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MAX LIEBICH THK GRAMMAR SCIIOOI^. nERTHIER EN HAtJX. P. Q. MON-TREA.TJ : E. M. RKNOXJF' a23S ST. CATHERINE STREET ■■™H2i'^'-""--^S^^SE- CONTENTS. KXERCI8E. T T^ PAOI. i. — Factoring j II.— Lea.«t Common Multiple 1 III- — <^'reatest Common >feasure 1 IV XIV.— ViilRar Fractionn .> XV-XXI.— Decimal Fraction.^ Ij XXII.— Square Root [I" jo ;XXIII.— Cube Root *...*.'.'.**.'.'.' 14 XXV.— Reduction '[ J7 XXVI-XXXI.— Knglish Monev and Simple Practice ig XXXIII-LXII.-Weight.s and Measures ,'...." 21 LXIII. — Miscellaneous Examples 28 L^IV.— Compound Practice 31 LX; V. — Invoices^ and .Vccounts ^i LXVI.-Problems '.'.'.'.'.!*.*.'.*.".*. 32 LXVII.— Simple Interest '.'.*.'.'.' 38 LXVIII.— Compound Interest .'"* 42 LXIX.— Present Worth and Discount 42 LXX. —Percentages and Averages 43 LXXL— Insurance, Taxes, etc 4.-, LXXII.— Miscellaneous Examples * 4g LXXIII.—Commi.ssion and Brokerage ' 47 LXXIV.— Profit and Loss .'.'.'",.'.'.'!."."". 47 LXXY.— Stocks and Shares ,50 LXX Va. —Proportional Parts r,.> LXX YIL -Partnership .".'".'.'.'.".!.'."..".* 52 LXX VIII.— MeasureiJ'ent of Area !.."...*.*.".!!] 53 LXX IX. —Measurement of Solidity .'.'.*.'.".'.' 57 LXXX.— Simple Equations [[[[ 5g LXXXI. —Miscellaneous Examples qq —Tables and Formuhe ]] y^h PREFACE. I una. am so ii.niiy Aritlimcticn almuly in txinu-nce tliiit, to uhi- a XM'll-worii I'liran', '• to add uimtlu'r to tiair iiuiiilxT ri'ciiiirt'si -oiiu' wouIh of jiistitifation." I liavo loiiK looked for a liook covering lertaiii poiiitH wliicli 1 in- dicate h 'low, but without siica'sc. In tlif lir>t placi' it lia> alwayn Hiiuod to nii- that tin- ArithnieticH placed in the hand;- of our j-chool-children seek to take the place of the teacher. The exi>lanatious jriven often o(TUi)y far more Hpace in the book than the examples themselves. Moreover, pa};o after page of ex- planation is given of the most elementary processes. Does anyone sup- I)Ose that a child learning addition and subtraction can understand tlie Uieori/ of the processes, and read the explanati(.ns for himself; if not, then for whose benefit are they given? ! have often asked myself " vviiy al this verbiage?" Cl.ikheii will learn nmch more easily from the verbal explanations of a competent teacher than from reading printed ones. 1 have tlierefore compiled a book of examples, leaving all explanations to the teacher. The only exceptions to the rule are certain formul:c for i.\Ti;ia>T and a chapter on clue hoot. The latter 1 have presented in a fortn 1 liave never seen in any Arithindic or Ahj^hm. The method usually given is cue \\hicli is very ditlicult for children to learn and s*ill more dithcult to reniendier, because there seems to b<' no ulii/ and uhtnj'on: I have n^ver \\i failed to make the mode here shown easily understood by a:i> child, and have found it, moreover, easily rttained. The formuhe for /)/^T<.i< are, as far as I am aware, Unt i.iiiai!'' n any book. 1 need hardly say that they should only l)e used after the o- ject has been reasoned oni. I think I can say, without fear ^ contradiction, that if my method ot stating these fortnulii* « adopted, it w-'l marvellously simplify the teacning of Inters*' Another reason for compiling this book is that 1 have often « to have more examples on the various rules than the number u given. In one Arithmetic largely in use in thi.>^ country th. xuhjirt of Interest is dismissed w ith ;!tj examples; other rules are trt-«: ed just a.s scantily; it is impossible to ojver the entire subject with s. few examples, and I have again and again been obliged to make ii| others myself. I am sure this is the experience of many teachers. It. ♦"le following pages 1 tiiink there will be no lack of examples. I woiii-i especially call attention to the largt- number in J^erceiJaijt and Intertill. Another point which I think most teadiers will welcome : The book does not contain the amwtn^. These are published separately and will be supplied 07,li/ to itaditm on application to iiie Tubiisher or myseh". >: I 6 I have addeC a chapter on Simple KquaticTiH witli one unknowr quantity. The ability to wilve thow; given involvcM to all intents and pn: potiea no knowledge uf Algebra, and an there are many problern which can be scjlved more readily by a Kiniple etpmtion than by tlu- ordin- ary procewseH of Arithmetic, I connider this addition a legitimat* one. This chapter may, if thought desirable, be taken after I'roblam (tnAi'. LXVI). The book being intended for those who have mastered the first four rules, I have begun with factoring. I shall be grateful for the pointing out of any errors, and also for any suggestions which may increase the usefulness of the book. MAX LIKBICII, unknown and pii: I which f ordiii- iat« one. i (CHAI'. the tint > for any 3IC1I. 4. ti. EXERCISE X. FA(TOI{IN<;. Find the Prime Factor!- of !t S. 42 15. i.. 10 !•• 121 Itl. n S 10. .V) 17. .» 14 11. tU IS. IM) 18 12. ;!« I'.t. ;!;o 21 la. 4!» 2(1. 4.">0 30 14. 56 21. 120 2:'.. 24. 2."). 2ti. 27. 28, Mi) 24;! • MM) 4! 18 5ti2 r.24 ••)25 2!t. ;«). 31. 32. ;w. ;;4. 740 .'AH 425 610 720 840 724 EXERCISE II. Find the L. C. M. of 1. 5.1.") 10. !H>.;tO 2. 4.12 17. 120.420 .!. 3.12 IS. ((50.1300 4. 5.25 1!». 24.5.70 5. 0.42 20. 030.i«l0 6. 7.:V 21. 420. .500 7. 5 3 22. .5(>J.S40 S. ».4 23. 5, 0, :!0 !». 0.5 24. 2, 5, 30 10. 12.15 25. 0, 8, 40 11. 14.10 2t>. 4, 0, 30 12. 16.18 27. 7,0,03 13. 24.28 28. 8, 14, 20 14. 60. (to 29. 8, 9, 10 15. 2.5.55 30. 9, 10, 12 EXERCISE III. .•;i. 34. .'!5. 30. 37 .38. .3 5(5- h 1%, I. i * S ' I I t, h ?. Ti, jfi ij, J. 23. 4;J0J. 24. 635 j. 25. 756^ 26. 247J. 27. 5644. 28. 426a. 29. 274 i. 30. 284i. EXERCISE VI. Reduce to Mixed Xnmbers. 1. 2. 3. 4. « a. y ; V I 5 . I« I > f V ; V V;V 7. V;l 204x46x85x200 14. 7x6x15x84x 1.') 12x225x49xl6~~ 15. 18x4x16x9x12 8x9x7x6x10 16. 14 X 17 X 85 X 53 159x187x21x2 17. 2x5x8x 9x12 40x44x54 18. 7x63x8x16x12 49x72x20x2 19. 5x4x6x7x8 x0 3x2x2x4x10x14 20. 705x16x15x243 486x32x5x1128 ZiXERCISE IX. ADDITION OF FRACTIONS. 1- \ + h 2- ^ + h 3. I + J. 4. t"t + rV- 5- t"t + f'j. ^- h + iS + .^ 7- A + t'(1 + TO- 8- A + V: + "7 + 2t' ■ »• Ti + A + ,', + ^. lo. ; + ;; + .! + ,',. 11- § + i + ^ 12. i + i + •■: 13. 5 + ^ + A- w- § + ^ + /.. 15. f + ft + t'o- 16- ^ + A + U- 17. i + ^v + J, 18- i + f^ + /.. 19. 20. 21. 22. 23. 24. 25. 2(J. . 27. 28. 2i». 30. ;ji. :;2. :w. 34. .Jo. .•J(i. i + J + I. A + t'o + /o- ^ + !J + A. r + ;; + J^ S + i + ,^. i + n + 'l + 1 ^ + ^ + I. + f,. t:;+ i. + n + J, 7 + A + i^ + ii. In the followinj; examples add the kkacttoxs first, then tlie wliolo num- t)ers. 1^ + 2j + 31. 2^ + 3,\ + 7,1. ■h'li + in + 7^a- n + 81', + 1^ 2fV + 3! foil. + f I + u, + f] + \l. + 4. ' * i i + i + 1^. I^ + .^ + ^^ + \i /« + i; + 5 + ^ A + i^ + i^ + \\. f'r + 51 + J + ,'_,. t + S + ^1 + rV- t + ^ + :1 + U- 37. 38. 40, 41. , 42. .5j + 3.] + 4,'. 43. 7# + .l-4). 17. 2j-Ii. 18. 7^-^rV. 19. 8rV-3ol. 20. •^H-2|. 21. 1:^5. loj. 22. ,. (b) 5 X L {b) i X A. 25. 4i X ;; X ri X 21. 2. (a) 5 X J. 10. 5 X s X §. 26. 31 X 2A X 10 X :,\ . (6) 6 X i 11. ? X ? X '^ 27. 