsterdam is 20 marks for /^u^'f ' ?^* °^ Amsterdam on Paris is 28 florins for 60 francs and that of Paris on Toronto is 4 francs for 72 cents, what is the value of £1 sterling in Canadian money ? 6. Exchange at Paris upon London is at the rate of 25.7 francs for £1 sterling, and exchange at Vienna upon Paris is at the rate of 40J Austrian florins for 20 francs. Find how many Austrian florins should be paid at Vienna for a ;f50 note. CUSTOM HOUSE BUSINESS The Customs Tariff is a book issued by the Department of Customs at Ottawa, giving a list of dutiable goods, together with rates of duty thereon, and also giving the statutes which regulate the matter of lev5dng duties. The General Tariff is the rate of duties to which goods are subject, unless specially provided for under the British preferential tariff, the intermediate tariff, or a surtax. The British Preferential Tariff applies to goods which are the produce or manufacture of British countries when imported direct from any British country. This duty is always less than the general tariff. The Intermediate Tariff is, as the name implies, a tariff between the general tariff and the British preferential tariff. It may by order in council be extended, in consideration of benefits, to any country the produce or manufactures of which have previously been subject to the general tariff. A Surtax is a rate duty above the general tariff, and is levied on the produce or manufactures of any foreign country which treats imports from Canada less favorably than those from any Other country. For instance, up to March 1, 1910, German goods low many francs CUSTOM HOUSE BUSINESS 319 imported into this country were snhippf ♦« above the general tariff ^ * *° ^ '"'*^^ ^^ * over and t^e'^vlTaZlZL^''''' - ^ -^^^" P— age of ^^^^^rf:^^^^ -ntit, as. for per barrel, and so on. ^ ^"'''^' °' P^^ ^'"shel, or Some articles imported are subiect fn hr.*u a , specific duties. ^ *° ^""^^ ^^ valorem and Dutiable goods arrive either bv vessel nr h the purpose of handling these imports Thf 1.^ f °' ^^ '''P^^^' ^^^ amount of goods imported bet3n the W h" '"''^' ^^^^^^^^ *« the AH goods coming by rail or veTil",! ! °"'^ ^"^ ^^^^ Short House matter what theUunto7theLtre Ct^'^ h ^'^ •''^"^ «°"««' ^ are passed through the Short House if the .^^ ? f ^'"'''"^ ^^ ^^P^^^s are made out-one for the ordimu^ "e o?,hf h T"°- ^'= ""*« other two for customs purpose! Ctj! , ° ''°>""8 «■■= «'^' «>e be certified by dating andl^ta^ the d,7 f' '"°™ ^"^"^ "'!»''« '» Two copies of the bil? of eutTlre made o'ut " "" "" '^'' "" «" -™'«- Germany, i, nevXltss: fiS i^iLir """°^ ^'^ ^'"P^^*^^- ^-n^ the case where the firm selling ttgod're'frr- ^'" " ^^^ °^*- exchange on London. It must not hff;^ ^f *° '^"^"^^ P^y'nent by invoice haa to be figured irshilWs Jt mL°st'"?'' '°"^^^^' *^^* ^^^ marks. '"°«*' ^ « might just aa weU be figured in the Scmc%-ufy"of1o*^^^^^^^^ ^-"^f * to two duties- certain percentage of the "vJZfT' ^ *^^ ^^ valorem duty, of a is levied as a surtL 33J p r celt of the or2 " T'^'^'" '"^ ^^^^tion^'ther^ combined) on account of tT.^^^'^rr^^^''''^''''''^^^^^^^^^^^^ Note 4.— The " Valn»7 J^ . ^ ^^""^ Germany. to the nearest doUal'^ Tht "• ^/"of l^": ^! ^^^^ ^ the Long House 5151.50 or J151.62 would be t^^StL"^ .''"'t^''''' ''^l. while exact amount of the invoice is used. *^' ^^°'* «°»«« the i ■ 'l 320 FOREIGN TRADE a < a (4 c i ^1 11 c o H^ O OJ Xi (N OJ O 'J' (N (M lO 10 O O . ? ■a 5.^ 11 SI a 3 m an i .s H o c— , ^ 3 ,^ rt i ^ H .J O CUSTOM HOUSE BUSINESS 321 ^ 3 ^ o lO CO 00 I— t CO en 3.1" « o J.^ CO :t 111 IN •&SS,€5 322 FOREiaN TRADE i \l ii ,1 i 1 i The general tarifE is 20%. SERIES 98 1. Gowans Kent & Co., Toronto. Ont., import from France V^'wu i"! dishes containing 10 sets, at 10 francs a set, on which the duty is 30%. The crate is invoiced at 9 francs. Show mT^ ^^^ passing goods at customs (B. 1) properly Note. — Cases where invoiced are dutiable. The preferential is 15%. 2. Greenshield, Son & Co., of Montreal, import from Germany I case of Buttons, containing 42 gross, invoiced at 10 marks a gross. The general tariff on these buttons is 35%. The case is invoiced av. 5 marks. Show mvoice and customs form properly filled out. 1 ^JT^\ ?^°/^® Hamilton, of Medicine Hat, imports from England : Wool Suit at £2 1 doz. Silk Ties at Is. 8d. each, 1 Silk Hat f t Tss. ^iS^ ^l?'""^^ f ^^': .^^^ ^""^y <^" *h« ^^t is 22*0/0, on the others of) ^. .ihe package is m voiced at 4s. Show invoice and customs lorras. 4. Messrs. Johnston & Co., Quebec, import from Williams, Humbert & Co.. Jerez De La Frontera, Spain, as follows : 1 butt Sherry Wme 108 gallons, at ^85 per butt, duty 30% and 43c per S'^j ^ ^o?' ^l 5^"'^ ^^^''y W'"«' 216 gallon?, at £96 Jer butt, ducy 30% and 46c per gallon ; 10 quarters (2J butts) SheSy Wme, 270 gallons, at £102 per butt, duty 30% and 40c per gallon Show mvoice and customs form. 5. Messrs. Foster & Smith, St. John, N.B., import from Warre . /^'A P^^*°' ^P,^^"' *^® following : 1 pipe Port Wine, 115 gallons at £70 per pipe, duty 30O/o and 43c per gallon ; 1 hhd. Port Wine,' 58 gallons (i pipe at £80 per pipe, duty 30% and 49c per gallon : l)Tl'Z\^'' ^'"^', ^^ ^±"^ ^^ P'P^^' ^° ^90 per^pipf, du"y 30% and 46c per gallon ; 100 cases Port Wine, 200 gallons at 50s. per case, and duty 30% and 49c per gallon. Show invoice and- customs p: per. 6. McLeod Bros., of Glasgow, sell to Brown. Morgan & Co. Montreal, a Ime of ready-made Skirts as follows • ? ^ T}J' 8 @ 21/-, 6 @ 27/3. 6 @ 35/6. Case 13/5. f ^ la^S' ? f 25/3. 6 @ 27/-. 6 @ 34/6, 4 @ 40/- Case i9/9. 14145/ ^|g/5 6@39/6, 4@40/6. 4@41/. Case x 7/1 ^ The duty on skirts is 30%. Show invoice and customs form. Note.— It is not always necessary that the bill of entry should show the detau oi the invoice. For instance, these goods may be entered as "3 cases wool clothing." 3ral tarifiE is 20%. klorgan & Co., CUSTOM HOUSE BUSINESS 323 & C^'ii"a"?sZ!^w* .'°- ^"°""'' ^-y from W.. A„de.s„„ oo2 gro-3 Pens ^^ " lOOA " " (@ i/- f 42203 (a) u 50 Binders M. 1 ^ ' ^ (T 1 " M 5 ® ^/* I " M7 ®'/- Case @^/^ custXTper '''''' '^'' -■ ■^^"^-' ■^^%- Sh'/w i. .ee and 10 reams r T a,vi r» r -^ng^and, the following : Deduct trade disronnf r.f J/ \ ^^' P^^ '■earn. »6 reams Pnntmg " Wa er Mill " Cr- """wing . lbs., at 2|d ner Ih • Q I ^ ^^^^"^ Wove, 17 bv 28 2^)^ lb., less loV 10 re^^^^^ ^"l,' 2"^^' 230 lbs., a^t f|d '^f ^rS= 2S'reiL"Sfng ''^WaSr\^'S '^'' at 2|d. ^'; £ 21. 420 lbs., at 2|d. per Ih. ^^ ^^^^m Wove, 16* by ^' iduct trade discount of '^Q/ f^^^ , , , .„ 7d. = duty ,5% Shtl/^iranttri plpe^ '"=' I £2 324 FOREIGN TRADE T V't^ ^' ??" ^.r^°" Vancouver, B.C., import from the American Lead Pencil Co., New York, the following : 6 gross 557 Pencils @ $3.50 3 ;; 450R " g loo 6 295Bx Penholders (a). 3.00 6 " 658 " g 1.40 12 " 6/379 6/383 Penholders .... @ 3.60 1 " 410 Eras. Pencils 01 3.00 J ;; 428 " " g 3.00 6 3/F, 3/H.V.D. Pencils @ 6.50 1 '; F.W./Prot. V.D. " @ 8.10 6 " Steno. " @ 3.00 Duty 27^%. Show invoice and customs paper. 1 the American AVERAGE AND ITS APPLICATIONS J. po„„„ 3„mL 5„. J: ■: sT.zziz:iX itt "^ '7 at 60c a pound give, the same return. Note tliaiT.,^1 „ °''°""''' a pound there i, a gain of 10c on i t,™,„h J '"^ ^ ™' '«» «' 60» pound there is a loss of lOc a ^und A ^ '" '"""« " ™' "> " «"= » the gain, just counterbalance tJ^Ce, '"""■''^'' """"" '"' »"■ "■" Again, a partner In a business invests SIS Onn fo- next month he invests $7,000. On an averL ^ ""^.'"^^th, and for the use of $6,000 a month. Note -i^ltZl. 'la ^''''"^ '^' ^"^^"^^^^ the he invests the first month^^^^^ S^ ^httrestrtJ^r T' ''''' The average is greater than the investm^nf f ^ ^^*^°"'^ month. .hat it i, less tL the inv.«:>rrtTe iTh:";^* ''"'""'^''■'»«"« Again, a man stores 500 bushels of grain in . <=f u and for the next month he stores 700 busheT On an 'f °"' '"°"*^' 600 bushels a month. This is 100 bushokTo ,?" \" ^^^^^&<^ he has in store but ,00 bushels less than ^: Ztl^: Zll'Zl'^T"' ^ '^^'''^ case exactly balances the deficiency in the "then '""P^"" ^ °°« QUESTIONS OF THE FIRST ASPECT Given the items, to find the average. Solution 25 lbs. at 30c .. . 20 lbs. at 50c ... ' f:-^^ 40 lbs. at 75c .. I?-^^ 15 lbs. at $1.00. ..■.■;.■ J2JS ___ 15.00 100 $fi2.50-.lOO=S.62J ^''•'' The tea is worth on an average 62^0 a pound. 326 ill'i ! I! AVERAGE AND ITS APPLICATIONS Solution From Jan. 1st to April 1st = 3 months Apnl 1st to Sept. lst= 5 months. $7,000 invest^l for 5 months = J35,000 for 1 month Sept. 1st to end of year = 4 months. «9,000 invented for 4 months = $36,000 for 1 month. «77 nnn Jf ^^ j'^^^st'^ent, $77,000 for 1 month. $77,000 -. 12 = $6,416|_average investment per month. Illustration 3.-A commission merchant places in store the following items : - Sept. 9th, 200 oarrels of pork. Oct. 17th, 500 " of beef. Nov. 10th. 250 " of pork. Dec. 1st, 150 " of beef. • On Dec. 8th he desires to make a settlement. Suppose he is charged at the rate of 4c a barrel for a period of 30 days, whai does he owe ? Solution The storage of 200 bbls. for 90 days = the storage of 18.000 bbls. for 1 day The storage o 500 bbls, for 52 days = the storage of 26.000 bbls or day The storage of 250 bbls. for 28 days = the storaL nf 7 nnn ilT I ! T^' Th. ..„age o, ISO bbR <„ 7 ,Iys = Z TZ ^i £ bS.' £ \ Z- AU = the storage of 52,050 bbls. for 1 day. The storage of 52,050 bbls. for 1 day= the storage of 52050 30 or 1,735 bbls. for 30 days. The storage bill will be 4c x 1735= $69.40. aces in store the 50 bbls. for 1 day. (»UESTIONS OP THE FIRST ASPECT SERIES 99 327 138 Ibsf f97 iTmtl^^lr'y 'f ^^^•' ^87 lbs., 164 lbs average weight ? ^^'' ^^^ ^^'•' ^"^ 169 lbs. What iTthdr costing l7frS'alV'^ 1^0^"^,^^ ^ P-"^' ^« ibs. ^^^%v-lueofthe^ix"ure%rpo,m^^^^^^^^ ' ' P°""^'- ^^^^ Aug. 12 sold 360 at $1.16 What was Lw.^' "' ^°^^ ^^^ at $.99 ; daily, (b) the average daily cash bLlii^ the average number sold Pnce ? ^ '"'^ ^^^^ business, and (c) the average selling on MiV.t8l.tejr 111 t'SS^ ^" J^"- ^' ^^«' HOOO; more. From Nov. 1 to the end of fhfS^.T'^ ^"^ ^°^- ^' ^^'OOO unchanged. What wJht. ^^^^ ^^^ investment remained (Calculate time in months ) ''^'''^' ^"^^^tment for the year 1 investd'^S.'JS^^^^^^^^^^^ 1 Weir invested $3,200, and on jUlry ^^^ $2 '^ ?f ^P"^. "^^^^^^ average investment of each for thT year ^'""^ *^^ ing tl' s'iartgl^l Inf iIST; ^ "!" ^" ^ ^"--' a^-- On May 10 Liddle invested $ ^ "^'"^t *° ^/.'^^^e investments, on Aug. 9, $700 morr On MaTlb T^Ji"''; ^^' ^^ "^°^^ ' ^"^ July 3, $600 more; and on Sent 2([ Sm '""^''^'^J^'^' on ship was dissolved on O^t 17 FinS" i^ '^'''^- ^^^ Partner- each. " ^^- ^^' Fmd the average investment of wheat at thTraL°"on'cV'nt'h\'^^^ ^"-titles of -erage storage • June%",%^ bt'^ ;?28^to^ f" ff l' is th?- stora^'Tul Mav'lS^n ^ ^?^^ ^^- ^^^^^^^ ^^^^^g^' what 125 bbls • Tan ?i 7^^ KK1 °" 5?® following receipts : Tan 20 bbls. ; M'ar. {sMo'b'bh ''1^ SVL?'^ '.'^^^ ^^^- "o. '^ April 9, 38 bbls ; April 15 100 hhlf ' a^^ 'oL "^P"^ ^' ^^5 bbls. ; 150 bbls. ? ^ ^' ^^ ^^^^' ' April 28, 50 bbls. ; May 10. 328 AVERAGE AND ITS APPLICATIONS 10. A farmer received for pasture : April 30, 12 head of cattle ; May 15, 14 head of cattle ; May 23, 27 head of cattle ; June 9, 5 head of cattle ; June 30, 8 head of cattle ; July 16, 40 head of cattle. If the charges were 75 cents per head for each week of 7 days of average pasture, what would be owing for the pasture on July 25 ? Illustration 4. — A warehouseman received and delivered the following : Received. Delivered. June 11, 150 bbls. June 26, 120 bbls. " 30, 200 " July 15, 150 " July 18, 90 " , " 25. 160 " " 28, 180 " ' Aug. 4, 190 " What was paid for storage at 3 cents per barrel for a period of 30 days' average storage, a settlement having been made Aug. 4 ? Solution Dates. Days. Barrels. June 11 to June 26= 15 x 150 (received) = 2,250 bbls. stored for 1 day " " 120 (delivered) 26 to 30 = 4 X 30 (in store) = 120 bbls. stored for 1 day. 200 (received) 30 to July 15 = 15 X 230 (in store) = 3,450 bbls. stored for 1 day. 150 (delivered) July 15 to 18 to 25 to 18 = 3 X 80 (in store) 90 (received) 240 bbls. stored for 1 day. 25 7 X 170 (in store) =1,190 bbls. stored for 1 day. 160 (delivered) (( l€ 28 = 3 X 10 (in store) = 30 bbls. stored for 1 day. 180 (received) 28 to Aug. 4= 7 X 190 (in store) = 1,330 bbls. stored for 1 day. Total storage = 8,610 bbls. st.vfed for 1 day. », . , /8610 V Total storage=^^ ij^— = 287j bbls. stored for 30 days. $.03 X 287= $8.61, required amount of storage. 30, 12 head of head of cattle ; :attle; July 16, er head for each 3e owing for the i and delivered ED. 20 bbls. 50 " 10 " •rel for a period ing been made . stored for 1 day. . stored for 1 day. . stored for 1 day. stored for 1 day. stored for 1 day. stored for 1 day. stored for 1 day. stared for 1 day. iays. .ge. QUESTIONS OF THE FIRST ASPECT 329 n,.nt';'''''T^'?u,^—'^^'" ^o^^oxvmg accounts show the invest- ments a nd withdrawals of two partners during a year Find the average ui vestment of each. ^ ^ ^ Dr. Frank Smith. 1908. Apr. 23 Aug. 17 Df. 19087" July 28 Dec. 4 Withdrawals. 81,000 900 '^®- Investments. J^°- ' $16,000 Oct. 20 3 noo Chas. Robertson. Withdrawal . $600 800 1908. Jan. 1 May 17 Investments. $12,000 600 Solution Smith's Account From Jan. , to Apr. 23 = "3 dys. Hence SiG.ooc for 113 dys. = |r,8o8,ooo for i day. Withdrawal 1,000 From Apr. 23 to Aug. 17 =1.6 dys. Henee l^for ,16 dys. = $1,740,000 for r day Withdrawal qoo Fron. Aug. 17 to Oct. 20 = 64 dys. Hence $^ for 64 dys. = $902,400 for r day. Investment 3,000 From Oct. ao to Jan. r = 73 dys. Hence ^^ for 73 dys. = $,,248,300 for x uay. Smith's total investment, $5,698,700 for i day. for f^etl *'''"''''' '"^ '''■ "' ''' ^''-''^^^ "^ '''' '-^^'^^'^g^ '--*--• Robertson's Account From Jan. , to May 17 = 137 dys. Hence $12,000 for ,37 dys. = 5,,r,44.ooo for i day Investment 600 From May 17 to July 28 = 72 dys. Hence $x2,6oo for 72 dys. = $907,200 for x day. Withdrawal 600 From July 28 to Dec. 4 = "9 dys Hen^e $x2,ooo for X29 dys. = $x.548,ooo for x day. Withdrawal 800 From Dec. 4 to Jan. x = 28 dys. Hence $;;;;;: for 28 days. = $3x3,600 for x day. Robertson's total Inves-fment, $4,4x2,800 -for x day, for thL'yirr' ^'•''''''' '^ '^^'"^ ^'' «J2.089f| as the average investment ii 330 AVERAGE AND ITS APPLICATIONS QuESTioN.-Suppose the gain for the year were $3,000, and the partners shared this gain in proportion to their average net investments, how much is each entitled to ? . Solution Smith's average net investment is $15,61291^ Robertson's average net investment is 12,089!?!} Total average net investment is $27,70254 Smith's share of the gain is ^|-^2f| ^^ ^^^^^^ ^^^^^^^ 'Robertson's share of the gain is ^^5^^|| of «3.000= $1,309.24 SERIES 100 1. Compute the storage on the following account at 1 cent per bushel for a period of 30 days of average storage : Received. Delivered. ^?*"oa' ^^^^ Oct. 1, 200 bu. Oct. 3, 180 " .' S' 7? .. , A. !^' l"" " u Nov. n: 140 " 2. At 4 cents per barrel for a period of 30 days of average recIfl'A ""^H* i' r^' ''r^' '^"^ ^"^- ^5 on the following prS? received and delivered as stated ? ""^"^c, Received June 9, 160 bb's. apples. 22, 140 July 14, 70 Aug. 5, 100 potatoes. turnips. onions. Delivered • me 21, 85 bbls. apples " 26, 110 " 29, 75 July 16, 30 " 30, 30 Aug. 10, 75 " 12, 40 15. 25 potatoes. apples. turnips. potatoes. onions. turnips. onions. 3. Find the pasturage, at 65 cents per head, for a period of dU days of average pasturage on the following account : Cattle Received. Cattle Withdrawn. J^P^ 3, 16 cattle. July 2, 18 cattle. lb, 27 " 18 20 " July 7, 11 ; Aug. 4, 9 " 15. 26 " iQ 1" " " 27. 7 " Sept. 5:2? " were $3,000, and their average net 2,0891/ il '.702?J = $1,690.78 ■■ $1,309.24 count at 1 cent age: ). K) bu. 15 " '5 " 10 " days of average Uowing produce, >bls. apples, potatoes, apples, turnips, potatoes, onions, turnips. " onions. for a period of int : AWN. tie. QUESTIONS OP THE SECOND ASPECT 331 first A put m ncS) fe'te'S "Z'^f "'•", 'nves.me„,s. At more and B $2,000. On S epi.*?' A^vi.fcw «, "Sf, '" ^l*^ Nov. Bwthdrew ftl Of)0 v^r. X ^^'"^arew $1,500, and on investments rer^aTnedS^h,„^°^^^ the year their $1,200. how much slllS eacfre^ ^'^^^ ^^"^ '^' ^'^^ ^^"g Hesf ;mJ?:sti!;gf^!!)05;-^^^^^^^^^^^ a^L^ ro^S 'f -^Z Hess mvested $2,000 additiomi hnf ^/c , ? " *o,W0- June 1 May i Dunn wilhdrewl2.'(!^"tjul^^^ investments ^ ' ^'^^^' '" Proportion to their average and'juty ^^t'Se pu^fn m^C^^'^'o^'"- 1''' ^^^\^ P"^ '" $7,500. and May 1st ^thd ew m'oS ? ' . ^t* '" J^"' ^^^ $'2,000. 1st he a'ddedTooran^'SS.' IstTeM^tlclreJ^ciSinA^f close of the year the profit was Sfi sn? r^""^ P'^^' ^* *^^ have, the gains being dSdacconi .. .u""^ """"^ °"S^* ^^^^ ^o (Calculate time in mS^) '-' to their average mvestment ? QUESTIONS OF THE SECOND ASPECT Given the average, to find the items. the mixture will te wlrih 2^"1 tund""!! '" "'='' ' ™^ '""' each wiU be used ? '^ ' "°" """"y P^^n^s of Solution ^ Jst Step : Find the gain or loss on each kind, considering it at the average 17c coffee gains 3c on 1 lb., or Ic on i lb. I8c coffee gams 2c on I lb., or Ic on I lb. 25c IT r '' °" ' '''■• °^ '' °" i lb. Onri «. .. ^^ ^°'^' ^'^ °° 1 lb., or Ic on 1 11, On ! K ° I." '"^'" ^^^"^^ *^ g^i" °f IC. Un i lb. of 24c coffee ther^ is in- -^ 1^ On J lb. Of ,8c coffee there' :; gain ;; ic. XVI1-, * °^ ^^' *^°^"^ tl^^^e is loss of Ic. •'■ ifl 332 AVERAGE AND ITS APPLICATIONS i lb. at 17c, i lb. at 24c. i lb. at 18c. I lb. at 25c. NoTE._At this stage it may be pointed out that there is no limit tn he number of correct answers that may be given to such a question If the quantities we have given will produce the required average so wm anv number of times these quantities. We can therefore get 2 manv cL^^ answers as we can find figures by which to multiply or'dlSeThe'obtS multloTvInf or"V"T °^''''' ^ "'"'''''''• ^"* ''''''''• »i«t of answers by mu tip ying or dividing any pair of quantities by any number or hv multiplying or dividing each pkir by different numbers ^ bv the TcZ ZTT' '' ''""' '"' °^*"^"'^' °' '^^^ti°°^' '""Itiply through by the l.c.m. of the denominators 60. This gives us. 20 lbs. at 17c. 15 lbs. at 24c. 30 lbs. at 18c. 12 lbs. at 25c. This will prove to be an average of 20c a pound r.Z'^lT'Z ^-^?P°^^ '^^' it i« desired to have twice as much 24c coffee as there is 18c coffee in the mixture, how can it be arranged ? Solution.