3J X 4A X -/',■ X .1. 3. (a) 6x1. 12. 3 X ^ X t!. 28. -^ X t^ X 43 X 6i (6) s> X ^ 13. 9 X ^ X }!. 29. Si X 2f X 33 X \. 4. (a) 5 X h. 14. " X 7 X :i. 30. 31 X 4§ X ,\ X t>. (6) 6 X i|. 15. 2i X 41. 31. •5} X 6i X 7i. 5. (a) 6x2. 16. 3i X 4!. 32. l.l X 3 X 5] X :U. (b) 9 X 4- 17. 4§ X 6J. 33. 2A X 5 X 6} X 4ii. 6. (a) s X 5. 18. 2J X 3,V. 34. H X i X J X 4i (6) § X 9. 19. 3? X .-SrS. .35. 31 X 5i X 1? X 3. 7. (a) ^ X 7. 20. 6i X iV- 36. 3.] X 4§ X ()§ X 5. (t) :5, X 12. 21. 4J X ,^,. 37. ill. X 4 X 1,'j X ,'„. 8. («) ^ X |. 22. 6§ X 5}. 38. 2 (4 X 3^) X ;; (4! x f, xf) (6) 3 X fj. 23. 2} X 5A X 3? . 39. 40. .; (^ X if) X ,', {{'f X X n)6 1. 5 ~6. 2. i -r3. 3. /r - 2. 4. A - 5. 5. lH-6. 6. 5! -^ «• 7. U -i- 3. 8. 11 H- 5. 9. iS-r 10 10. H 4- 2. 11. 1-^ ^ 4. 12. SH-4. 13. JH- 6. 14. 2J-^2. 15 5} -5-3, EXERCISE XII. DIVISION OF FRACTIONS. 16. 4J -r- 2. 17. IJ -;- 2 18. 6i -7- 2 19. 3i -^ 2 20. 8? -r 2 21. 8f -f .1 22. 2J ^ i 23. 4J -r .1. 24. 61 ^ i 25. 7J -=- J 26. 8i -r 4, 27. 3J 4- i 28. 6J-5-5i. 29. 5i -r 2|. 30. 81 ^4i. 35. .36. 37. 31. 4^, -T- 3/j. 32. 8f -r 24*. 33. 6| -r 3,\. 34. 3A -=- 6f . 21 -^ 4?. 4X -=- 2i. 62 -^ 4!. 38. 6,V, -H 83. 39. 5J -^ 81. 9-=- i. 9-r 1. 10 T- h- 12 -T- ^. 18 ■^ ^ 15i -=- 1 vV! 40. 41. 42 43. 44. 45. J-r' ' fe .1 COMPLEX 1. ^ + i 5i-3] 2. 3i + 2? «i - 43 3. 4. oi + :n - 2i 6* + 4^- 3J a. «S-5^ 5/^7 -4^ 6. 6I + 4J oi-2T'j 7. 2? X 5J 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 3S-^ J _6_ 6 4|-3i oi +4} 10^-3} 5t'2 X 8if 3f X 2}i sV X 8tV 5?-f 7^ 2^-1^ 6J +4J 3i + 8i 11* ^ 5 4i X 2} 51 + 21 51 + 6' 3f-2^ 5a + 6# 3i + 2i i of i of 2 iof i of 1,5 t of A of r\ I of f of 2J i + (§ofa) f-^lofT^ff) I - ^1 -^ 3) MUBRCISB xm. AND MISCELLANEOUS FRACTIONS. 30. 25. |-{?-f-5i) 26- * + J X (6f - 4f ) 27. (t X *)-(|of^) 28. 1+^ 29. 6t\ iTxT) If X /, 31. 3i + 2* 79 23 H X u 32. 3J 2 7 "^10^ "V 18 ^ 7 y 33. 6K7j 2Jx8i "ol ~' X -, ■^ M+a^ 36. 2t + i; 3f - 2» 4A X 2f 5* -4.1 36. _6IJJ5l^ 4S) (>^-5J) X (4K2i) 37. L+jJLziiJLii) 2^+4j 3aH-(4-4 ) 3i x i 38. 38 25 4-i 3T1 4 2 14-^ n 39. 384 7 3j 6j-i 5"^ 2^ 73 90 40. (4}+3i-7J)(6J-=-4J) 41. 5+H-l i[iy5i4-16A)]'r 42. 44. 4i 5i 5r3(5^x6i)1-r(4ix|) ?(H§)'5) i of 40 is x% of what I of 64 ,8 5 of what S of 42 is y\ of what x'(j of 80 is ^ of what ^ 6f 60 is t of what f of 48 is I of what i of 21 is J of what J of 81 is I of what i of 45 is 'i of V hat i of 2J is i of wnat t'j of J is § of what j'ij of § is f of what number ? number? number? number? number? numl)er? number? numlier ? number? number ? number? number? EXERCISE XXV. EXAMPLES LVVOLVIXG FRACTIONS. ] 2 3, 4. ."). 0. 7. «. i>. 10. 11. 12. 13. 14. 1.5. 16. 17. 18. What change did I get from a I bouglit 4J yards silk at $2J a yard. $20 bill ? If I bought 15J lbs tea at 40c., 10} Wm. coffee at 48c., what change did I get from a $oO hiU ? . A man paid off i his debt at one time, and i of it a week later. The final instalment was $.!). What was the total debt originally? 1 + A of a debt a.,iounted to $(>}. What was the total debt? , If one day I walked 4:5 miles, another day o^ miles, a third day fif miles, and another day 7* miles. What was tiie total distance walked, and what was the average distance per day ? I bought .">i gross at $i>\ per gross, ?,} gross at $5i per gross ; what was the total amount I spent ? If I sold : of i of an estate for $600, what was the entire value of the estate ? I sold H of ] of another estate for S1200. What was the total value • if the estate? llow many articles at f.ii can I buy for $48J ? How many articles at $7 J can I buy for |170} ? I bought ISj yards of cloth (Ta $2\ a yard and 4.ii yards ® $3t. What change did I receive out of a ^100 bill? A man sold J of ;j of his farm for ^,000. What was the value of the whole farm? A man said i of f,; of .! hou-^es for !^4,200. What was the price of each house ? A father's age is ^j that of his eldest son. The youngest is 2 years ■Id, and his age is ,V that of his brother ; v'lat are the ages of the father and eldest son? f of I'l of a pole is in the ground ; the rest is 27 feet long. What is the entire length of the pole? A owned ii of an estate ; he sold \ of his share to B, who sold J of his share to C for $12)0. What was the value of the entire estate at the same rate ? A owned * of s of an estate ; he sold B | of « of his share for $.5,600 What was the whole estate worth? A man dies leaving i of liis estate to his wife, and the other fif»'.i to his two sons ; one of them after selling \ of his share had a piece left worth $2000. What was the estate worth? What was the mother's share worth? 1st. 20. 21. 22. 23. 24. 26. 27. 23. 29. 30. 31. 32. 3.".. 34. 3o. I ^old a l.oi>e to B for l more than it cost lue. Ho sold it to C fo $4i), which wa.« J of what it cost hin. What did I give for the liorse? Dividf $1000 aiuoiijj A, B and C ^o thai A may have H oi B's share and C as mucli a.s A and B together. Divide ?2400 an.ong A, B, C and D so that B may have lof J of A^ .hare, wiiich will be i of C's share ; P to have a« much as all the rest together. Divide $320 among A. BandC, so that B will have ^ of A's share and C as much as A and B together. A horse and saddle are worth $1<50. If ? of the value of the saddle is 'i of $20, what is tiie value of the horse ? i of t", of a ship is worth |22,0(X). What is the value of H of ?^ of three such ships? I bought lOi lbs. raisins (S 10 cents, 11 5 lbs. tea q 30 cents, 4i lbs cheese '^" .36 cents, 2i lbs. coffee at 40 ce.-.t-, 2] lbs. nmstaru at 40 cts. How much change did I get from a ten dollar bill ? I bought 3i vards of cloth rv, $1}. 4S yds. («> $31, 2.\ yds.^at m- AVhat change did I receive if I tendered a fifty dollar bill . A's age is H of B's : B's is i of ("s ; C's is ', of D's, who ten years ago was .">3. What are their respective ages? How many articles @ $.3} can I buy for ¥30? How many for $48^? How many for JKiSj ? The -um of $loO is to be divided among four people ; the first is to receive i of the whole ; the next ^ of the remainder ; the thml 1? of what is left, and the fourth is to have the rest. How much does each one rect-ive? Which will cost «ore, r>', yards at $3} or 4! yards at $3i, and by how much ? How much clot , at §4 a yard must be given for a hogshead of sugar, if 7 of it cost $48? A pole is i in the water, J in the mud, and 14 feet out of the water ; how long is the pole ? .John's age is J of William's, and the sum of their ages, diminished by 5, is equal to 70 ; what is the age of each ? Two bovs were counting their marbles, and one said he had 16 ; th" other said, | of yours is exactly i of mine ; now, if you tell me how many I have, I will give you the difference between yours and mine ; how many had he ? A person, being a.sked his age, said, that i of 80 was t of 5 times his age ; what was his age? 36. IC 37. 38. 39. 40. 41. 42, 43. 44. 4ry. 4(i. 47. 48. 4<». 50 51. 