— Looking at the answer as we have it there arp IS ih= «f oa cofiee and 30 lbs. o, .he ,8c coffee. To ge. .he ,„a„u" S^r '^ed .a (our .„„cs .he quan.uies ih .h= firs, pair and leave the second paU touched The quantities will be : ^ untoucnea. 80 lbs. at 18c. 60 lbs. at 24c. 30 lbs. at 18c. 12 lbs. at 25c. of n!rFT/-;^"PP°'' '^"* '^''' '' ^"* ^ ^•"^'t^d quantity of one kind of coffee-say, 40 lbs. of the 17c variety-how can we arrange to include just this quantity in the mixture ? Solution.— In the answer as stated there are 20 lbs at 17c Tn mico this to 40. multiply first pair through by 2. The result rUs : 40 lbs. at 17c. 30 ibs. at 24c. 30 lbs. at iSc. 12 lbs. at 25c. QUESTIONS OP THE SECOND ASPECT m these four coffees, s, multiply through 333 •iO lbs. at 17c. 30 lbs. at 24c. 60 lbs. at 18c. 24 lbs. at 25c. 154 lbs. SERIES loi worth 54c per pound ? "='P"'='"'^'y' ^e mixed to g,ve a mixture pou'nd «spectl^irb^'m,xS't'rar"'''.f'=' '"'■ -<> «^ P<=r which will be worth 34c™er pound , "" ' ""»' "* '°"™"^ 3- A liquor dealer has wines wnrfh cinA> -= |5.l, wh":1 mixfu^e'ot.2l,i^'\?bra:k^V3',l^' "' «-> ^ -"> $5.73. Find the value per pound of each ° «'''" '" ^^h 8.ut4s^^w:"?h',^5?^Pi:^^^X1f^r ' ^^-^ """ mus?- JfteTeS,t''JasevLtru"nt'""? '^ ','*'^" '-'• ^-at of the seven 10 S43 feet ? '"°™'^» «« "a^e the mean height I of'lhtprofltf and B ^^^'2?'^ i°^ ^ ^-^i ^^^ ^ receives the second year and at 7 h/»^H 1 1 ^ '°^^" «2,000 additional How much V/'e^ct rtS the t?;!:^ '^'"^^^ ' "' '"^ P™*'- 9. The average of seven numbers is "fi^o ^h Ae first two is 34.5. and of the next three 193" pTnH .r'^^' °* «i the remaining two. " ^^"" *"^ average I H 334 AVERAGE AND ITS APPLICATIONS I ► 10. A dishonest milk-dealer buys 135 gallons of pure milk at 23c a gallon, and, after mixing it with water, sells the mixture at 4Jc a quart, thereby gaining $2.43. How much water has he used ? 11. A, B, and C engage in manufacturing shoes. A puts in $1,920 for 6 months, B a sum not specified for 12 months, and C $1,280 for a time not specified. A received $2,400 for his stock and profits, B $4,800 for his, and C $2,080 for his. Requin^d B s stock and C's time. ^ 12. Dodd and Brown became partners June 1, 1907 Dodd mvesting $10,000 and Brown $8,000. On Oct. 1. Dodd invested $2,000 additional, and Brown withdrew $2,000. How much should Brown invest on Jan. 1, 1908, to entitle him to half the year's profits ? 13. How much tea worth, respectively, 55c and 75c per pound must be mixed with 30 lbs., worth 90c per pound, in order that the mixture may be sold for 70c per pound ? 14. How much water will it require to dilute 60 gallons of alcohol, worth $1.50 per gallon, so that the mixture may be worth only $1.20 per gallon ? 15. How many gallons of kerosene oil, worth 60c per gallon must be mixed with 12 gallons of coal oil, worth 36c, and 8 gallons of Aurora oil, worth 56c, so that the mixture may be sold for 50c per gallon ? 1(5. A farmer has 16 bushels of corn, worth 48c per bushel and 12 bushels of oats, worth 34c per bushel, which he wishes to mix with rye, at 60c, and barley, at 80c, in order to sell the mixture at 56c per bushel. How many bushels of rye and barley will be required ? 17. A farmer has three different qualities of wool, worth 33c 37c, and 45c per pound respectively. He wishes to make up a package amounting to 120 lbs., which he can afford to sell at 39c per pound. How many pounds of each kind must he take ? 18. A confectioner mixes three different qualities of candy, worth 14c, 18c, and 30c per pound respectively, so as to make a box of 84 lbs. How many pounds of each sort must he take so as to sell the mixture at an average price of 24c per pound ? 19. How much sugar at 10c, 13c, 15c, 17c, and 18c per pound must be taken to make a mixture worth 16c ? 20. A dealer mixed two kinds of wines, worth respectively $2.40 and $3.20 per gallon, in such proportion that by selling QUESTIONS OF THE SECOND ASPECT 335 in the mixture were interXred it! v^l? ' ''"*,/u*^^ Proportions the price of oats perZshel "^ "^^"^^ ^ ^70. Find is the strength of tSe Cx^Se then ? ^'^ "^^^ ^^*^- ^^^ 80of^ctho?^\^^I?i ^ ^eh waVr' ^^f^ ^^ ^^^ -"tains strength to 62io>^7 it^uchT ^, ^^^'^ *° "^^^"^^ ^^e increase its strength .u 6/^% ? ^ ^'°^°^ "^^^ ^ added to of ^-gS^ItTs^'ald Vi^^^^^^ V.^-l-ture of 16 quarts may be worth lie the quart ? *^^* *^^ ^^^^^ ™«t«re xvu 4 t , li PARTNERSHIP A Partnership or Co-Partnership is the contract relation sub- sisting between persons who have combined their property, labor, or skill in an enterprise or business as principals for the purpose of joint profit. The contracting parties are called partners or co-partners. Collectively they are called a firm, a house, or a company. There are two kinds of partnership, general and hmited. A General Partnership is composed of two or more general partners. That is, partners who are liable not only as partners for the debts of the firm, but also personally liable if the resources of the firm are not sufficient to pay its debts in full. A Limited Partnership is composed of one or more general partners, who are liable as general partners always are, and one or more limited partners, who are not liable for the debts of the firm beyond the amount of their investment. A limited partner must take no active interest in the business. The Liabilities of a firm are its entire debts. These are of twc kinds : first, its debts to the public ; second, its debts to the partners. The Resources of a firm are the available means it has for the payment of its debts. A perfectly solvent partnership should be able not only to pay its debts to the public, but to return to the partners the amount of their investment. The Investment of a partner is the aggregate of the sums con- tributed by him for the purpose of carrying on the business. The contributions need not be in money, but may be in. goods, real estate, trade marks, trade secrets, patent rights, or any other resources. It will be understood that a partner in entering a business may invest resources, and he may also bring with him certain liabilities, which are assumed by the firm. Then, again, he may, during the course of the business, withdraw a part of his investmenr. or, on the other hand, he may add additional amounts to his original leans it has for PARTNERSHIP ADJUSTMENTS ^37 The Net Investment or Net Credit of a partner is tlie diiJerence lor him and withdrawals on the other hand. As the object of any business is to make a profit for those concerned m it. it is clear that the results of a yearVtradin^or aTottlT' ""?""^ ^^"* ^ ^^^^"^^ - the' wa; of dL; a profit to the investment or subtracting a loss therefrom. ^ of a^usfnTss' ""''' " " '*'''"'"' °' ''^ ^^^^^^^^ -^ "abilities whidl" thf r ^^^ "^ ^?"'* ^^"^^ °^ ^ fi^"^ i« the amount by which the resources exceed the Habilities to the pubUc. exceed! ^e^n^ "^ ' !'"" ^' '^' ""^"""^ ^^ ""^'^ *he net capital exceeds the net investment. In double-entry bookke-pinff this figure should be the same as the difference beLen Tetrsidt a. r K^'^" ''''""*• "^^'^^ *^^ -^dit side is the large^ or. as It may be more broadly called, the revenue account 1; mcome and expenditure account. "** ""' the Itt cankar V"^ 'T"' '^ "'^'' *^^ "^^ ^"^'^^*'"«"t exceeds me net capital. In double-entry bookkeeping this is the s^m^ ;,« the am»„t by wi>ich the debit of the loss L'gain accolr^S to tSi^^irdr^estrr^^""""'-'^***''^"^^^^^^^ PARTNERSHIP ADJUSTMENTS Partnership adjustments involve ffenerallv th^ a- .