52. "nme rate? "^ '''« ««'" on the whole at the A gent] -nan left to liis eldest son *-inn i • , ^-econd 8on had, and wice the «I , ' '"'""'' '"^ * "^ "»'«» t^e what the third on re. Ived L? T" ' ^'"""^ ^^^ J""^* ^ ^""^8 Three bov.s receiv^ amnn '.. :?"'' "'^ *''^ ^^^^-^^ «"«ii ? dollar, andThero;rn "' '""""' "'^ '^'^^ ^^'^'^^ ^J In a «/hnni , n '' ''"'"^ = ^'^"^ '^'^ the third receive'' in a school, i of the scholars study gramnar - » .^ and the remainder study aritZetic .? ' ' ^'' ^^^-^^^P^'y. arithmetic? ^ «ntnmetic , how many are studying A^per^on owing 5J dollars, paid 3^ dolla. ; how much did he still U^ZTZ?'"''" ' '"*" '"- * ««'<^ "^ «iacre. if he mows ^^7^:^l^r'' ^' -- '" ^ ^ay. how ...any men ~i^tS^:^;rL^:;-i:™i";^- ^^^-^-^^^ the boat in floating that distance? ' ""' "'«">■ l>o"rs was A carpenter worked 6 davs nf 1 1 ^ u -ilk, a. 1, doii.„ . v.^*:;:;,, ;»";,".' ■^-^ ^ '"" '""">• ■'"<" «' can he save enough to buy thVclockT '' ' '" " ''** *'™« If 40 oranges can be bought for one dnlla. i be bought for 2,v dollars? ' ""' ''"'"•' '^'■'»"^«« °«" If a steamer sails 18 mi lea in or. i. hours? In5Jhoulr '"' '°" ^^' ^'^"'^ '^ ^'-^i 11 53. What w ill be the cost of {»| vardH of silk, at 2 dollars a yard V 54. If 12 men can do a pi>ce of work in 5J days, how many men could do it in one day ? 56. In a day there are 24 hourH ; how many hours are there in 31^1 days? 56. At 9centh a yard, what Aill a piece of calico, that containf< 36} yards, cost ? 57. If one bushel of oats will supply 12 horses for one day, how many horses would 7/, bushels supply ? 58. At 6 dollars a week, to what will i»5 weeks' board amount? 59. At 4 cents a mile, what is the cost of traveling 25f miles ? 60. If ono gallon of wine will fill 8 bottles, how many bottles will be filled by 7 J gallons ? EXEIIOI8E XV. DECIMAL FKACTIOXS. Convert the following into vulgar fracticns. 1. .1, .01, .001, .002, .0;5, .(107, .000 .00001 2. .5, .05, .0(i, .OS, .(HW, .(I«i8, .075, 0075. 3. .75, .25, .12.'), .625, .875, .OS75, .00125 4. .3, .6, .35. M7, .1428i)7, :.\b, .46, 1 .t», 5. .3, .5 .6, .24, .57, .54, .75, .11, .;j.51 6. .14, .25, .36, .484, .(>5('i, .757 7. .6556, .7.%8, .8435, .7t)o4 ..^i96 EXERCISE XTI. 1. 2. 3. Convert the following into decimal fractions. Till ijt Hit i> ?) s> 1 i(\> SlJl ;5) t 12 'I TiJci, -i(hs(i SO) 3 J 4. J, i, i .>:, H, TT EXERCISE XVII. together. 1. .5, .65, .375 7. 4.6, 5.8, 7.635 2. .02, .(X)2, .oa5. 8. 3.4, 42.5, 815.3 3. .1, .001, .059 9. .•5.95, 4.50, .621 4. .65, .765, .864 10. 8.45, 0.12, 6345 5. .605, .81, .459 6. .35, .0001, .586 11. 4.23, 5.67, 840 12. 1.1, 2.5, 3.04, 51.864 M 12 EXERCISE XVIII. >*rBTHACTIOX. Find the difference between :— ■4.-. and .25, ..^.5 an.! ..T,, .4(i and .27 .5 and .2.5, . whip worth at the nann' rati'? 2. A pound of t+^a coHtc .oa") of $150. What \^ tho vahu- of .6^5 of a lb 3. If .5 of a pole is colort'd red, .It gretMi, .01 hhie and tlie rect i:* 1.14 feet, what ic the entire U-iit'th of tiie jxiie? 4. If I own .))05 of an estate and i^>ll .25 of my ttliare for $250, w hat in .75 t)f tlie estate 'sorlh '.' 5. Divide 180 ainonjf A, B and (" in proportion of ..">. .25, ._'. 6. Divide $2,0.">2 anionjr A, H, (" and !> in the proportion of .:), .12. 24 and .024. 7. A liorf^ and caddie are worth .'J;i20. If .75 of the value of tiiesiddJe is worth $15, what in tlie value of the horm;? 8. 1 sold an estate for l.ti of what it cost me. The nurcha.>'er sold ..'15 of it for $77,0(X) and made :«i7,00ti profit. What did it cost me? ». I bought 4.5 yd.-, ofclotii (iether? 10. If .15 of i of an estate is worth $7,000, wh.U is the value of .5tj of the estate ' 11. What is tlie difference between .5 of « and .:{ of ?, ? 12. Whatvultfar fraction is wpiivaient to the sum of 1.55 anil 15.5 divided by tiieir difference? 13. If 1 can do .157 of a piece of work in a day, how mucii of the work will Ir' accomplished in 5.5 days? 14. Ketluce .5757 to a vulgar fraction, and 4 i ,, to a decim.ih 15. A man leaves .8 of his estate to his wife and tlie rest to his two sons. One of them after gelling .:!5 of hia share had a portion left worth $.580. What was the amount of the whole estatr originally, and wl'."t was the share of each one ? 1. 2. 7. 11. 14. 17. 20. 23. 28. 34. EXERCISE XXXI. SQUARE KOOT. Find the square root of : — 121, 144, 256, 625, 1^25, 3025, 20241, 58081 729. 3. 5184. 8. 942841. 12. 697225. 15. 236144689. 4160580062500. n- 24. iH AYt- 29. r. .6. 35. .1. 441. 3844. 751689. 189475225. 18. 21. 4. 9. 13 16. 5*09022560300001. 71690512350625. 5329. 14884 .550183936. 20857489. o. 3481. 6. 10. 49042009. 2t«109. 19. 00 »'§* 25. 30. 36. .5. ins B2J' 26. 31. .09. 32, 38. .121. 81197580:U0900. 20858.3110fi.«*l, 27 < « 2 ' ,0001. 33. 2..1. 39. .00004. m I The cube of 1 is i. " " 2 " 8 " " 3 " 27. " " 4 " »M. " " 5 " 12.5. " " « " 21«. " " 7 " 343. " " 8 " 612. " " 9 " 729. u ■*«»oiM xxm. CUBE ROOT.* Therefore the Cube Root of 1 i« I. 8 " 2. 27 " 3. " " 64 " 4. " " 126 " 5. " " 216 " 6. " " 343 '< 7. " " 612 " 8^ " " 729 " 9. III the extraction of the cube rnnt .^i ^.i the algebraical formula : * '"" ""'"'^" '^^ ""ke use of «'+3ff»v'.3a6» + 63 By the use of this f orir ila th« «.qb«« t ulabu heart. "X remembered. Learn the form- Extract the cube root of iihoj e- ^ .. . 13 I 821 Then : what is tlie cube root of l.i^ Th*.« h^- take the root next lower, which we find to be 2 ^n7 "! T' '""' '"' quotient, at the same time putting a «:!,,. tent ""''' *'''* '" '^' 13 ( 824(2 cube'o'Tra'f '•" '"'""'''• "^"^^-^ »»- a'= 8 13 I 824(2 Bring down one figure. (8) and get a nt .V divisor. e " » Remember this :~r/,.„«^ rfmW i, aZ- wai/i 3a-. "' 13 I 824(2 8 * _ 3a2=12) 58 This Chapter m.y . „, cour.a. b, taken later. „ d-lred. 1ft In this instance a'=4, therefore M' is 12. 12 into r)8 goeH 4 ; place 4 in the quot- ient and call it b. Now j'ubtni'-^ 3a'6==48. Bring down another figure ; and subtract 3«6\ (hereOxl«)=y«J. Brin« down another ti^^ure and subtract 6»(4')=ti4. 13 I 824(24 a' 8 :{«^6= 48 102 3a6'= iW 6'= M Talce another example. Divide into groups of tliree figures, be- ginning at the right. The nearest cube root lower than 140 is 5. Call it a Subtract a3=125. Bring down on« figure and get the new divisor — (.'{a^)=75. 75 into 1.56 goes twice. We call the 2 h. Subtract 3 a'fc=1.50. B- ing down another figure and subtract 3a6- il.5x4)=60. Bri, '. down another figure and subtract 140 I 608(62 o'=126 3a»=75) 15<} Sa'fc- 150 Sab' GO 60 6'= Tal4 3a^=48) 271 ;]a=ft= 240 312 .3a6'= 300 01 I 125(i5 6»- 125 125 w a b 428 I Otil I d(yi(i^\ .'!((- = 147)85t) '.\a-b= 735 16 In the next example we shall see how to proceed when there are more than 2 figures in the answer. Kxtract the cube-root of 42HG«10()4 First mark off the groups of 3 figures. Find the nearest culje-root ). Bring dowi: another figure and subtract ^'(=12.5). Then bring down another figure (0) and get a fresh divisor .(:ia- ) . We now take the wltoli- of the quotient, (75) for o, and 3a'- ^^1(1875. It goes 4 times ; call 4 h, subtract 3a-/>= 07500. Bring down a figure and subtract 3a6-=3 X 75 X l(i=3()()0. Bring down a figure and subtract 6'=ti4. Wah-. 1,^: 121() 52.J G'.tll = 125 ■U>875) 67860 :'<(i-b= 67500 3606 ?,ab-= :«>00 b'= (54 64 Should there be more figures, one would then take the wiroLE QUOTIENT as a, and again subtract :]a'b, 3a6-, b\ bringing down one figure at a time. Find the Cube Roots of 1. 