• nr^fit*^ T/r °* '"* -«- - tlT'L* .iofoT thf ^Lmt! °'l ' ■"' '"^^ '"^ P'''™'"' <" '-l^i^^ according to agr«men , or the payment of interest according to agreement!' It will be understood that, as a Dart..e„hip i, ,h- outcome any agreement that they may see lit. No matter how abmrd ' 338 PARTNERSHIP tliat agreement may appear, it must be followed in the adjust- ment of the affairs. There .s, therefore, no set rule for the di'vision of gains and losses, for instance, between partners, for the simple reason *hat partners may agree to divide gams and losses as they choose. The same thing is true concerning allowances for salary or allowances for interest. If, however, the agreement is silent on such points, it may be implied that gains and losses are to be divided proportionately to the number of partners. Unless there is a specific agreement, it could not be inferred that interest or salary was to be allowed. Partners may also be brought into contact with the public through failure of their resources to cancel the iebts to the public. In such cases general partners must expect to contribute from their private means. Here, again, partners must make adjustments between themselves. We recommend a careful study of the following principles which must guide one in making partnership adjustments, and which will be understood to apply in aU cases unless modified by agreement : (a) Losses, including losses and deficiencies of capital, shall be paid, first, out of profits, next out of capital, and, lastly, if necessar}', by the partners individually in the proportion in which they were entitled to share in the profits. (b) The assets of the firm, including the sums, if any, con- tributed by the partners to make up losses or deficiencies of capital, shall be applied in the following manner and order : 1. In paying the debts and liabilities of the firm to persons who are not partners therein. 2. In paying to each partner rateably what is due from the firm to him for advances as distinguished from capital. 3. In paying to each partner rateably what is due from the firm to him in respect to capital. 4. The ultimate residue, if any, shall be di\nded among the partners in the proportion in wl#fh profits are divisible. ^.3^. i in the adjust- ! for the division 5, for the simple id losses as they ances for salary nent is silent on losses are to be Unless there is nterest or salary ivith the public ts to the public, ibute from their ke adjustments wing principles Ijustments, and unless modified s, if any, con- ncies of capital, irm to persons due from the PARTNERSHIP ADJUSTMENTS 339 in inver.ment, 8% interest war.oh n ^.^^^'''''''"^'"^'y investments, and inter^t at T I ""''' '^'^ P^'"'"' »» all withdrawals. I^i Turther L eT/tStVT '" "^ '"''''" °" salary of cooo a year ^nlhZlT^L^t^^iVm'^''' The adjustment of both interest and <.Ur 7 u * '^ ^ y^^^' adjustment of the ordinJv nl? i! f ^ *^ ^' "^^^^ ^^^^' the ™ade. .He -o;°JrtIl-St°reCt^? at^ J. Coleman. 1907. Apr. 3 June 7 Oct. 15 1908. Jan. 1 Withdrawal i loss from interest ad- justment . . i loss from salary ad- justment . . Present worth $3,000.00 1,500.00 800.00 601.75 1,500.00 16,208.30 1907. Jan. 1 Mar. 14 July 3 Sept. 18 1908. Investment . , Jan. 1 1 1 i net gain of $5,800 ... Net credit int. $6,000.0 4,000.00 3,000.00 5,000.00 2.900.00 710.05 $23,610.05 Salary 2,000.00 Dr. iootT Mar. 8 AHg. 15 Sept. 30 1908. 1 R. Dawson. $23,610.05 Withdrawal. Jan. i loss from interest ad- justment . i loss from salary ad- justment . Present worth $2,000.00 1,000.00 1.200.00 601.76 1,500.00 10,591.70 1907. ' Jan. I May 12 July 16 Oct. 5 1908. Jan. Cr. 1 1 1 Investment i net gain of $5,800 ... Net credit int. $4,000.00 5,000.00 2.000.00 1,500.00 2,900.00 493.46 Salary 1,000.00 $16,893.46 $16,893.46 340 PARTNERSHIP r li'i Solution Note.— It is presumed that the detail work of figuring interest on invest- ments and withdrawals is already familiar to the student from that section of the text which deals with interest on partners' accounts. It might not be out of place to mention here that a close acquaintance with the work on sharing, and also on average as it applies to partners- accounts, will help the student in work on partnership adjustments. 1st Step : The gain of $5,800, according to agreement, is to be divided equaUy. Therefore each partner is credited with $2,900 as his share of this gain. 2nd Step : Having found the net interest due to Coleman to be $710.05 and the net interest due to Dawson to be $493.46, these amounts are credited to their respective accounts. It ;is here that the p inciple of double-entry bookkeeping must be kept in mind. We cannot credit the partners with these interest amounts without taking into consideration the fact that some other account would have to be debited with these amounts. If we followed the bookkeeping for the transactions right through, we would find these amounts are debited to interest account. This, being a loss and gain account, would, in due course, be closed into loss and gain account. Loss and gain account, in turn, would be closed into the partners' accounts. Thus it is that the partners, who are credited with their net interests, are, in turn, debited, each for his share of the complete loss ($1,203.51) it would occasion to the business by paying these interests. 3rd Step : Each partner is credited for the amount of salary due to him as per agreement— namely, $2,000 to Cok.nan and $1,000 to Dawson. As in the case of the interest, the loss to the business occasioned by paying this salary ( $3,000) will be divided equally between the partners, and each partner debited with his share, $1,500. 4th Step : With all the entries thus made in the accounts, a comparison of the debits with the credits will give us the present worth of each of the partners. Illustration 2. —Adams, Wilson, and Green enter into partnership as grain dealers. Green is a special or limited partner, putting $10,000 into the business. Wilson contributes $15,000, and Adams nothing. Wilson and Adams are each allowed $1,500 a year salary. Profits are divided equally. Partnership deed duly drawn and registered. In the second year Green, being on a holiday trip, sees a chance of buying a quantity of grain, which he I I PARTNEllSHIP ADJUSTMENTS Ui lerest ot invest- jm that section le acquaintance ies to partners' stments. 3 to be divided is his share of 1 to be $710.05 ats are credited jf double-entry : partners with fact that some If we followed )uld find these d gain account, Loss and gain ts. Thus it is I, are, in turn, would occasion iry due to him I Dawson. As by paying this id each partner , a comparison of each of the enter into ited partner, tes $15,000, awed $1,500 ership deed , being on a in, which he buys at a profitable figure, with the consent of his partners. He sells part of the lot on his way home, but, after his r ;turn, the market takes a disastrous turn, and the firm is obliged to assign. Their statement of affairs is as follows : Liabilities. Bills Payable to Bank $75,000 (Secured by warehouse receipts on 100,000 bushels of wheat at $1 . 10. Wheat reahzes $80,000.) Trade Creditors 25,000 Capital Account : Green $10,000 Wilson 15,000 25,000 $125,000 Assets. Office Furniture $ 500 Grain in Elevator, hypothecated to Bank.. 110,000 $110,500 Deficiency 14,500 $125,000 Partners have sufficient personal assets to pay all creditors. Furniture sells for $500. Adjust the loss and show the partners' accounts, including final adjustment with one another, it being understood that no payments have been made on account of salary. Dr. Solution Green (Capital). Cr. To i Loss $15,833J By Investment $10,000 ., Cash to Settle 5,833 J Dr. $15,833 J Wilson (Capital). $15,833^ Cr. To i Loss $15,833^ „ Cash to Settle 666§ $16,500 By Investment $15,000 " Salary j 50c $16,500 1 Vm :f\f 342 Dr. PARTNERSmp Adams (Capital). ^°*^^s 115,833^ Cr. ^y Salary | , 5^,0 Cash to Settle 14,3J31 Surplus from Wheat |5 000 , P-^uVrTT, TT^ Received ,0, F„„u„e .... Z '"^ ^r'"-' from Green . . 5,833J " Adams.. 14,333 J $15,833^ Cr. $25,000 6663 125,6669 $25,6663 vio£TSThei^ri„'L^rr"' "' r'""' ^"" '" "■= »-". J-.ne,*ip,, ano LTrZr ST: t^^^^JZ''^ 'T" retained by the bank fo «Pf+i» IT. '°[ f "•"W> > $75,000 of this amount is s-rp-s .„::. II .t.ten^Xe/^.hte S^t^taf^.. "^ f ^-^ tare, makes a total of S5 500 c^h «,h,vt, , received for the office fumi- a shortage or deficiencv of «IQ "snft u- u " ""^°" °^ $-^5,000, thus showing The loss of the partSip is L '1 „^^^^ '■'' *° '^ '"^^^ "P ''^ ^^^^ P-^ners' sheet, together withTheg^g 500 n . '^\'^^^'^^^^ shown on the balance- for salary, making a total ofV47 500 o' V T^Vl!' ^"°"'^*^' ^°^ «^'0«« $I5,833J. When these amnnn!?' T '''^ ^^'^ ^^^ *« ^ear one-third, or willsho^Green^Jhrder J„rj ^-P^ ^ ^s of «14,333J, and Wilson with a credit bSStf 866^^ T ' "'"'^ '^'""^^ must pay sufficient cash intn fh» « '^^ oaiance of J666§. Green and Adams When thl is do^: th?fi ^hL I'reeeVr^r .f *'^'^ """P^^*^^^ — ^• paid over to the t;ade creditors anH !f ^ ^^^^^^' '^^' °^ '^^'''^ »25,000 is the accounts will then bSficTi shfvl"™"""^ ''^'^ ^° ^^^^ ^^ <>* SERIES 102 $9,«ioV40o!fnd^87'SS \?f *"^^^h^P; ^njesting respectively equally, and^ aUow inSt JnH^^'l *^ '^^^" ^^^"^ ^"^ losse? on aUV.thdra""3k T/"i * " al investments and charge .