46656. 8. 194104539. 15. 2. 175616. 9. 1953125. 16. 3. 86184. 10. 5785339. 17. 4. 13824. 11. .32157432. 18. 5. 531441. 12. 3375. 19. 6. 85184. 13. 12167. 20. 7. 438976. 14. 74088. 21. Additional examples in Cube Root can be made by cubing any desired number and then extracting the cube root. It is excellent as an exercise, and leads to a marvellous increate in speed and accuracy in the pupils' work. 1860867. 324617.59. 44738875. 70087408S67. 2617755.32773. 176369715712. 869070026007. 17 EXERCISE XXV. HEDl'CTION. N.B.— In the followiiig calculate years on the basis of 4 weeks to a month and 12 months to a vear. 1. 2. 3. 4. 5. 6. Reduce £4.10.6 to pence. " £10.11.0 to lialf-pence. " £ll.lo.7i tofartliings. " £9.17.11} to farthings. " £10.18.4J to farthinp?. " £18. 15.4^ to half-pence. 7. " 1584 pence to shillings. 8. " 1784 half-pence to shil- lings. 9. " 1680 farthings to sliil- lings. 10. " 15810 farthings to £.s.d. 11. " 16757 " •' " 12. " 20473 " " " 13. " 84762 " " " 14. " 4 years to hours. 15. " 7 years, 11 months, to minutes. 16 " 8 years, 4 months, 3 days, to seconds. 17. " 5 weeks, 6 days, 17 hours, 14 sec, to sec. 18. " 18476 seconds to hours. 19. " 204763 seconds to days. 20. " 94762384 sec. to years. 21. " 5 miles to inches. 22. " 7 miles, 8 yds., to inches. 23. " Smiles, 5 furlgs., 4 yds., 7 ft., to inches. 24. "8 miles, 7 poles, 2 in., to inches. Ii5. "2 miles, 3 furlgs., 2 yds., 3 ft., to inches. 26. " 46789 inches to feet. 27. " 7635 inches to yards. 28. " 94673 inclies to poles. 29. " 10567 inches to poles. 30. " 96754 inches to poles. 31. " 847630 inches to furlgs. 32. " 1976.35 inches to miles. 33. " 584G731 Inches lu iiiiies. 34. Reduce 7 n miles to u feet. 35. n 4 n miles to n inches. .36. It 4 roods to n inches. 37. 1( 2 miles, 500 ac, 3 roods, 30 yds., 8ft., 120 in., to n inclies. 38. ti 1 mile, 250 ac, 1 rood, 20 yds., 7 ft., 130 in., to □ inclies. 39. ti 75844 a in. to yards. 40. (t 984732 D in. to poles. 41. It 8473294760 □ in. to acres 42. (i 9327849904 n in. torn' la. 43. ti 45 cub. ft. to cub. in. 44. tt 40 cub. yds. to cub. in. 45. tt 4 cub. yds., 13 ft., 1500 inches, to inches. 46. II 18000 cub. in. to yds. 47. 11 198756 cub. in. to yds. 48. l( 4 bushels to pints. 49. It 3 bushels, 3 gals., to pints. 50. II 5 bush., 3 pecks, 1 gal., 2 qt., 1 pint, to gills. 51. tt 8 quarters. 3 bush., 1 peck, 1 gal., 3qts., 1 pint, to gills. 52. l< 75 quarts to i>ecks. 53. II 850 pints to bushels. 54. It 95620 pints to quarters. 55. II 4 tons to lbs. 56. It 3 tons, 4 cwt. to oz. 57. II 2tons,2cwt., 1 quarter, 3 '')s., to oz. 58. 11 3 qr., 20 lbs., 15 oz., 12 drs., to drams. 59. II 4 tons, 5 cwt. , 3 qr. , 15 lbs., 6oz., to drams. (50. It 1800 drams to lbs. 61. It 19560 drams to quarters. 62. li 18647 oz. to cwt. . 18 63. 64. 65. 66. 67. 1. 2. 3. 4. Reduce 1673589 oz. to tons. " 2357467 oz. to tone. ' ' 2560 grains to oz. (Troy) " 84673 grains to lbs. " " 84675 grains to lb8.( Av). 68. Reduce 94 lbs. (Troy) to grains. 69. " 10Ibe.,10oz.,10grainB, to grains. 70. " 21be., loz., lldwt.,20 grains, to grains. ENGLISH MONEY. EZIOtCISE XXVZ. ADDITION. £4. 6.3 3. 8.9 10.11.3 5.14.6 8. 5.2 5. 6. £25.16. 4J 63.15. SJ 25. 8. 4i 23. S.llf 8.14. 7i £15.16.81 9. £115.18.4} 321. 6.8} 419. 4.3J 227.16.9} 581.14.6J £ 7. 6.9 10. £589.14.7} 4. 8.3 2. 7.5 18.14.3 21. 0.5 16.10.8 12.15.4J 25.18.3} 29.17.5i 31.15.9} 28.14.6J 245.16.8J 298.15.4} 356.17.3} 715.15. 4J 565.17.3} £ 3. 5.4 7. £13.15. 9J 11. £243.16.8} 9. 8.7 16.15.3 19.19.7 21.14.8 15.15. 8J 17.18.2t 5.14.6} 7.19.3} 416.15.9J 254. 6.0} 298.16.8} 846.15.7J £5.16.8 7. 3.8 9.16.4 3. 7.9 4. 6.5 8. £15.16..3J 15.13.5} 13.15.8J 15.14.8} 3. 5.9} 12. £463. 9.8} 765.18.7J 243.15.4} 598. 14. 6 J 367.15 4 J 1. £14.16.8 3. ,5.6 2. £15.18.11 12. 5. 9 szERcisE xzvn. SUBTRACTION. 3. £18.19.8 16.13.5 4. £58.16. 8 29.18.11 6. £65.14. 6 27.15.10 6. £1S. 0.7 16.3.10 19 7. £48.8.0 36.4.6 8. £19. 7.3 J 14.8.2J 9. £21.15.4} 17.19.8J 10. £18.16.4* 15.18.5} 11. £19.14.6} 15. 9.8J 12. £20.10.10 5.19.11} 0.14.7 16.17.9} 17. £20. 0.0 18.11.8 18. £18.0.0 l").7.6} 14. £21.1.5. 19.18.10} 15. £21.4.0 18.6..S} 19. £15. 0. 1 10.10.11} 2C. £8. 0.0 7.19.8* 16. £19.0.0 14.6.8 21. £8. 1. 7.19.11} EXERCISE XXVIII. MULTIPLICATION. 1 £8.4.3 3 10. 11. 12. 13. 14. 15. 16. 17. 18. £15.18.6} 15 2. £9.15.2 5 £19.17.11} 24 3. i " 18.6 2 £18.14.6* 50 4. £9.14.7 6 £25.16.7} 64 5. £6.17.5 9 £84.17.6} 90 6. £8.14.6} 4 £97.13.7} 121 7. £18.]5.9J 9 £98.17.6* 144 8. £18 19.11} 5 £85.14.6} 144 9. £12.15.10} 12 £84.17.9} 84 19. Multiply £84.17.6} bv a)150;6)160, 165 d) 275, e) 845, f) 1000 20. Multiply £7351(i.5} by «) 160, S) 200, c) 275, rf) 463, *) 765,/) 1200. 21. Multiply £354.15.11} by rt) 151, b) 762, e) 943, d) 1584, t) 2000. 22. Multiply £849.]'7.11} by a) 463, 6) 769, c) 824, d) 946, e) 1100. 20 1. r> I ll'ii i.-..1{» 2. 4 -'.•'■. 111. 8 H. a I x;'>.. If,.:; 4. ;{ I xi'.i.is.r 1. 3. 4. 1. 2. 3. 4. a. r,. 8. EXERCISE XXIX. I>l\IS'(lV. ■>. S I £24. 1(1.2 (1. <» I £|<».IS.3 7. II) I £8.14. () 8 !•. 10. 11. i:i8.1.').0 -^ ,5 i;U>.l!t.4^. -^ 4 jEks.u.::,' -f- 8 £11».IM.7; -t- <) 1(1. 17 18. 19. 20. 12. £14.1G.8i -^ .T 13. £L'.5.1(i.7i -^ 7 14. i;i!),]S.7J-^5 15. X2I.1').8A -M2 ^IS. |.-,.s^ -^ („) 7, (/,) 8, (r) '.), on 10, (<■) 12 £14.8.4.; -:- („) 14. (/,) 1.-,. {c) 17, ((/) 20 X2.-,.8. l.i -■ <) l.%0. (r):?.'>0 21. £195. 10.8:1 ^ (a) 4.-)0, (/<) 750, (r) 890 EXERCISE XXX. II iw often is £4.0.0 ( taiiied in £:U.8.0 3.7.0 1.5.10 l.(5.3i 10.17.6 9.0.10 .3.18. 10.', 0, 8. £7.0.5^ foutained in £05 18.1 J 4.2.01 12.5.11 4.11.(iJ 32 10.2 307.9. .51 457.10 3 EXERCISE XXXI. ]'U.\(TI('K. Find tlie value of 705 artiric-; '•■ X'5.().:! each " 849 Of 9:!S| (^ {,!) ei7.l'i.il (»l 94ti7 Oi i'l I CI5. 18.11 Of S4';!) Or ('I ! CIO. i!».2; of :l57s (« , 'M €15. is.u; .'iVi <.-'). Ill en t;2">. IS.:;; I /I I £.">:!. 7. 1 Of ( >f 2750 (■! Of .'>;;7i f" (" £IO.I7.iM'aeh, . h) (-1: fl'i.r. in] ; ( • il< '„. fOi. ].-,. 1 I 1 ; !>i <>, JLi;*. l(i.2i ; if i<\ f" £21 .4.;;; ; >•■ >,■ (,>, jti.-,. Ki.s ; I,- ;; I /yi Cr<, £1'.).:;. 1 ; io f,/ £40. jii, 1 1;,'. ; : 'h) (o £25. ir,.:;^, ; (c) 0< £02. 19. 11 J EXERCISE XXXII. ■) r.' £151.15..5J. '■) <'< £25.14.10J. <" £:!7.17.lOi. <■' £\S. I9.11J. (" £75.18.1 If. How thUfli i> ' . 2. 2. How iniicii is i a) ^ of £;;.tij' i /, ; ', of .t'lii. 7.4 i ( <■ i (»f£1.4.3|. Add tuL'ctiier [n • ,; of £s, < '. ; ; of £12, and , ci £(■ ' vf j^r^O. Wliat is I '/ ) .05 iif £15 ? ( /, . ..", (if £:!. 10 i ,-, ..-,7 , |q_q_ 0.5 of £."). 10 4- 4.75 of £.;. iO + 4 25 of >.- + i, ^, 2 . 5.5 of £ 1 5 + 3 of 9/- + 5 . 25 of 7d. 21 EXERCISE XXXIII. DJVI.HoX („ iniK. Add tojjrctlicr. 1. 3 hours, 4(. ,niniik.s I'd s.ro.uls. -•• 7 Uum^. (. vnunu,. i:. so.^nds. - 10 " i:, .' 12 " 15 {» " 12 " „j .. !!• " 4.-. 14 " 1.-, " ..,! .. <•'•> " -i^ ' -lit .■;s 4!» year In the following take. 4 w.ek. to tho n.ontl., a.ul iL' months ,o , he 3. 4 days, 17 liotirs, .",.-> minutes, L'o second- ' ' l« •• IN '• 15 " ■ n lit •• !'