•nt-re'=+ -! — u w-viiararrais at ihe rate of fi"/ Af +1,^ j r r ° -"s^-it; •• "^ °^ " /o- At the end of four months li, PARTNERSHIP ADJUSTMENTS 848 Cr. I 1,500 14,3.(3^ $15,833^ Cr. )rs $25,000 6663 125,6663 lin for the firm, joverning limited :ner. This being may be charged :y may be. The f this amount is m. The $5,000 ■ the office fumi- issetsofthefirm. '0, thus showing by the partners. 1 on the balance- nts, and $3,000 ar one-third, or apital accounts a debit balance een and Adams Jctive accounts, hich $25,000 is Wilson. All of respectively IS and losses arge interest four months A invested $3,000 more, B $1,000, and C $1 200 Af *»,. ^ . & 5- .J has been divided and entered up. The interit i. X?,ret^;d,^tz tte'i t?-t t£:t Hi^".^ busmess. (Calculate time in months ) "^""^ ^^^^ ^ou^s as .hey Lnd onX"" f^iZ. l^J^'^t sundry creditors^ wSoo'r'b,H!'"p^aife '"$,^000""'^ ' %^eeriginal ?d among them, each partner is p Jan. I, 1907, ). During the 1 capital, which, during the year ts on which no Wilson, $2,000. I ; and Wilson, oth partners at Jan. 1, 19D7, ally gains and on the excess squired invest- or. 15, $5,600 JOO on August Jan. 1, $9,000 OO on Mar. 26, 5ted $7,500 on and withdrew )n Aug. 2. If ^as G's capital lid H owe the N? illy insolvent. .440.60; bills The liabilities J, $1,340.33. r paid sundry as a net gain commencing ? II. S, G, and H are partners in business, and on the date of settlement the books of the concern show that S drew out for private use $590, that the firm assumed a private debt of $930 for G, and that H s account was overdrawn $125. On the dale of the last settlement each partner had an equal sum standing to his credit. The resources closing were: Cash, «8 294- personal accounts $1,560; bills receivable, $4,400 merc-ndise, $18,220 The liabilities at closing were: Bills pa, ahl..-, $7 V8 ; personal accounts due $lJ,b5l ; interest on not( ^ iipaid, $190 What •fi-^'? P"""*"*"''^ "^' ''^P'^^^ ""^ '''"^•"S' ^''"''- l^^i" • a net gain of 12. L and W are equal partners, but, having become finanr'aily involved, they arrange a compromise with their creditors at 50c on the dollar, and wind up the business. Their balance-sheet at time of compromise stood as follows : Liabilities. L (Capital Acct.) $ 190 Sundry Creditors 3,910 Assets. Cash $ 50 Sundry Debtors 535 ^oods 1,800 Furniture 330 Machinery and Plant ... 1,000 W (Capital Acct.) 335 $4,100 I $4,100 The assets realize as follows: Cash, as stated, $50 ; sundry debtors, S/^' ^r""^^'- ^l'^^^' ^"^niture, $150; machinery and i)lant »5U0. W s private estate being insolvent, he is unable to contribute towards the debt. The creditors are paid as arranged. How should the partners settle with each other ? Show ledger accounts dealt with m handling winding-up proceedings. 13. C, G, M, and F are partners, sharing profits or losses in the proportions of A- I I and ^V. The balance-sheet, after realizing on the estate and settling with the creditors, is as follows Liabilities. i Assets ^ l?P'*^l ^^*^*-) ^280 M (Capital Acct.) ' $400 G (Capital Acct.) 800 F (Capital Acct.) 223 Cash 457 $1,080 $1,080 As none of the partners are able to contribute anything further .0 the busmes:,, r-xplum clearly the settlement, and show the disposition of the $457 cash. I I . Hi 346 'f'i wii PARTNERSHIP $40,910. 15 and T's J537 201 lo u' !, u *^' '"^'^^'P*^ ^^^^ and T's $26^70 il If ?! " ' ^''^^'^^^^^^s were $50,912,24, for Ssl 7m m. . i i' '"^ °^ '^^ P^"°d ^he business was sold or $53,700.00, of which $30,000 was received in cash, and banked to their jomt credit. A note of $23,700 was taken for the blnce and then afterwards tran<;fprr«:.ri +^ u * j- uaiance farp A finoi +.1 ^'^^"^^^^^^^ to H at a discount of 10% on its cheques. ""^ ^"'°'"" "' *he respective stJI^^foul"™" °' ^ ''"^™-- '"e balance-sheet of which Liabilities. ?^,?.'*°ff • $10,000 A (Capital) 70^000 $80,000 Assets Stock-in-trade ...;... $50,000 ^^i\. 12,000 ™^'"&- 15.000 oooK Debts 3 000 $80,000 s.rthe rj^^'tm^'t r T ^i- ^' "■"» ^^^^ p"«'"s «io/w> • lw".U«) cash, and each paying A nersomllv $18,000 „ cash. Show the balance-sheet of fte new 31 opened (6) supposing goodwiU account opened. ■Ch^rrtZf- ^ ^'^".f"'"^"^' sharing profits and losses equaUy. Iheir respeCve capital accounts are : A, $6,000 ; B SI 500 Their habihties amo,,„t to $15,000, which inc nde ^mZ ::~;r :;Snenr '"---^' - -' - — '= D, the former in- ider. They agree The business has e of by H and the his receipts and otal receipts were 5 were $50,912,24, business was sold cash, and banked 1 for the balance nt of 10% on its eceived a cheque of the respective e-sheet of which ISETS. $50,000 12,000 ....... 15,000 3,000 $80,000 ion each putting g A personally e new firm on account to be losses equally, 0; B, $1,500. les $3,000 due account. The do the partners "t and accounts APPENDIX THE METRIC SYSTEM OF MEASUREMENT The Metric System of Measurement tets its namp fmrr, +», IS the unit of length of the system. ^ ''°"' *^^ '"^*''e. which metre" "'' "''''' °' measurement are derived in a simple manner from the This system of measurement is used in all countries fnr =rio„*fi poses on account of its exactness, and in Snrcountries if f ^^^^r" ordmary purposes. ' countries it is used for Measures of Length lengt^of'rtn'^iJSo^t? ?H?^^r"Sbota V^^^^ ^° '^ *^« earth's circumference, measurXg^ hue pS22 thmu^h T'*'' ,?^ *^" from the equator to the pole. passing through Pans, France, Table 10 millimetres, marked mm., are 1 centimetre marked rm — i centimetres, " cm., " 1 decinSre ' •' h^' Z ^ ""^ -^l «"?*« 10 centimetres, 10 decimetres, 10 metres, 10 dekametres, 10 hektometres, 10 Kilometres, cm., dm., m., Dm., Hm., Tm., dm. = jJ^ or . 1 m. Dm. = 10 metres Hm. = 100 Km. = 1000 Mm. = lOOOO " 1 decimetre, 1 metre, 1 dekametre, 1 hektometre, 1 Kilometre, 1 Myriametre, Comparative Lengtus are as follows : 1 HT ^ Inches. 1 Metre = 39.37079 1 Decimetre = 3.93708 1 Centimetre = .39371 I Millimetre = 03937 is us?d'ifmt:Li"g^Lng"SS:='°^' ^""^ ^'°'-* ^'^^-^ = th« Kilometre timel*ariarg: TS ^Hn ir^n"" '\^ ^^""^^^ °"«' ^'"«« -<=h unit is 10 1.000. etc-.tfme" tt^taTdard o °I' TT'^ T ^'f.^'^'^ ""^* ^^ '^- '^^ relation among the uni^<5 Pvi=f= iW' ^^^' ^F?; *^" °* *"^ standard. This that, if the standard "s knoSi all thp'n^i;^ ^^^^f °^ ^^^ "^^^^"^ system. So the same syllablS to the^Sdids " ''" ^' '^"""'^ "^^ P^^«^^"g The prefix milh is derived from the latin mme, meaning thousand. Feet. 3.2808992 .3280899 .032809 .0032809 Yards. 1.0936331 . 1093633 .0109363 .0010936 centi deci /deca or) Ideka / fhecto or ^ ihekto / kilo myria centum, decern, Greek deka. hundred, ten. ten. hekaton ' kilioi, ' . , , . " myria, ■■ ten " 3 hundred. thousand, ten , i f I ^ 1 ' i ■ 14, 1 j II ! J ,1 s 1 ■I '■ ■ , s i ■ i . 1 - ■'i i 1 :: ' I • f ii L ;;ii , ' 348 APPENDIX Since, in the Metric System, lO. 100 1000 Ptr «nu= * denon^tioa make a unit 'of a high. denoSii -uToL ^h\ ^ one of the metoc measures may be expressed in term; of another measu"! by simply moving the decimal point to the right or left. Land or Surface Measure The Are is the unit of land measure ^or arpa\ t+ ;„ ^ is 10 metres. "leasure (or area). It is a square whose side Table 100 centiarcs. marked ca.. are 1 ^^^e,^m.rked a^ are J^e^^"'""""^ °*'" '''''''''' ^^"^^^ °^ ^^e mkre and ft. subdivisions An Are is 100 square metres, marked m». It is shnnt no c »„ yards. The Hektar is nearly 2^ acres (2.47). ^'^ ^'^"'"''^ ..^J^^ ^* '^- *^^ principal unit of surface of small plots of lanrf Th„ area of a farm ,s expressed in hektars ; of a countrrin sqSSe Lomeires Measures of Capacity who^^^d'i^^rsVd^^cSii^nr'"- " " ' ^'^'^'^ '"'"^^"•- *^^* '^' -"-^^ Table IS ssr "'^J^^' a* '"' ; ;?s"'"' '"^'^^'^ ?•• m fT:. '.'. '- ' " ' dekalitre. " m. 10 dekahtres. " Dl.. " 1 hektoUtre. " H] The measures commonly used are the litre and the hektnlifr^ ti,. grain, fruit, roots, etc fn large quantises. * ^ ' '* '' "'''^ '° "'^^"""« cub.^ft)."'''''"""^ ''"'''^ *^' ^*"' ^^ ""''^ ' i* i^ ^ ^"bic metre (= 35.316 Measures of Weight It is the weight of a cubic centimetre The Gram is the unit of Weight, of water. Table W c^Sa^,' '^^'^"' Z^- ^r.^ 1 'i'^'^^^' "^-rl'ed eg. 10 centigrams, 10 decigrams, 10 grams, 10 dekagrams, 10 hektograms, 10 kilograms, 10 myriagrams. eg., dg.. g- Dg., Hg., Kg., Mg., 1 decigram, 1 gram, 1 dekagram, 1 hektogram, 1 kilogram, 1 mjn-iagram, 1 quintal, dg. g- Dg. Hg. Kg. Mg. Q. 1ft • , S '--„ ■'"S-i 1 quintal, " f) 10 quintals or 1000 kilograms are ! Metric ton, marked MT .Th JrLZ^'^ commonly used are the Gram, Kilogram, and Metric Ton monlvcalled thp "T<-nr."finL 1 • f '^f^l^'ed. The kilogram (com- «.elung ha, :;„d other heavy „Ud.s ; it is about 204 lbs. iiore tiSi m APPENDIX 349 c, units of a lower , it follows that any s of another measure s a square whose side ced a. ' • Ha. I and its subdivisions about 119.6 square plots of land. The square kilometres. Legal and Approximate Values are as follows: DENOMINAXrON. LEGAL Vai iitt a Metre .... ^oi^ ■ t Approximate Value. Centimetre . .