•' '• 4<) .< • 4.) '• .JO .' EXERCISE XXXIV. SIBTK ACTION-. 1. 1' years, :i months, 5 davs. 1 " 7 " 15 ■ -'. 5 years, (i months, 8 davs, 4 hours 2 " 8 " <) "• 1,; u ' 3. 20 years, months, 9 .lays, hour., 40 nu-.uites. '^ ' ' •> " 17 '• 5,-, 4. 5 years momhs, da^s. 7 hours, minutes, seconds. 50 o. 4 weeks, 15 hours, 10 minutes, 20 seeonds. ^ 17 " 20 " 5r) EXERCISE XXXV. -AIULTIl'LICATlOX. Multiply 5 years, (i mos 2 wks., 5 davs, li \ (d) 9, Ce) 10, (/) i; Multiply 1 mo., 5 days, lit hours, 20 (<■) 'J, ((/)!>, (e)2i lys hy (a) 5, (/,) 7, (r) 12. (,/) 45. lours, 2 mts., 20 sec, by Oo .-.,(/,) . 3. Divide ti years, 7 inoa., I'l days, 8 hours, 7 ints., by (o) 5, (b) 6. (c) 9. (rf)12, (<')31. 4. How often is 5 days, 3 houre, contained in 2 nios., 27 days, 3 hours. "■- How often is 3 wks., 2 days, 5 hours, 18 sec, contained in 3 wks., 1 day, 2 hours, 3 uits. &. ExiaiciSE xxxvn. LONG MEASURE. Add together : 1. 4 miles, 3 furlgs. 2 poles, 1 yard, 2 feet, 6 inches. " 2 " 3 " 2 " 1 " 11 " 2 " .-) " 18 " 3 •' 1 " 10 " 9 " 7 " 35 i< 2 " 2 " 9 " 2. 3 miles, , furlgs. 30 poles, 1 yard, 2 feet, 11 inches, o " 5 " 24 " .-) " 1 « 10 " 9 " « " 14 " 3 " 1 " 6 " 12 " .") " H i " 5 " 2 " 10 " 3. 4 miles 7 poles, 3 miles .") yards, (i furlg. 5 yards, 3 miles 18 yards. 4. 2 poles 3ti yards, 4 furlgs. (i yards, 8 feet 10 in., 7 poles 4 yds. 6 in. EXERCISE XXXVin. Find the difference between ; 1. 2 miles, 4 furlgs., ■") yards, and 1 mile, 't yards, 6 inches. 2. 7 miles, 3 furlgs., 2 yards, and 2 miles, 8 poles, 2 yards, 2 feet. 3. 3 poles, 4 yards, 2 feet, G inches, and 5 yards, 1 foot, 11 inches. 4. 8 miles, and 7 miles, 7 furlgs., 39 yards. 2 ft^t, 6 inches, 5. 9 miles, 4 feet, and ti milef», r, yards, 2 inches. EXERCISE XXXIX. Multiply : 1. ;! yds., 2 it., (i in. by (a) 5, (6) «, (c) 7, (d) 10, (e) 12, (/) 13, (g) 35. 2. 15 poles, 2 yds., 7 in. by (a) .3, (6) 7, (c) 9, (d) 11, (e) 15, (/) 25. (g) &i, {h) S3. 3. 3 miles, 7 furlgs., ;iO poles, 4 yds., (i in., by (o) 3, (6) 5, (c) 7, {d)B {e)9,(f)l0,(9)io,(h)m. 23 EXERCISE XL. Divide : 1- 4 yds., 2 ft., 6 in., by (a) H, (h) .",, (r) 7. 2. JPole8,.5yd« 2ft.,10in.,by(«)3,(6)7,(c)9,(d)20,(O2.5. EXERCISE XU. SQUARE MEASURE. Add together : 1- sq. yd. sq. ft. sq. in. 3 8 40 5 7 65 3 .5 100 sq. rods. sq. vds. sq. ft. sq. ill 8 5 1 100 2 4 3 H5 3 17 8 90 4 25 7 (i •"■ sq. miles acr^s roods 5 300 1 2 540 3 « 600 1 2 44 2 «[. miles acres roods sq. y 5 15 3 20 5 600 2 15 s 47 1 16 9 143 2 15 EXERCISE XLn. Find the difference between : 1- 3 square miles and 250 acres. 2. 4 acres and 2 roods, 20 square vards. 3. 25 acres, 3 roods, and 5 acres, i rood, 7 yards. 4. 8 acres, 2 roods, 14 poles, 15 yards, and 2 acres, 5 square feet. EXERCISE XLin. Multiply : 1. 3 miles, 20 acres, 4 poles, by («)3, (6) 5, (c) 7, (d) 9, {e) 11, (/) 12, (g) 2. 4 acres 2 roods 5 poles, 30 yards, 4 feet, by (a) 2, (b) 3, (c) 5, (d) 7, W w, (J) 11, (g) 15. EXERCISE XUV. Divide : 1. 17 square miles, 600 acres, 5 poles, 16 inches, by (a) 2, (6) 3, (c) 5, (d) 7, (e) 9, (0 13, (g) 1,5. 2. 11 square miles, 250 acres, 2 roods, 35 poles, 20 yards, 8 feet, 100 inches, by (a) 7, (6) 9, (c) 15, {d) 20. 24 3. 14 square miles, 250 acres, 2 roods, 5 rods, 20 yards, (i feet, by (o) 3, (6) 4, (c)5, (d) ti, (0 7, {f){),(g)2o. EXERCISE ZLV. -MEASUREMENT OF CIRCLES AND (iLOBES. OlHERVATION. TTr^^.HKi. r= radius. Circumference of circle=2 r.T Area of circle =i-^.t Area of Globe=4 r^'.T Contents of (ilobe= 4r. 1. Wliat is the circumference of circles with radii as follows ? (a) 2 in., (b) (5 in., 0) H in.. ( m in., (<) 3 ft., (f) 4 ft. ) 8 in., (r) 10 in., (d) 1 ft., (*; 1 ft., 3 in., (0 5 ft., (.7) 7 ft., (A) 10 ft., (!) 12 ft. 4. What is the cubic capacity of tlie same globes ? EXERCISE XLVX. CrBIC MEASURE. Add togetlier : 1. cub. vds. ft. in. 5 17 1000 3 24 1500 4 15 lt}t)6 3 10 56 2. cub. yd;-. ft. in. 3. cub. vds. ft. in. 8 20 115 5 1(> 400 <) 15 215 8 13 576 7 24 85 25 842 <> 13 ItitX) 12 16 987 EXERCISE XLVII. Find the difference between : 1. 7 cubic yards, 8 feet, and 3 yards, 10 feet. 2. 8 cubic yards, 9 inches, and 3 feet, 1600 inches. 3. 5 cubic yards, 20 inches, and 4 yards, 3 feet, 170 inches. EXERCISE XLVin. Multiply : 1. 3 cubic feet, 1150 inches, by (a) 3, (b) 5, (c) 9, (rf) 25, (e) 100. 2. 4 cubic yards, 15 feet, 116 inches, by (a) 7,(6) 9, (c) 11, (d) 25. (e) 100. 25 EXSBCISE XUX. Divide : 1. 114 cubic yarclH, 17 feet, 1600 inclieg, bv («) '2, (h) ;{, (r) <), ((/) 15, («) 25, (0 lOO. 2. 765 cubic yardn, 18 feet, 15 iiicIieH, bv (a) :5, (/.) 4, (r) 5, (,/) ti, (,) 7,{f) 35, (3) 84, (/O 16.1. Add together : 1. gals. qts. ptH. gills. n :; \ 1 6 3 11 7 2 11 EXERCISE L. DRY .MKAHUKE. 2. bush, pecks, gals. (jts. pts. 7 3 111 .3 2 110 7 1 Oil EXERCISE LI. Find the differetice between : 1. 8 quarters, 3 bush., 1 gal. and 1 qrs., 2 bus))., 1 peck, 1 pt. 2. 4 gals., 1 peck, 1 pt. and 3 gals., 2 qts , 1 gill. EXERCISE Ln. Multiply : 1. 3 gals., 1 qt., 1 gill, by (a) 3, {!,) 7, (,•) 5, (,/) |5, (f) 25, {f) 36. 2. 3 pecks, 1 gal,, 1 qt., 1 gill, by («) .!, (h) 5, (c) 7, (d) 9, (e) 11, (j) .15, ((/) 45. EXERCISE LIII. Divide : 1. 3 bush., 1 peck, 1 gal., 1 qt., by (o) 2, (h) 3, (c) 5, (d) 7. 2. 9 quarters, 7 bush., by (>,) 2, (6) 3, {r) 5, (,/) 7, (e) !>, (/) 12. EXERCISE LIV. AVOIRDUPOIS wp:ight. Add together : 1. tons cwt. qr. lbs. oz. drs. 2. tons cwt. qr. lbs. oz dr« 2 I'J 2 10 5 12 7 15 2 23 14 \.< t lo 1 15 12 10 S 1!( 1 14 10 1' JL_gO. 3 20 15 14 7 14 3 20 11 14 '■** I) KCBKCISB ZV. Find the difference between : 1. Stons, 4cwt.,Bndlton, 15cwt., lOIbe 2. 4 tons, 2 qre., 10 oz., and 1 ton, 1»J Ibe., 10 drama. ■i. 2 tons, 15 cwt., 5:ibe., and 18 cwt, 2 ors., «J oi. EXEBOUB X.VI. Multiply : 2 2 ,™.'' f„"";' '."" " "'■• '" '"' "■ '" '2. M '5. W) 35, (0 75. szEsoias Lvn. Divide : (/.'.M^i f^) ^ of 5 miles, 3 rods, 10 in. 4. (a) ^4 of 6 acres ; (6) ^ of J o' 2 acres, 2 roods. 6. fi of a year + ^{Otb weeks p ,', of a day. 6. .05 of 3 miles + .75 of 15 yards + .5 of 7 feet. 7. Express £1.9.2 as the fraction of £20. H. «' £i.4.6i " " £7.2Ai. »» " £6.2.8 •' " £22.1210. 10- " 48 «d " " 2 guineas. 11. " 2 weeks" " ,} years. 12 Wliat fraction of 3 miles is 450 yards ? 13. " " 2 furlongs is 50 yards ? 14. '• " a ton is 7 cwt., 15 lb.i. ? 15. " " 3 cwt. is 45 lbs ? Ki. '« " 6 lbs. is 15 oz. ? 17. " " 3J feet of 3i poles ? IK. What decimal fraction of £5 is 48 (id ? 19. " " 3 mileg is 350 yds. ? 20 " " alb. troy is I of a dwt.? 21. Divide 17 cubic feet, 9 inches by (a) 16, (6) 18. 22. Multiply 15 grains, Troy, by (a) r>i4, (b) 650. 23. " 3 oz., 14 drams by (a) tj.-,, (6) 75. 24. Divide 18 bush., 1 gal. by (a) 5, (b) 6. 25. " 13 miles, 2 fur., 3 yds. by (a) 4, (b) 7. 26. " 40 miles, 3 fur., 3 pis. 3 yds. by (a) 15, (6) 17. 27. " 28 tons, 3 cwt., 4 lbs. by (a) 6, (6) 9, 28. Multiply H.5 yards, 2 feet, 3 inches by (a) 10, (b) 13 29. " 5 .'•quare yards, 5 feet, 75 inches by (a) 12, (b) 15. 30. "3 bush., 2 pecks, 1 gal., 1 pt. by (a) 9, (6) 13. 31. i of £5.10.4 + 5 of £7.0.6 + i of 9.4} + J of 1.10}. 32. -jV ot 3 miles + i of 15 yards + .