\\V.\'.V.\\\\', . 39371 '°^^^^ ^ft. ^ inches. Kilometre fioifj? „,i i inch. Square Metre.. { Al\^'^^\ § mile. Are iifit^-^''^' .....lOJsq.feet. Hektar A^J^? ^'^- y^rds 4 gq! rods. Cubic Metre ," ," f 'qna T^^^ '^ 2* acres. Stere 9?2o T J ^'^^ 35J cub. feet. T •i..„ z/59 cord 1 j tj'^;:.;: 1.76077 pints Va*^"^- Hektolitre «,,« u u 1 •• IJ pints Gram xklll^Jt^^-f^ 2 bush' 3 J pk Kilogram '^204fi fh I'"^ ^^J griins. Met^c Ton (or tonneau')! i \ [ ! 2204 6 lb'" ' '"■" {% P^-^- ^*"* . 27590 cord . . . .*. 1 T. 204 lbs. i cord. 1l ! netre; that is, a cube J*' larked dl. " 1. " Dl. It HI the hektolitre. The wine, etc., in modern 3 used in measuring lie metre (= 35.316 f a cubic centimetre marked eg. " dg. Kg. " m|. " Q. 1, marked M.T. n. and Metric Ton. le precious metals, he kilogram (com- i and coarse articles 'ic ton is used for ! lbs. more than oui ANSWERS nine y-three thousand, five hundS .n^°*^"°"® "'""°"' t^o hundred and seven thousand, four hundred and thi.?^.^ '?i"'°^'^"« ^""d^r^d and twen?v 12, Four bilhon. two hundred irt S.™!,!. .u ^' ""^ '■""'Jfeii and eiuht Opo hundred and eteh»vT™„?^T: "'''""y-'lu-ee thousand and one i j 4, Eight bUiion and Wnt?",'S?°-|l™on^t'r''- "^^ '>»°>i'ed anTsevl? ind rSr,"," '^^ <^X'fJh°Sl^i T ''"^"^ million Z' Wed.. $2,847.60; Thur 'JiVn '•?« ^^S-"'- ^^'^^^^S ; Tues. 82183??: total. $17,370.69. X Tan l SQ. |6 ^f.Ss! Serj^r 5_.|, 34.311. 2. 74,15*\ 3,51.053. 4,93.497. q. i54 893 6, 7n.3ai. 7, see'-. a 180,523. *0, 458.261.* 10, 26.651^4 |f' ?^''*if'f^®- '2, 15.-^ '.363 rS, $381' 14. 23,938. R 8,382 lbs 16,66.661. 17, $13.9. <- i; .$143,W;4.:^5. 19, $6,675. §). 5 156 943 21, $26,670.58. 22, 32S262. 21, 13.^72.85. *»L I66,637^£^r;s25' $1,882. 26, $251, a <•.%«' 23 $7,775. ». $2,150. ??; $m 31. $34:00 32, SHO. '^^, ',^82,736,83. 34, 64,6§4 35, $4709^ 36! 4, 4.693.23S, 5, . . . 9, 148,384. 10, 13, 5.962,405. 14, 30,804,t«2. Senes fr-|. 69,316. 2, 223,917. 3, 1.037,504. Ml^'it^- *• 3.407.075. 7, 6.683.976. ft 6.078.438 2.802.986. 11,3.024.041. |2, 1,835.568 " " 15, 6.256.941,040. |6, 28.820,824,863. 903.384. 19, $14 16. 20, $1,268.25. !ft^ds. 23, $3,412.30. 24, 17,010 bu. SJ' VJJ'^^'l^^.P' *'°30- 29. $3,288.60.^" 30. $1,258,250 32, $600. 33, $82.88. ^ 34, $1,907. 35, $502J5. 17, 26,174,900,220 21. 247,632 hills. 25, $2,352. 26, 18, 82,05*5,. 22, 41,2^0 $22.25 gain. 31,786.50. Senf^7— I, 282f 2, 1.496. 3, 1.2842. 4, 1.965.311*. 5. 4 152- 240*. 6. l,352.549j. f $2,891.19.* & $4^24505.' 9, 882.40 iV 10 16.802.883. II, 1.146U. |2, 3.123Jg. 13, 70.349f|3. |4 145lo84M '5- L!29.470||§: lU 13l',!87iii." |7,'^1,439,J& J iih^M'. 589,2838t|. aD, 5,274fm. " 21. 14 hrs. 'E 795 bu. 23. fit. 57 imn. 25, $16.75. 26. $35,156.25. 27. 41 bbls. 28. 175 ac. 42 yds^ 30. A. $1,368.75; B. $2,372.50 ;'c. $3,923.75. 3|, $765. 35, 75 lbs. ; 100 lbs. 36, 80c. 37, 40. 10 mos. 41, $14. 42. 25 gals. 46, 4,547. 47, $45. 48, 800 bbls. ; 51, 160 yds. 52, $135. 53, $3.75, 15 days. 57, $537.20. 58, $42.25. 50, 18 bu. 62, $4,736.70. 63, 13 miles, fo 33,30. 19, n, 29, 32, 32c. _„ 70 bbls. 38, 12 men, 43, $36.08. 44, 7,485. $5.75. 49, $7,500. 54, 325 ba. 55, 15c. 106 lbs. 60. $869.50. $432.60. 65. $37.49. over, 69. 45 years. Basswood, $17.13; piue, 1st. $31.22; 2nd, $31.00. 34. 205 apples. 39. $240. 45. $78.96. 50, $1,370. 56. 61. 66. 22c. 67, $395.25. 70, 354. 71, 120 days. $17.70; ash. $18.65. 68. 46 bicycles ; 72, 1,888. » 73, 185. 75, 2nd by 54 ^c. $28 Series 8— I, 27. 2. 135. 3, 1924. 4, 720. 26i pes. a 156 pes. 9, 42i33C, ^Q, 75c. 5,1155. 6, 200 lb'.: Series 9— 1,3. 2,5. 3,2. 5, MS- 6.14. Series IQ— I, 3.039.653. 2. 586,», • 15. i- 16. 4. 23. im ,24. 4, 6f lbs. 5, 5, m. 16. " I, «250.40. 22. 00. 27, 44 bbls. m miles. 32, ncs. 36, 34,8.. ■s; R. 6J9days; 44, m 'bs. 45. 3urs. 49, 13|. 87^88 lbs. 54, NEW METHOD ARITHMETIC 3, m- 59, 3, 246 ac. 130 ; 9,645. 6, A. , $911. 8, 1st, 1,135 mi. ; 3rd, it. 3,779J ; 2nd. I; 3,573. 14, cargo, $11,250. I. 760 lbs. ; 3rd. 21, $26,160. .n. $1.50. 24, 6, 1st. $134.20, 55.20. 28. H- 51, 6c. 32. A. 0. 34. Horses, 36, A. . $49.50 ; igar, $26.48iSJ| 1, A, $3,529^; C. $875. 43, 72. 46, N.. 95; A. 50 ; B, 60 ; , Man, 833.60 ; J4c. ; boy, 60c. , $7.56; $5.04. ac. 59, $200. vder, 133 J cwt. ; C. $254. 65, c, $4,000. 67, e thousandths, undred-twenty- hs. 6, .Two- - twenty - five bhs. 9, Six- lundred-thirtv- n-thousandths. ten-miUionths. ^ 20/ ELht and £n^;h'^"*^°."'.^°^-^'S^*-^"°dred-tS and ten-million-s^entv-tL?«nH ^*K?"'^"'^-^^« ten-millionths. 21 Six One and fifteenAhousand ei^ft t;^'^^^ hundred-millionths. ^'' o? thousand-eight-hVnStw;?y^'tl<^t"^^^^^^^ 23. Six and St andten-m^Hon-seventy-fiveihou^XlM^itC^^^^^^^ Serfts 28—1, .7. .004165. 19, 0034 J^^ 7-^^T o o 6' 0000625. |7,^'.00324 I' 225.000324.'^' 25. 6b022?' 'L 2SJ'oOOn2« 22. 9175 23. 25.3125. H', 29, .00005. 30. .500 31 2 5 S X^' rr,^ •^^^'^^- 28, 6000.00045 36, -013. 37; .002400.^' M 24^2' 2^^. ^ .5. ^34, .125. 35. .000204. 42.^^43,4.035. 44. i20^ob6r- 45'W8'7'.- 46%r47, ?2'do.2T^- ?i%r^^s'«*"ll.H" 12, M.^' ^^h ^i ^- ,5't\7.«. 8,,V ^':Jf24,JJr^^^' '«'^5'' •9;W|'/'2o.i'^iih. %!'t. 7. .3^25" ^J333 + . 2'9^|666 + •^' J'nrl^- .?' '^^^^ 6' -5555 + . ^1:58^3%. '%Si- C1§1?J«^^ •?r4i^s.62 1': Ts 23. 15.54545+ 24 46 342^ I %% %, 2I-' 675555 + . 22, 8.05468 + . 27. 73.418333+. 1. 2 9117787'^;. . ^'h'^^iem + ^^' '"''^'"^ ^• 5. 2|?4^5fl5-'' 6^%T9277h2f'-Ti.\.Ji ''''■''''■ 4. 970.17047. 10. 627.176875. ?!, SSMSlT'tz, 4ls^9m- «' '■'''"• ■ 9' 3r§«§,. 6.3^1^^^ 3^r- 8.?:45f \ il.^-,o.^bi-^1: .6^-^;^ Series 33—1, .6. .318971. J, — 2, .153. .., -^..' :t\.^« ^r% .o«^''^ «-«^ •Yk ^„„''"''' + L i4, 1.168+. 15,^0553+. 16.2.80246+ 12. 19, '0277 +r 24. 2,548 + n, 1 1075+ . 18, .020+' 1.6666 + . 23,4 051927 + 20, 1120+. 21, 1.7T+ 5; 26. 78^^s. 8 ANSWERS (J ' ( '■ I , ;-■ j i 1 Lli,.. :^ Series 36— I, 50c. 2. 0025 mi. bv .01 rd. 3, .992. 4, $15 82f? ?i^te',.i' ^■^®' .l'«^- 8'-^^^. '9, .000372. 10, .11. ||.168,0(5(). ?• ^.".?a a1?.^ °^^« i?Ai*t- 14.30.98. |5, 4?n ow .^^ 1 6, 4.66.5. 17, «J19.37J. 18, 2000 ■iheep. I9, W.. .«?? ;.oJ , U.. $5,110. on. $6,120. 2>, $1'13. 22, ?«77.50. 23.488. 24. 63.295 ac. 25-012! 26, 304.212 ga!s. ZT, -0013. 28, 40 gals. 29, 102.983 tons. 30, 9.045 bus. 31, 263.2702. 32, $42,880 33, 150.08 ac. 34, 5.0420168 + . 35, /472, 12s, ^:',d. 36 $76.4953125. 37, 1,411,141.19 c. in. nearly. S4.90.''54, .^ 1&. *°' ''''■''^- *'' *'''•'''• *2. ^mih. 43. Series 37— I, 256.915 in. 2, 12604d. 3, 709 pts. A, 203 qts. 5. 155,243'. S, 505 gi 7, 215,842 02s. 8, 333,515 cu. in. 9, 7,448,775 !^- i°;o,,'0, 17043. II, 136,049 0Z3. .|2, J-^H dwt. |3, 3.965 in. 14, 4,131J sq. ft 15, 444,088^ sq. ft. 16, 4.989,931 sec. IT 218 cu. ft. 18, 34,636 grs. |9, 269 pts. 20, 129,832 in.. ' Series 38— I, 25 tons 8 cwt. 46 lbs. IS 02. 2, 8 lb. 3 oz. 16 dwt. 16 gr. (Troy) ; 8 lb. 3 oz. 6 dr. 2 sc. (Apoth.) ; 6 lbs. 1 » ozs. 232 ,V gr. (Avoir ) 3, 120 rd. 9 in. 4, 7 tons, 13 cwts. 1 st. ^3, 534 gals. 2 qid. 6. 2 days 3 hrs.. 36 nun. 7, 5 cu. yds., 26 cu. ft., 432 cu. in. 8, £33 14s. Id. 3 far 9, 3734 cords. 8 cu. ft. |0, 444 reams. 17 quires. 18 sheets. |, 78 half crowns, 2s. 4d. |2, 4 I'.-.. 1 oz. 9 dwt. 18 grs. |3, $45.63. |4, 587 mi. 4 ch. 2 rds. 6 Ik. |5, 40 bu. 1 qt. Series 39—1. 18 hrs. 2, 186 rds. 3 yds. 2 ft. 3, 17 dys. 3 hrs. 25 min. 42f sec. 4, 101 sq. rds. 24 sq. yds. 6 sq. ft. 108 sq. in. 5, 11 ^u ft. 432 cu. in. 6, 3 qts. li pts. 7, ipt. 8. H\j in. 9, 200 rds. |0, 14 cwt. 54 lbs. II, 100 sq. rds. |2, 3 cd. ft. 3.08 cu. ft. |3, 2.15 qts. |4, 5 ozs. 1 dr. 8^ gr. Senes40— (,iji- 2, -7083. 3, H 4.0128 5, Jj^. 7. s¥%- 8. mi- 9. S231.78. JO, Si ^20.50. Jj, $367.66. 13, $858.90. 14, $145.43. |5, $1034.03. 6, .6961805 12, $606.57 Series 4|— |, ^^279 63. Id. 2, '"^" 'bs. 1 oz. 4 dwts. 17 grs. 7, 189 mi 307 rds. 4 yds. 1 ft. 4 in. 4, 22 ga,d. 1 pt. 5, ^^19 ' .' ^. 6, 21 to;. ■; 17 cwfs. 31 lbs. 11 ozs. 7, 3 pks. 1 gal. 3 quj. 1 pt. 8, 21.9 16 s 9, 3 gair 1.75 pts. Series 42— I, 32 lbs. 8 ozs. 14 dwts. 13 gr- 2 ft. 6 ins. 3, 1 bu. 2 pks. 1 qt. 4, 20 gals lbs. 6, £2955 17s. 3 far. 7, 40.75 yds. 8, K< fc .1 mi. 76 rds. 4 yds. ts. r , 5 tons 18 cwts. 41 q. i. Senes 43—-!, 142 bus. 2 pks. 3 qts. 2, 21. ,'als. 3, 119 cd. 53 cu. ft. 432 cu. ms. 4, 140 wks. 1 day 17 hrs. 5, 4,.''38 acs. 23 sq. rds. 21 sq. y ' 5 sq. f<: sq. ins. 6, 121 tons 37 lbs. 8 ozs. 7, 1,373 bus. 2 pks. 6, 1518 gius. 9, 1010 mi. 35 rds. 2 ft. 6 ins. |0, 167 ozs. 10 dwts. , ,^VI^ ^t'^o^*'^- ^ P^^- ^ g^l- 3J qts. 2, 1 ton 1 cwt. 82 lbs. 8 oz.s. 3, £* 15s. lOd. 3§ far. 4, 1 yr. 320 days 1 J hrs. 5, 1 lb. 2 ozs. 18 dwt. 19 grs. 6, $19.97. 7, $4.99+ . or $5 to nearest cent. 9, (a) /38 3»ld. ; (t) £513 13s. ll^|d. Series 45— 1, 10560 tiinvs, 2, 369 bags. 3, 1628 paicels. 4. 154 iwoplfi. 5, 15 fields. 6, 225 portions. 7, 231 persons. 8, 9 days. NEW METHOD yRIlHMETIC 9 I. 4, 8i5.82n. II. 11,168.000. •bs. 16, 4.665. ., $5,119. 20. •5 ac. 25, .012. tors. 30, 9.045 W, 5.0420168 + . 19 c. in. nearly. 12, Milh- 43, 4, 203 qts. 5, 1. 9, 7.448.775 13, 3.965 in. 17, 218 cu. ft. z. 16 dwt. 16 gr. 2\ gr. (Avoir.). :}ts. 6, 2 days 33 14s. Id. 3 far. ts. II, 78 half i3. 14, 587 mi. s. 3 hrs. 25 min. 5, 11 ^11 ft. 432 Is. 10, 14 cwt. 2.15 qts. 14. ■. 6, .6961805 6. 12, $606.57 rrs. ^, 189 mi. 21 toil-. 17cw(3. 9, 3 gair 76 rds. 4 yds. oas 18 cwts. 41 9 cd. 53 cu. ft. . rds. 21 sq. y ' >us. 2 pks. 0, ;s. i. 82 lbs. 8 ozs OZ3. 18 dwt. 19 ;^38 3^5d.; (t) xcels. ' days. 4, 154 Series 46— 1,625. .390.625. 4. gj: j;,^ 7!o. »Sg;42J;204,*, ; 12 2. 125 13,824; 4,741,632. 5,216; 81 ; 4,096 J. or 129.746337890625. Series 47—1, 24. 2, 35. 8,321. 9,199. 10,297. | 16, H- 17, 3 45. 18, 203.1 19.40103. 23, 3.58092. 24. 121ft. 28.9 ft. 29,56 ft. 612 ft. 34, 152 168 sq. yds. 2.487 rds. 38, 8466.66J. 3, 256 ; 4.096 ; 65,536 ; 100.000; 12,167. A. 7, 34775. . \.^^- 4, 66. 5, 105. 6. 135. 7, 123. 1,867. 12,327. 13. H- 14,18. 15, «. • ^ 19, .835. 20, 7.39" 21 1.73205. g 66.08479. 25. 40 rods. 26, 176 yds. 27 30, 18 yds. 31, 3C 805 ft. 32,272 ft. 33. 35, 18.978 ft. 36, 30 rds. and 18 rds. §7 8. Series 48 — |, 438. 9, 708. 16. 2, 32. 10, 8.765. 15,1.26. 'i6, 2.444. ' 17, U. 23,6.3. _24, 13. 25, 33iQ. 543 ft 29, ^ ft. 6 in. ; 5 ft. 3, 42. 4, 79. 5, 63. II, 4.968. 12, 7.3. 13, \6, ?. 19, .908. 20, 7^. 26, 15 m.; 15 in. ; 30 in. 7 ft. 6 in. 30, 4225 sq. ft. 6, 85. 7, 245. 579. 14, 36.4. 21.27. 22,45. 27, 84 ft. 28, 31, 61.3 in. 32, 65 ft. 42, 12 17 J in. Series 49-|, 990 sq, ft. 2, 10 acres. 3, 51H sq. yds. 4. 20} sq 10, jVi lli II, 147,840 blocks. 2, 843.09J; |3, J40 8U lA. 43H u. 15, 100 rods. |6, $69.30. |7, $36 I8 13* sq ft 1056 yd 20, «364.80. 2 , 11.536 sq ft. 22, 259H ^ V J?' ^£^^*-^^ -^.fV°°«- 24,8'ft. 25,198 ft. ^,24^21/ 27,2 48/ ^; . W'/-^ "\® '"• 29. 25 sq. in. 30, $323.3?^ 3|, $6.00 % $63 33, (a) 30 ft. : lb) 600 sq. ft. 34, 8 ft.'^'35. $82.13j.'*'' 36 50 ft^' J/ A i,"?; \, ?% «449.07}?. 40, $14l 41, 107^-^ yardl; **• -^-"oi\.".- 44,4ft. Im. 45, 24.748 + in. 46. lOaft. 47 .»- t22S -Si' ^^« l*^',^^-^^ ^^- "• 50' 2,142f sq^ft. ^51 822?.' 52, »225^2J 53, . 1/ ft. 54, 1,948^ sq. yds. 55. .54 yds 56. H"'■^.^^^"7^= 2^^"°- 58,22.4878 ft. ^59. 15.512 iii. 60, 3*? ?J yf 61, 508i tons. 62, 729 bricks. 63, 8 ft. 64, i in. 6?^72 rods S', ?n° '''5^'- a.^7, 6 ft. 68, 1.200 gair* 69. 216lc* 70. Sf ft 1\ 7A i?4Q J?' tU^t '^'-.^J^k «264. 7iri48J miles. '"^ 1.687 Vt! 76. $3.49^-; $3.43|. 77,849.60. 78, 27 miles. 79, 34 lbs. 80 830 fi:7n«'°' •^' ^LJ^t '^'*^°"t ^tt°^)- 83. 49.402 gals. (1 gal ' 277.118 cu. in.. 84, 46.765368 cu. ft. 85, I2I cords flfi 64' so 87, 243.tf 88. 9.518 in. nearly. 89. Il68 sj. ?n. 90, ?3.75y Iq %ds Sf '& 9 • '^ '^ ";.o 92, 9.799 gals' nearly. 93, I2|?'lbs. 94. 49 m fS, 22 J mil^ 96, 488 coins. 97, 9.69 in nearly. ^, 9.9 11?^ nearly cu.ft. 103. 202.19 cu. in. |04, 97f sq. in. , -.^/!f.? 50—1, 65J vds. 2, 42f yds. 3, $15.62*. 4, $142. 6, $16.00. 7, 813.50. 8, 128Jycl. ; 130 yd. ; 8327.25. % $12.80. ,o^"*u,5l--l, 59 strips. 2, 60 strips. 3, 75 single rolls. l^ double rolls; ceiling. 6 double rolls. 5, 10 double rolls 88.75 ; ceiling, $3.75. ' 7, 14 rolls 9, Walls. 839.60; ceiling. $21.60. border (23 J yds.), $1.65. Series 52— |, 180 ft. 2, $67.20. 6, $11.6( 7, $24 18. 8, $21.78. 12, $184.80. 13, $153.60. (a) $7.65; (6) $27; (c) $6 8, Walls. $15.20, 10, Walls, $7.20 5, $54.50. 10. 18 ft. 4, Walls. 6, Walls, ceiling. $11.40. ceiling, $4.40; CI. ©"" $36,90. 28. $41.00. 3. 15,100 ft. 4, 810 ft. 5, 36 ft. .. .J' *^^2. 10, $132.44. II, $4,752. 14. $82.60. 15, $5.76. 16, $396. |7, 18. $330.75. 19, $506.88. 20, $120.96. i», 10 It. 24, id it. 25. iS iu. 26, 8 m. 27. Il I- a TD ANSWERS Series 53-1 800 shingles. 2. '^20 shingles. 3, 18 squares, i, $252 Series, 54— I, 20 bundles. 5, 22 l.iinrlles. 6, 812.59. 2, 59 bundles. 7, 820.89 i. Series 55— |, 8,\J cords. 2. 44 cu. yds. yds. 5, 31,584 brick g, 4G,7(iO bricks. 3, 40JJ sq. yds. 4, $47.19. 3, 18i cords. 4, 94 j\ cu. Series 56—2, 90 >ds. 3, $602,68. 4, $26,250 5, 2.S3 girls. 6 sheep. 7, 862.T90. 8,8624.12. 9, R E., $'4,320 ■ B S SO 480 • 15, SI, 890. 16, $0,26.40. I7. $27,324 18, $76,50. 19, $22 20, 8150, 21, S216. 22. 8143,43* 23. $420 OA ^v>fi'in !^3li- 26, 8136.80. ^27. 8155,52. gl $219^6. 9^. llS 2188,03. 31, $36,19. 32, 8428.40. 33rS234 $12,96. 62%. 34^:.r 35, 41, 47> "■•■j'lT'/o S,r., 8173,25, 837,50. 57, '.50. 390. 29, 8192.24 44. 34, Latter ; $2. 40% 60. 83,937. 67, 840.50 88,563,75. $228.92, 87, 8360, 93. 8176. 99. 8112. 104, 8629,63 no, 8975 36, 160 hats, 37, 28%. 38, 40%. 39; 42. 46%. 43. 37'',,, '44, 37J%. 45, 214% 48, $322.87, 49, 84,863,75 ; $4.62^56. * 50 51, 86 406,25, 52, Gain, $74. 53, Gain, $105 Com,. $225; Pra, $11,025. 53, ,$93.75 40. 4930,,. ^46. 56|%. G,. $24,75; 54. Gain, 59. 81.110, J^'Af^of- f^'l-,H^,^5- 64.82,004,20, 65785,62,80, ^ !^o=^^-,,69. SI 17. 70, $840, 72, $7 236. 73, «« T^A ^'^^' 76, 822,40, 77, 8412.,SO. % $112.50 70 80. 8210, 83, §420. 84, SG60. 85, 8637 so ^ $5lo 88,8385, 89.8675. %, 81.071. 9, $350. 92 $262 5o" 94, $181. 95. S216, %^' 8416,25. 97, 8503 25.^^8, j350 100, 81,087,50. 101, 8656.25. |02i 8876.38. inl $324 06, $1,958.75. 107, 86,000. (08, $900 |& 875 III, 8192, 112, $399"'' i,'3. $i.ij'& 114, Irdisll: Ll^' ^^*?l«^«o."6, $1,970,90, 118,815, 119,830, 1 26, 824 191 $40, 22, 821.60. 123, 812.60, 124, 818 125 $72 I9f. ill' 127, 865. 128,857.60.' 129, 8124. ['^8120 131,824 |32 $62^80 133, $51.60, 134, 81.60. 135, 87.80,^' |36, $4.50 137, $216 i|q l?«^n '.% IW-^Jr '41' «5-89. 142. 833.97. 143, $51 98 S' fii? S72 6i*.^'«9*.'if ■ .cl^iol'.'f -^^iinJ ff ' ^^'- 149. 8Ul.44 ; $235'.S- 150, 872,68; $93.43. |5|, $99,24; $107.50. |52, $158.02; $182.33 Series 57—2. 12i%, 3, 29J%. 4, 10%. 5. 3% fi 900/ 7 775%. 8,27%. 9,84J% II, 6|%. 12? 15% 13 2- M 20"/' 15,75% |6,i%. I7,i%. I8,i% 19742?% 20,25%. itiSof 22. 13%. 23, 100%. 24, 16°% 25 90/0 26 20% J>7 250/ " ^' Tp' ^' /?%• 30, S%. 31, 5%: 32, 40/r 33, 2%- 34 i°/' ?iof ik'l^\ 4!',i%-«44,ll%. 45,96c. A6 i%: 87jc. 47 }J%. 49, 3 mills ; $12. SQ, 12 mills. 5|, 9 mills. 52 11 mills « 138c. 54, 98c. 55, 6 mills 57, 5J%. 'tft. 5% 50 410/ """Ja ^Z m m\\7€i\¥^^'^ ^^ ^„, Series 58— 2, $4,500. 3,1,000 bu. 4, 63 gals. ; 57 96 eals H ff\VPVfn"'- ^,'.*lll^^'- 8, $260^' 9, $1,010.60 |0r$3,600: ll'o!?^^- . '2' 'Oc. 3, $30. 4, $4.80. 15, $2.25. If $14 17 SIu,. ;0.40. 24. $yu.UUU. 25, 50 bales. 26. $536. 27. 7.360 bU: res. 4, $252. ) 131 bunches ; 3. 4, $47.19. 4. Q*i\ cu. Rirls. 6, 544 S0,480; C.L.. '84. 14, $70. 19, $22,500. ? 128.30. 25, SI 92.21. 30, atter ; ,§2.10. , 40, m%. 46. 56|%. I, G.. $24.75 ; '5. 54, Gain, 59. « 1.1 10. 65. $5,162.80. 57,236, 73, JI 12.50. 79, 86. $520. 92, S262.50. ). 98, 8350. 103, S324. 109. «75. 4, $4,278.38. I, $24. 121, 126, S64. 132. J62,80. $216. 139, 51.98. 144. .44 ; $235.73. $182.33 •l > 14, 20''/„ 0- 21, 20%. , 27. 25%. ^o- M, i%. 4i%. 40, 87Jc. 47, I mills, si ^o. 60, 6o/„. E.- 67, 3%. Vo' 75,3«%. 6 gals. 5, 10, 13,600. «14. 17, b"- 23. 7, 7.360 bu. NEW METHOD ARITHMETIC S' Vo'i^n°Ann30,i300,000,_ 3|, $12,873.56. 11 ¥.' ':^.f2:'''- »37,„!3,.>- ' 387 112 M' J'«;«^«. 43...iL".92o.- 44:' Ji3.'r?S 32, •47.733J. 34, $56,000. 500. 39, $17,000 48, ?750. 49, ,|j33J 54, 8ii.iO. 55, $975. ^^ 40, $11,700. 45, $60,100. 47, $1, '.•}()() Series 59—3, 3610. 4 50, $192. 51, $300.' 52 $350 « «ss $840. 57, $5(K).' 58, $1,000.' ' 5'' •^^• 8, $160 $2,158.50. yo Ills. '' i^i^nA''^^"*^- 10,5,850.' 11,1 '.';''.« J, $975._6, $9780,,^ 7. ,„ 578. 14, 500 ac .?°' 5i'L. 21, $14^1.' _22. sI^gI 800. 121, 500 sheep. ' |3 i^'ii,?^.^-*- 27.$63."28 15, $3,400. 16, $153. 1'/, $563 50 18. 32. n% loss 38, H I 23, $41.15. 24, s;^.64. 76. $3 432. 77, $190. 78, $10.15. 79,4^%. 80, 14 mills. 81, $1888 82 84 000 9%o?''^^= li^'^'^ = «°"2. 85. $22%. 86 $95ri'2r 8?; ^?^7°' ^\ ^^^, '^°''''' ^'^'^ ; 8'"°^c''y '■tore, S3,000. 90 $102. _92,.4igr/o. 93,28^0/^. 94, S368. 95, '48c; $76.80.' 99, $2.21 jJjy. 100, $32.20; $1,«12.80. 102, $1,200 103, S8.65. f04, $250.92. 83, 33J%. 8700. 88, 5i%. 91, 96, $77,000. 101, $3,300 • 97. 35°^. '98,"6o/J atj%: $900at§%. 123, 128. $4. 138. Ids. $5,600. "106, $70 and $25 over. |07, 17^% irw 1 p "' pain !?^' ^'^^i-onl '0'. ?^ ^^^o ' ' «• «''5- 1 12 «36.V Hh, WccJ) 84,190. wheat, $4,275. 4, $8. 1 5, 800 shares. ||6. $99 02i« 117 40/ "8' !