} of 7 feet. 33. I of 7 tons + f of 7 cwt. + | of .3' qrs. + ,», of 4 lbs. 34. Find the value of 4 . 25 of £3 . 1 0. 35. " " " 3.15 of 4 miles. 36. " " " .75 of 3 acres. 37. " " " 2.125 of a cwt. 38. ■ .5 of IS tons. 39. " " " .35of90mile8, 45vard8. 28 SXKROISE XJCIU. -MISCKLLANEors K.\ A M I'LKH. I. 3 4. I.nnar^ 1. ,.s "•""' '••••l.nmry... Lsih!. ,.. Mar,.,; How long would it tak.. light ... travd .-.. ,nilli„n.-..f ,„iU.. if i, takoH H .nunues for the light fron. th. sun t- n-ad. „.. a.s„ ,g tl.i hm • distance at !>2,00().(KH» mJleB ? ^ The light fr..,n siri... take., .ay, « year, to reaoh n. ; how far i. the nuring a th,„,,ier.torm the thunder w.ib heard!.-! .second, after the 1 XT,:;:';- .""" •"" "^'' • ^"""- "-"•"'"« ""• «!>-• -" infinite) ^■'' *""" " ''"'"'^ '"' "'"" '" ''^ ♦"'^^n •" a ter he lightning is se.-n ? I low long if .-, miles awav. How long will a train take to travel l(H^, miles, if ii .over. {„) ■>:, .vard.a.eeond.'(6)32yardsasec.on.lV (-. ,!5 vanl. a ..econd ? " at hat time w. 1 it arrive there, if it travel. L'o uule. an hour, and «ops 4 tnne.«. .allowi..« .-, minutes for each .to|.page. ""^rifo^r'' ''"""'■''''■''■ '"'"''■' '""""'' ""•■ ^^'"'"^'^ [,1 ^^;f '""•""•■'"'"' ^''^'"'' ^^ ""»-^k- I'-v much willLavo mfoh Ji'?r''T' "'"'r'"'' "^•''•^■""^^ ' ''«^« ^''^-' ^^-x): I'ow -nucli did I .{HMid a month ? The circumference of a carriage wheel is li? feet • how manv revolutions will it make i„ goi.,. „) . n,ilesV (.) ,o .oi.es^ ^U If a carriage wheel with a circumference of l.', tVet make« -V, 000 ^evolut^, how far did It travel. ... How .. .:th^::;r Sineh!^ > '' — "">^' tl.a. every two stroke.s advances the machine A cent being an inch in diameter, how many may b«. laid on a table ^ lol:;'^^ '^ider'^' '''^' '"""^ "-"««- of a room 20 Z^nlrZlVf "T '""' "' •'•' '''''' •" ^ ^'»>-' ^^"-'•'^ "'« "^'"i could be purchased hy p'.,cmg 2', cent pieces on it, a.«uming the diameter of the quarter to be 1 inch? uiameier 29 1(1 17 18 ly. 20. 21. 22. 23. 24. 25. 2(i. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. Mow many .lice, 1 in. .jdf. culd bt.' cut from n block nf ivorv 7 in l)> 3 ill. by 2 in 7 ■ " A man t'xchanKe.1 I.", lb., tea f-, 40c. for oatn G .TO centn a bushel lloH many biifiu'l.s djil be got? A Krain fi.vntur, buviiiRa raiwoity of i.'.-m,(»o buBbeln, in } f»|| fio„ many bav'., . acli cmtaiiiini.' 1 bu.-b. 2 jra! . can ..m. till, and li.,w loHK would It take to fill ,be 1«.k., aliowin^t .30 seconds for everv out of I'm benn, 50 laid an ew each day ; 75 laid one every other day ; the other, laid 2 ewrs every :i day. ; how many canen of eww could one III with the e^gs laid in :!.i days, each raHe holdiuKT^ ilozen, and what would W the value at 15 (viitH a dozen ' If I buy 10 llw. (.WoirduiKjis) (., .r, cent.- an oz., and wll by Trov at 42 cents an oz., d.. I ^aiii or lose, and bow much ? What is the number of square miles on the mirface of the earth assuming the diameter to l,e s,m^ miles T What is the numlHjr of cubic miles it contains ? "•■ni»er oi How many times would a wheel 5 ft. in diameter revolve in a jofir- ney of < miles? s.l miles? 10 miles? What is the area <.f a circle with a diameter of Iti feet ' 17 vRr,i. -> 40 yards ? 50 yards ? KX) yards ? " ' With what radius must one draw a circular track so as to make the length of the track \ mile? 1 mile? * Two concentric circles are drawn; the first has „ radiu.. of « feet the second of 10 feet ; what is the area of the outer rinc " Divide X410 among A, Band V, so that A may receive £5 for every X.} B gets, and (' may have X4. 10 for every Xti B has ^Tf^([ ^'T'!--^ ''• ^' ""^ ^' '" "'"* '^ '"^>- ''«^« -^2 for everv X3 that B has, C X, for c-very X,s A ha.-, and 1) as much as \ a. d C together. " ^ If A of a long ton is worth X4. 10, what is the value of l of a snort ton " After drawin,M>ut of a bank i of my balance, j of the remainder was ^(^10 ; what was the amount of the balance •> A man buys 40 lbs. drugs by Troy weight for $2 Find the value of 713 articles at X4..s.o^ What is the cost of (i cwt., 2 qr., 5 Ite., at X4.16.3 a cwt. ? 30 3S. 3y 40. 41. 42. 5»3. 44. 45. 46. 47, 48. 49. .50. 51. 52. 53. 54. If a labourer's wajres are is.s (id a week, how mucli will 45 labourers receive for 12 weekf? All estate of $18,000 is to be divided between a mother and 4 c ;'cl- ren in the following proportion : The mother is to receive (. .,;; tho whole ; the eldest son :,ir^ of the remainder and .*!20U l)et li-s • the next sou .25 of the remainder, and the other two sons to h.i the balance equally ; find the t-hare of each one. . Divide $450 among two persons so that one may receive naU as much again as the other. A railway car weighing 20,000 lbs. is l.nided with 75 bags of flour, each weighing its lbs., and ID barrels <.f sugar, each weighing :m lbs. Find the total weight of the loaded car. If I take a step of 27 inches, how many miles do I walk in taking 10,.")t>0 steps ? How far with 12,000 steps ? How many steps do 1 take in going ti furlongs, if each step niea.sure.! 2 feet, 6 inches. After taking CyQO steps I find I have walked 2J furlongs ; what was the length of the step? AVhat would te the length of the step if the distance walked measured .5.50 yards? A farmer has two fields, each containing 2 acres, 2 roods, 25 poles and another of 5 acres, 3 roods, 20 poles ; what is the area of the 3 fields together ? If I went out Friday at (>.20 p.m. and returned Saturdayat 7.45 p.m., how many seconds wa.s I out ? How many seconds from 8.40 p.m., Sept. 5, to Oct. 30, 9 a.m.? If the first day of the year is a Wednesday, how many Wednesdavs will there be in the year ? A cistern is emptied in 3 hours, 40 minutes, by a tap which dis- charges a pint in 10 seconds. How many gallons did the cistern contain, and what was the weight of the water, if a pint weighs "0 07.. ? Find the weight (Avoirdupois) of (a) .$1000 in gold, assuming a $5.00 gold piece to weigh 125 grains ; (6) $7,550. An engine wheel has a circumference of 15 feet ; how many times does it re\.)lve in going (a) 84 miles ; in going {b) 1.50 miles? (c) If it makes 5000 revolutions, how far does it go? If I have 64 acres of land, and mark off 3 divisions of 3400 square yards each, how much land is left? Find the value of («) a pile of wood 200 feet long, 5 feet, 6 inches high, 4 feet wide, at |2. 75 a cord ; (b) another pile 250 feet long, 6 feet high , .3 feet, 6 inches wide. If I mix 75 lbs. of tea at 45 cents a lb. with 85 lbs. at 40 cents, what must t.'ie mixture be sold at to gain 10 cents a lb. 31 55. 56. 57. 58. 59. 60. 61. 62. 63. A man has 7 cowp, each yielding on an average 2 gals 1 qt i pt per day. If he nells the milk at 5 cents a quart, how much monev does he take in in the course of a week ? Another has 15 cows, each yielding on an average 2 gals. .3 qts 1 pt daily. If he sells his milk at 6 cents a .juart, how much doe« he take in during the months of November, December and January. A boy walked a million inches ; how many miles did he walk " If I undertook to make a million strokes, making 1 stroke each second, how many hours would it take me? Supposing I worked 5 hours a day, how many days should I Ik? over the task '' If I walked ir, miles, how many inches would that be? How m«,.v inches in 3* miles ? 