\f;^o^- '.'9' «70: $80=*' 120, $80,000. ''1^21, $750/^122 S5W0 $15,229. 24, $2,400. |25. 84 800 I9fi mo/ 197 S4KR8R« ?ii^-.J29. $47,000. 130. 475 bbls |3ir's76k' j'slMi.'''^ 't?*' ''®^««yfo^'-. "35. $480; $45. 136,865:01^. ^^1, $125,000.' _,. House, $812; farm. $3,045. |39, 20 lbs. 140. Mv loss 82 180 • Sii' 'Ifs^'^^l^ 'fJ'A^;% . '«• '€§^*%- 143, S46,9^5.'°l44. $250: ilS' ff^Vj5lite^%^mck^-'^4.ll)S^in1^Sc^^- i^'$i;S 153, $115.25. 154, 30; 155, (a), $54; (6) 2 mills. 1 56, 85,086.25: If ^'^ ANSWERS • 57, 5rp^%. 158. Mine. $5,600; my brother's, $4,200. |5Q $B less and 534 bbls.; $1.42. 79, $51,834.92. IRO. (a) 2o'i • b) M"^ iqi rV* $lSyO ''park iuEd'f gr'^' 8113.95'oTcffi in't^ Ws 850 f fre'e^ .bra^ /M iooc' P^"^"* ^""'^^ ^^'2^^ ; gc°- expense, $245,125. IM (a) 41 rarlmflT^ (6 $285 unexpended; {.) $965 comi^ssion m eOollUs P ^he^t Cr$2SSV l88r$lS L'^«n>°°»I'^- Co., $1,280; Hamburg I°nL' 6. s^S ^USi"\ s^^!/'^^ J:^:-^o, iJ8,^?r- '' '^''^ e ^^n!^^„^2— I. 4,507.425. 2. 9.063,404. 3. 8 739 450 fl 2 2isnfi4 , ,^oi,^-^~'' *'^24. 2,4,268. 3,891. 4,2.208. 5 4 108 A 1 12S 7.1.836. 8.3,713. 9,1,512. loT 2.625. || 4 200 12 19 053 ?l Series 66—1, 158.44. 6. 19.162. 7, .26007. , .Series 67— I, 6.328. 2, 485.46 6. 11.8629. 7, .992425. 8. -021. 2. 19,303.821. 3, 1.4019. 4, .316. 3, .11233. 4, 11.221. 5, .000.5. 5, 332.941. Series 69— I, $351.76. 2. $232.46. 3. $280 44 A id'i'i'in e Ki.''S7.69.^' ''■'''■''• 7: «2,664.n. ''8*'lM5a25.* 9 $2,664.5!: $20^ii?l'6' \\-^^-i\^ lJi'J\^'h. 3. SI. $3. $5. 4. $8. $12. 9. $2. |4,'$i6*'' Votsif: 5.l4l.'- ,J: lf4 Ves |S50«' ^^2 'Is' ITo ii. i. 'yS. S687s'' *"'■''• '8' «^''-''' '''■''• ''''■^'- '9. 41 *M?w^''J,^^P^«2, S18.23. 3, $52.65. 4. $69.26. 5, $47 09 fe S43 13 M^ifito ^'.^-^^•oo..9'*'.'^^2. 10. $104.08. ||:$956.87 $2,386.26. '^.Tl'.32lV67.'?4.l2"5ri2. l, Vm9?.-66 "'' ^'^^^ ^2, 159. $6 less and 163, 84,087.50. 168, 8%. 169. 0. 173, i2jo/„: mu lbs. 178, 2%. 181, City 50 ; free library, (a) 4 1 carloads • 184, S.P. wheat. 5, $4,080. 187, Hamburg Ins. 500. 5, 65.975. 4, 2,218,064. 44. 9, 21,454. '15. 5, 15,904. 720,896. II, 15, 11,367,504 ,108. 6, 1.125. 2, 19.053. 13, 8. 18, 24.180. , 310.504. 24, 5, 662SS. 6, i\- 12, 362H. 316. 5, .0005. I. 5, 332.941. . 8953.30. 5, 9, $2,664.54. >. 4, $8. SI 2. t, $6, $18. $50. 12, S6. $10, 16, 863. $99. $409.94. 19, 6. 5, $47.cy II, $956.87. 1,094.98. 17, $859.77. 22- NEW METHOD ARITHMETIC Series 6, $11.20. 12, $7.36. 18, 13.27, 24, « 44. 30, «9.50. $100.62. 71-1, $2 44. 2, S7 26. 7. I71.45. a 16.21. 13, $4.11. 14, $21.90. 19, $23.21, 20, $7.20. 25, 9, $128.17. (S.66. 35, Series 72—1, $11.25. 2, $56.64. 3, $78.62. 4, $33.32. 5,57.25. 6, $210. 7, $39.59. 8, $15.55. Q, $26.08. |0, $54.80. M, 90 days. $23.30: 30 days, $12.45; net. $14.25; total. $50.00. 1 2, 90 days. $26.10; 30 days. $26.18; net, $32.91 ; total. $85.19. 1 3, 90 days. $17.94 ; 30 days. $17.44; net, 13.20; total, $48.58. |4, $23.04. K, $119.15. |6. $330.70. 17, $51.41. 18, $51.85. \% $347.45. 20, 30 days. $103.90 net, $1.20; 90 days, $4.95; total. ;^110.05. 21, $16.58. 22, $18.26. 23, 10 days. $199.96; net. $11.20; total. $211.16. 24, 10 days, $135.59; net. $17.85; total. $153.84. 25, $16.57. 26, $54.47. 27, $1151. 28. $226.32. 29, $453.49. 30, $2,055.54. 3|, $223.21, Series73— I, $79.40. 2, $52.20. 3, $215.50. Series 74— |, Feb. 6, 1907 ; 33 days. 2, Feb. 7. 1907 ; 34 days. 3, Mar. 14. 1907 ; 33 days. 4, Mar. 12, 1907 ; 31 days. 5, Mar. 13. 1908 ; 33 days. 6, Mar. 12. 1908 ; 32 days, 7, Mar. 1, 1907 ; 63 days. 8, Mar, 3. 1907 ; 65 days. 9, Mar. 3, 1907 ; 64 days. |0, Mar. 3, 1907 ; 63 days. M, Mar. 3, 1907 ; 62 days. |2, Sept. 3, 1907 ; 34 days. |3, Oct. 3, 1907 ; 64 days. |4, Jan. 4. 1908; 34 days. |5, Jan. 2. 1908; 34 days, |6, $500.00; $501.51; $531.10. |7, $506.14; $507.65; $537.24. |8, $503.51; $505.02; $534.61. |9, $506.14; $508.25; $549.67, 20, $504.38; $505.89; $535.48. 21. Apr. 17, 1907 ; $425.00; $428.61, 22, Apr. 20, 1907 ; $425.00 ; $428.43. Series 75— I, Apr. 8, 1908; 94 days ; $5.68; $361.82. 2, Mar. 3. 1908; Sidays; $1.80; $421.90. 3, Mar. 2, 1908 ; 52 days; $.99; $125.46. 4, Sept. 1, 1908 ; 185 days ; $16.84 ; $536.75. 5, April 16. 1908 ; 60 days ; $1.36; $164.33. 6, Dec. 18, 1907 ; 33 days ; $41; $75.16. /, Mar. 3. 1908; 89 days; $3.00; $242.71. 8, Dec. 21. 1908; 219 days ; $13.11; $351.12. 9, June 17. 1907 ;' 47 days ; $1.30 ; $167.45. |0, Sept. 3. 1907, 33 days; $1.32; $241.93. ||, $473.01. j 2, $573.99. |3, $1,506.61. 14, $129.36. 15, $417.65 in their favor. [6, 161.17. |7, $59.34. Series 76— I, $913.97. 5, $622.52. 6, $356.12. 2, 81.340.23. 3, $430.96. 4, $3,528.25. -I, $484; $19.36. 2, $720. $32.40. 3, $108 ; $1.89. . 5, $584; $4.80. 6, $74 ; $1.85. 7, $912.50; $6.00. 8, $2,555; $30.87. 9, $1,478.13; $21.87. |0, $3.24. ||, $28.50. |2, $22.67. 13, $6.75 cash, by 19c per bbl. |4, $1,368.13. |5, Latter by Series 77— $127.75; $1.26. 41c per bbl. 16, By paying on 10th day $5.03 4.9956 + % «ain. |8, 20.4456 + % gain. I9, 21, $100.80. 22, $3.52. 23, $37.09; 25, A. 26, i- 27, $72. 28, $374.22^. 32, $33. 33, $785.46. 34, $450 ; 5S% $675.25. $20.31, 31, $78. !J32.50. e^7 « ^^.IS. An -TW! l.S mnntVic 42, $645.83J. 43. $83.32,VA. 44, $: 46, 8 mos. 47, 1.5c nearly. 48, $62.39giH. $11,000. 51, $1,922.75. would be saved. Former by $56. 9.0068% nearly. 29. $119- 30, 35, $38tV. 36, 4hTrue 20: 6%. 17, 20, 24, $150. $210. g79.50 : Bank, 45, '50 days. 49, 80.83. $32. 50, 14 Series «A%. hA^%' ANSWERS 2, 8jvyt%. _3. 4m%. ^tov- '7, MV/o.'" e: 8o/;r7lia. 9, ^WI?••,§: -Senes 7»-|, |543.09. 26.83. ^, 1814.13. T . WIS.IS. 12, $713 ^•i fiO^'2?-«aof J^^^-^^- 4, «1.242.12. 5, '60. 8» $221.92. 9,1192.60. 10 1817 TP 15, 13.690.75. 14, »4:998.9a^. '"ig, $90?; S.i*tl71357*^%f ^^'^^^ 9J}&. 10. $81^,9: 10, #100, 1908 5. {«) 1122.33 (6) Fei. 22 lJo9 T/a) Vlli^' 7v'a <*^^"- ^^ 7. o) $198.04; (6) June 3 1908 tL(a\ »lS97 . m i/*^ ^"8^' ®' ^^07. j6. sept. 25. 19i^ %/?a^7%,90'7*' "?? iV?7!- 19o'l' ""rA^f July 18. 190^ e, S5.35JVl : A*g:Tfe. ' ^^^ 5. 17.365.48; ♦73.89^' 4. BrS%48f.27f JaiJT3°28 9f'^i, "^^^ P^^ J°''"^^ 5, Kent. $774.98- Todd 1500 ?n W V PoT^ P^^ J^^ 84-83. 153.44. Ken\ creditU^s.'XoSd cr?dS'$S^^ '""^'^ '^^^'^^'^ 5. $^f23o^~'' •'•''^•**- 2. Sl.287.00. 3. $1,438.75. 4, $822.14. Oct^^L^W^Ssall' Tl6\49.\*^^^^^^^^^^^^ 5. $^.9^.9^'^ V247 4^^' 7^4i'ir'i. .?l;o\«^«^- 4. $2,083.40. 2.012197. Il,2^5j^r-,2,VS'-,3^?07'?|- 9.1.1698585. (O,' .ailsr ^7f.osV.^: 7SSf aU'.'^'^-^^- 4* $4,448.99. 5, Series 88-r, 60/^. 2, 7o/„. 3, 4o/„. 4,30/^. Series 89-1. 20 yrs. ^ 13 y«. 3, 22 yrs. 4, 7 yrs 11, 11 yeap. 12, 9J yean. '| 3, 22 year!' ' i2 ifi '' ®%- »0. 7%. '>mn%. 5, » 1.242. 12. 5, 10. 1817.19. >• 15, $900. >-91 ; (6) Nov. ; (*) Dec. 9. Aug. 8, 1907. 25. 1908. 9. >8. " 4> Mar. 20, ?2 months, or 5. 1908. 12, ^ay20, 1907. 19, July 21. 3, 1908. 3, i, 17.365.48 ; :aldwell $20. Martyn and jsses divided ay Johnson lames $4.83. »dd debited 4, 1822.14. !4.47 (using 02.95. 12,083.40. 8585. 10, 48.99. 5. 17,246.46. .^10, 7%. \5, 20.147 NEW METHOD ARITHMETIC ti «^fiw^'r';.f,1':?!>^28. 2, $4,150.29. 3, 13,155.42. 5, 11.659. e, 15.013.28 7, $5,963.97 B, $318.50. « ^I'^^h I^^iliJJi- 2' »27,173.59. 3, $2,660.97. 5, $77.88. 6, (a) $9,979.28; (6) $9,962.55; (c) $9.91o!44 15 4, $3,700.88. 4. $1,131.06. S27?98 * ^K~iA 9*<:'a***^^®- 2' »»1.H8.39. 3. $7,122.92. 4 1232 29- 13, $102.72. 14 $956 71 ^'St^nfuJ^' ^^^^P.^fo, '2. $10,560.14. lfl«lQ'?9S9 ik .fo; ;:, 15, $2,084.25. 16, $101.37. 17. $6 640 07 18, $1,93282. .I?,.$JA1.57. 20 $310 26. 21 $328.30. 22,a)$16M95; 24, $404.22. 25, $306.32. *" ^ ' * * '"• (6) $474.79. '23, $5,385.12. _ ,^''51 94_|, $1,805,32. 5.»7 993 3^ 5,^4,611.59. 10, $586.72. II, $3,492.42 15, $700.20. 16; $1,438.56 2, $938.74. 7, $1,865.53. 12, $1,731.48. 3, $4,091.39. 8, $2,890.40. 13. $754.80. 4, $2,550.79. 9, $1,300.80. 14, $955.68. Series 95— I, l09i 2, 109}. 7, 5.185+ . 8, 5.086J. 9, 5.108. 3, 108J. 4,95*. 5,94. 6,40.37+. 2, $838.19 3,2.13fr. 4, $166.05. 5, $4,86. fr. ^5*/?l95"'l7f 6^Sh^^- c ^l^^^2k '' ^5.000 marks. 4, 11160.89* SeOO^^ders ■*■**• ^' '^^^-^^ "^"^^ °^"'y- 7, 4 888 fr. i 3, W4^''iu^- ifJl' ^jJ^^T *^V^«o 2. 1°^- 425 marks, duty $35.20. dutv 4794 IS CiJrho /' I^""- ^^^2. duty $1030.50. 5. Inv /405 te>H.^- •^•'55t\«,-. w&^isrs. 30gkls. kVq^s ^' •^- 21.35c. 22, SOo/^. 23, («) H gals. ; (6) 812^77? '^iV ,;^'' .''■'^- S'6,987i; B's P.w.. $13,635*- C's pw ^.t !?i^iJt69.833J ; B's P.w. $21,600 : C.'b p w m -jcci *^'^ * . _ _* fi!,« i!?'. ^"^ ''•W' »i;^.342,92; C's pav $11 879 05° c'rvm '"''i' $420. 7. A. $833J ; B. $1.033j ; C. $1,133*'. ' 8 Sompson^ STcredit i ! Id $15.972.50 : ANSWERS VM lital. $18,396.28; W $620.88. 10, :y at commerice- 's net capital at G'a net capital Wright's account ere is only $405 50 which Wright (, H. $9,335.67 ; .3331 ; C's P.W.. I6> The proceeds iditors. $10,500; oO. :^r^-^:^