2J miles ? ^ If a $5.00 gold piece weighs 125 grains, what is the weight of a million dollars in gold ? (Avoir.) A cubic foot of gold weighs 1210 lbs.; what is the weight of a e„ld brick 6 inches long, 2 inches thick,:! inches wide? Of another S inches long, 4 inches wide, U inches thick ? A bushel of wheat weighs .io'lb.«. What is the weight of 1000 batrs each containing 1 J bushels ? ^ ' A rectangular field m yards long, 30 rods wide, is to be fenced with wire, 5 strands high. What will be the length of the wire required ? EXiatcisE Lxrv. COMPOIND PRACTICE. Find the price of : '■ 'i^'^^TJo' ,-'"''"' '"' '' ''■''- "" '''''■' (^) ® ^'-'^ - acre , (r) («> iio. lo an acre. 2. 3 acres, :i roods, 25 poles, (a) @ £.-,.l(). a rood ; (b) (ii £7 1,5 a rood 3. 4 tons, 15 cwt., 15 lbs., (a) (.. X5.,2 a ton ; (.) kitd a ton ; J;, x^O Jo a ton. '■ qimrter;'"'"''''*^-' ''"'•• <"> ^-^ =^3.10.. a quarter ; (6)@£7.15a 6. 15 oz., 12 dwt., 16 grs., (a) Oi^ £8.1.->.6 an oa. ; (6) (,r, £4 15 „„ „, 6. . acres, 2 roods, 4 yds., (a) (a £5. 10 an acre ; (6) @ i:i,i,« « rood. EXERCISE rxv. INVOICES AND AC COINTS. Make invoices of the following sales : 5 yds. velvet ® $3 J5 ; 4J yds. silk 9: $2.50 ; 2} yd., cloth @ $3.60 • 2. 15 yds. calico (2^: 10 cent^ ; 4 yds. ribb.n. (?; 55 cents. 13 yds. oilcloth @ 80 cents ; 70 yds. Brussels carpet ® |1.15 ; 75 vds Kidderminster carpet ® f 1.20 ; 15 yds. matting @ 75cente 6. 5 lb., tea ©40 cents; SA lbs. coffee @, 48 cents; .libs, sugar @ 5 cents ; 10 lbs. rice (Tr, fiA cents ; 5 lbs. raisins ® 8 cents ; « lbs- cur- rants Oi , cents. 4J lbs coffee @ 40 cents ; 20 lbs. sxhite .ngar Oi, 5A cents ; 25 lbs. brown sugar (^,4 cents ; 2 lbs. grapes Or. 15 cents ; 2 doz. oranges ® 40 cents doz.; 5 doz egps ^, 25 cents ; :! lbs. raisins (T, 10 cents ; 4 lbs. currants % 8 cents ; 2 b. ••..^s pickles (o 45 cents ; (> lbs. prunes ® 15 cents. l!'Z ^^^"T"^ ^' *"*-''^ ' ' 'P""^ '"^"'•«*^^ @ ^2.75 ; 1 hair mattress ©110 50; Mvash-stand©Ki..50; .i chai.^ © $1.50 ; 1 rocking chair at bi.oO ; 1 chest of drawers Or. $I8.(X). ;« lbs nails r<< 4 cents ; 15 packets screws ® 15 cents ; 2 hammers @ 3o cents ; 2 files OJ) 4o cents ; 1 saw at $1.50 ; 1 plane at $1.75. 6 shirts® $1.25; .'J silk handkerchiefs © 75 cents ; 4 nightshirts © 80 cents ; 6 pairs socks © 40 cents ; 2 pairs stockings © 55 cents ; I pair kid gloves © $1 . 75 ; 1 pair woollen gloves © .55 cents . 3 reams note paper ^ 7 cents a quire ; 5,000 envelopes © $1.25 per 1,000 ; doz. lead pencils © 3 cents each ; 2 doz. pen-holders © 2 cents each ; 2 pieces India rubber © 10 cents. EXERCISE LXVI. PliOBLEMS. If a man can plough <; acres in 5 days, how many can he plough in 15 days? If 15 horses cost $750, what will IS horses cost ? If I walk 84 miles in 7 days, how far can I walk in 43 days ? How many days will it take me to walk 54 miles? If the rent of 18 acres is $540, what is the rent of (a) 25 acres? (6) of 03 acres ? (c) of 95 acres ? 5. If the price of eggs is 50 cents a ..core, how manv can be bought for 'a) $7.20 ? (6) for $8.00 ? (.) for $1 2.00 7 " ^ ^' fulJZ^^ "'" '* '"""^ *" ''''"' "^^ "'''^'' '^ ^ '^" ^'^"^ ^2 »"'«« '" ' "rd^i^^l^da,^'^^^^^'"^" '' '''' ' ^'^'^ of work which 9 8. How many men can do in 15 days what 70 men can do in 228 days? 9. If a man earns .S45 in m weeks, in how many weeks will he earn («) $3.i0? (6) .$700 ? (c) $\ar(lsol nialiTi;.'. arc wurtli si'.-.T), ln.w iimny yard- raii be bouglit fur.^d.:,")? lor^li.ni? for $i:).()0? for $i 17.0.') ? 12. If I walk 54 niilew in 4 days, li<>\\ luiij: will it take to walk dd milfs'.' 70 iiiile.s? .s,"> iiiile;-'.' lC>inilc:J'.' i;i. If I walk 17 miU's iii4 hours, liipw far can I wall; in II lioii!--'.' IJ lours? 1.') hours? ItU hours? 14. of ail estate is worth !^40(i. wliaf is the value of : of the e.-iaie? j„ . OI s . OI i„,| . 15. If :!il lbs. of tea cost $1.7.".. what will 41 lbs. cost'.' r, Ihs. ? 7] lbs." How much can 1 get for f;!.00 ? for$.').50? for$7.'>0? for*!t.O(i? 16. What is the value of % of § of an estate if ii of 4 can be bouL'iu for |2,(K)()? 17. ,1, of i'_. of a ship is worth iJo(K). what is the value of ]',: of the shii.'.' 18. A man who owns } of an estate, sells ^ of ,; of his share for $7'M. What if the value of .05 of the estate? of .45? of .35? of .■'w; " 19. If the freight on 4 tons, Ki cwt. be $.H.' ), how much will be the freight on (a) 3 tons, 12 cwt.? (6) 5 tons, S cwt.? 20. If 20 tons can be carried 50 miles for IS. 00, how far can (a) 15 tons be carried for the same money ? (b) IS cwt.? (c) 24 tons ? 21. If 5 men earn $75 in 4 days, how much will l> men earn in 7 days? 22. If 9 men earn |]10 in 5J days, how much will 3 men earn in 1.'. lays ? 23. If 4 horse-s can plough 10 acres in 3 days, in how many days will hi horses plough 1 5 acres ? 24. If 5 horses plough 12 acres in 2 days, how many acres will Iti h. 4... ;i4 • If I can , ,,.y I.K, p,g.,, ,,,„ Laving 'J7 Vun:. ^.i,l, an .wn.,. of 12 .o".> a -ay ...nld I l.av.. r.. w-.k f„r . .lays t.. copv ,.,. ^.J^^l ■ t 1 )bu.l,Hs „, ;;,.aiM uill ie..,l |,>.i f.,„ls ,„r 10 ,lav< l,ou- ma„v '"■■-Ii.'l. u 111 s„(li,,, ,„r ,10 ,„„ I. ,„,. ,..-, .1,,,... l'«H.Ifal,an.,.an.liga t.vnrl, 4.(HH. yar.i. |.,„jj, ,s ,Vel vvicU- and 10 f '■''''"''"''"'" '''•--'' ^'''l-w-anv.l'j^w -c M.an,;.K,„avvies,li,a t.vnd. ::...«, yanis I,...., . i...-, .. "" -Mi.v,^ assnnnng n,a, 4 .avvi.. ..an .1.. .,s ,un..|, u :,,.k as;. Italians" 10 horses i,,r!i ni.inllis lor .*4.-.0 (H) ^''" «n I'tlu. fn.i.H,t lor 5.-, lb.. f,.r „; ...j,,.^ j, 4,, cents. wl,a( oujiht t., be <;l'a.ve,l lor :! pa.ka.es „f .V, |h,.. „a,.|, ...r 2.; n,ile<' ^ I> 4 tons CM,, h.. carried ,s n.iles for ^4, l,.,w far can UO tt tons he !tl" •;:;;::''"■'"'■■'''• ''■■'' ^•■•'^"-'—i-p.-an be ,11.0,11. .q'> ■-. ".o ,„„„„es, now Ion. w,il „ tal.. ,o nil lo cisterns. -. Vet ■-• ' '' ' ••'''' • ' '>■<-•! (ic-i'p, with ,s taps'.' 12.. peopi,. can earn $r,-S> in lo days, working S honrs a dav eaoh u „,.,ch can 40 pe..ple earn in 12 .lays, w,.rki„. 10 ,,o.,rs a lav ' .""",""''"' ' " '•".^- i^« -'<«'- .■ . -i ., ""gnior ;:;;:,i":"r::,v;:,r,;; ■'■•-'••'•.■■■<■)'". -.^^j A l.iii, ,,■ «.!„ «,.i,|,, „ ,.,M,„| , , ,,„,„,.,, „.|.,„ i, ,1 (.tt.-;,„. (> jeare ^ IS 47. If I can travul ">S inilcs by rail for $1.74, how far ought I to l)e car- ried for (./) i?;;.(H>? (6) ■fS.W! 4S. If a man owi's $.">,.5(>" ami pays (Ml rent> in tin- liollar, how much will a creditor for $-IO() receive? 4!t. If IL' men can reaj) a Held of 7 acres in 4 drty,< of S hours each, liow t. my hours a day nMi>^t 1.') men work to reaii ."> lield:^ of ti acren each in L'(» days'.' TiO. If 72 ton- oi -.'.(KK) lbs. each, cost -SKio. wlial will !..• the cost of tiO Ions of L',4(H) lbs. r>l. Ilo\\ niiich must i)e ;,Mven ioi ((() 1.") arucie> al the rale of 7s. (id. for 1 2 art ides? how much for (l>) 2:'>. 52. If a hiishei of malt is worth .*l.2o. how much can 1 bny for ("> $i;;.7.")? (In for$IS..i(l? 5.">. In what time will 2.5 men perform a jiiece of wck that 20 men per- form in 20 i!a>s ? r)4. If a man can walk i)2 miles in 2 days, walkin- S lionr> a day. how- far will he walk in .'> days, walkintr 5 hours a day? ii.i. ll .4."> of ,' of an estate is woitii $U,7.")0. w iial is 1 In- value ol ."i.'i ol 1 he n nuiiiidr; ? 5<). A man workinLr >* hours a da\' does .27.') of a piece of work in II days ; how irai"- horns a day nmst he work to do the remainder in 2!tday'-'.' 1)7. In a certain irarri.son there nn- eiioiiirh previsions lo last 2-")0 men (J weeks; after 2 weeks I.")0 additional men come: how louir will the provision- la>I '.' SS. If 14 lior-c- i:in be kej.t for 20 days for §2s w hat will it cost lo keep !) horses for il') days? .M'. If 2l(i men can dii; a trench 40.") yarUs lony. ;i yards w ide, and (i feet ileep, in 27 ilays of 11 hours each, liow many men will Ik.- reiinired to dii; IJO >arils long. -") yards wide, 12 fict dee]!, in 110 days of 12 hours each ? CO. If 2(1 cannons, each liriiig ;; rounds every ."> mimiles, reipiire (),0(K) Ibj!. of i;un]>ow(ler ]M'r hour, liow many His. of powder would be recpiired for rt{) cannons, (irinj,' 4 rounds every 10 miimtes for 3 hours? 61. If thecliar-Lrc for carrx inu' :' 'Wt., 1") lbs., for 7") miles is 4-'» cents, what should be charged loi carryini; S similar iiackajres for 22.5 miles ? 02. If 2.5 men in 7 weeks earn $l,4(HI, what will ('/) :!-5 men earn in .5 weeks? (/<) 40 men in li weeks? fi">. If 40 men t'an build a wall 140 yarils long, lo feet high. I ft. thick in ;! days, WMrkiiig lo hotii> a day. in how manv da>.s of !• liourw can 50 men build a wall 210 yards lonir, 12 feet hiirh, 15 inchess thick 7 04. 65. 66. 67. 68. 69. 70. 7J. 72. 7.3. 76. 78. 7!>. 80. 81. 82. 83. 84. 36 IfOnmn can perform a picT.. of work in l.", days, huw u.a.n n,en will iH- r,.,,u,r<.,l to perforn. a pi.-c.. of work o.u-tlnrd oi th,> Hjzt' 111 one-lift 1) of the time? If 5 horses can i .,<■!. draw a load of S tons for the snm „f ,*7..-.0. u liat should \>e the charge for s hor.-es each drawing I.-, t.m." If4field.sof4am..seach,.an be ploughed hv 10 hors.- in ;i dav<. how many horses will be r.^uired to ploiij;!. i2 fields of ti acres each in .> days? If 9 persons .spend $(iOO in 2 month.s. how much «ill -erve 00 % persons tor 1-J months 7 (h) 40 persons for ;! months ? 1 12 horses plough 4,! acres in UU liours, how n-anv hor.s«.s would p ough (a) 35 acres in 20 hours ? (6) 40 acres in 10 hours ? I 40 bushels of corn serve 12 horsen :W days, how manv davs will l!>o bushels serve <> horses ? How many men will \,e required to dig a trench l.iO feet long, 5 feet wide 4 feet deep in 6 hours, 20 minutes, if 8 men can digatrench 100 teet long, .3 feet broad, 54 inches deep in i» hour«^ V ^fw """u ^^'■" ^ ^y '""''^'"^ 2 ^«>'«' ^" ^^'^^ e«cl. day, what should be the wages of 9 men for .3 .lays, working 8 hours a dav ^ II .■) o.xen or , horses consume the gra^s in a fiehl in s? dav- in" how many days will 2 oxen and .3 horses eat it ? ' ' If 9 men <.r l(i boys can do a piece of work in 10 .lavs, working 8 hours a day, in how manv days of i» hours could 5 men and ;! bovs do tlie same work ? If 2<»cwt. of fodder be required for 2.^ animals fur l> w.-ek- l,uw much will be required for 40 animals for 50 weeks ' If it cost me .51.75 a week to burn two ](i can.lle-power electric lights in rooms for 5 hours each evening, what will l,e the cost to burn three 12 candle-power lights in 8 rooms for 2(i weeks, using them 4 hours each day? If 5 men earn $50 by working 5 days for 10 hours a .lav. h„w much will 10 men earn, working 8 hours a day for 4^. days ? ' •A certain swimming bath is 00 yanls long. 2.5 yards wide and « feet deep. How many gallons of water does it contain, and what is the animal amount paid for water, assuming the charge to Ix- 20 cents per 1,(MK) gallons and the water to l)e changed every 5 days'.' I of an article is worth .$1.80,:what is the value of"^ „f the article' ■■ " " •' ' 4.24, " " " •' <. ■ .. « " " " " 8.50, " « •' u <■ ^ .. f. " " " " .3.75, " " " " '• I a » " '■ " " 4.80. '• " " " " i u If 3 of a piece of cloth cost* fSj, what will ' pieces cost" If i of a barrel of cider costs ,', of a dollar, what will -: of a barrel cost ? 37 S"). If s (iriiin.'cs are worth 24 coiitn, liow iimicIi arc 'J i)raiiue.s worth'.' xc. If :',]■ yards of cloth cost $(1^, what will 14 yanl.s I'o.-t? H7. If a family toiiMuiH's 2^ btishi'lH of yraiii in :!j wreks, how iiiuch will they consume in «'4 weeks? ss. If 4 apples are worth l.l oranges, and 1 oranjie is worth i' lemons ; liow many leii, ms will 12 apples buy? s». If 2 tons of liay cost |1!»J, w hat will M cwt. cost ? 90. If t of a barrel >f flour costs .">! dollars, what will bo the cost of ^ of a barrel ? 91. If :> men can mow 15 acres in 2} days, Imw long will it take 11 men to mow 44 acres? 9-. If a farmer can plough 9 acres in 4 days with one team, how much can he i>loutrli with two teams in 81 days? v:.. If a pa>tnrc of s acres will Iced :> horses for 2 months, how niuny a(ies will feed 4 horses for •') months? 94. If (i horses sat 2^ tons »i hay in 12 weeks, h' w much will !♦> liorses eat in 1.'. weeks? 9.'). 9<). 97. 9S. W. 109. 101. 102. lo:{. 104. ior>. 10«i. 107. If a man travels 48 n.iles in 2 days, travelling ti hours a day, how far will he travel in :! da.\ ■-, travelling at the same rat«, 5 hours a day ? If a barrel of Hour w ill serve a family of tJ persons SJ months, how much wiU serve a family of !t ihts ns 4^; months? If ,. of a bushel of oats will feed 2 horses J of a day, how uuich will be required to feed 4 horses 4^ days '■ If 1 man can do a piece of work jn a certain time, how much could 4 men do in the same time ? If 5 men, in 4 days, can do a certain piece of work ; how long will it take 1 man to do it? If 8 men can build a wall in •> days, in how many days can 12 men build it? If a Ijarrel of flour lasts !."> men 20 days, how long will it la,st 25 men ? If 2 men can build a wall in 4 days, how long will it take 5 men to build it ? If 5 men can do a certain work ii; (> days, how long will it take 3 men to do 5 times the work ? If 9 men can do a piece of work in 4? days, how many men should be employed to do the same work in .seven days? If (i n)eii can do a piece of work in 20 days, how many men could do it in 8 days ? How many dozen of eggs, at 10 cents a dozen, imist be given for 32 oranges, at the rate of 5 cents for 8 ? If lemons are worth 1 1 cents, how many oranges at :! cents apiece, can be Iwught for 54 lemons? •^1 i^ II tin U)8- Ilti|).imi.Is.)i ImtttT arowoilli 13 shilliii^r-. h„\\ many yiinU ..i" «alic.). at -2 sliillinjrs a yuni, oaii Iw Ixiujilit In,- -Ji poiiiulM ni biitttT? lat. How iiiiiny calvfs, worth fti apietv, uwn't be ^rivt-n Inr 12 ^lii-ep, if :. sliecj) cost $i'(i? 110. Two jifrsons an- !Mi miles aiwrt, aixl an- Iravdin- toward facli otliiT, OIK" at tlic rate of ."> iiiiltM an lionr, ami tim utlicr at the rati- of M miles an hour ; in liow many hours will tlu-y mi-iM ? 111. Two jM-rsons an- Kt iniK-s apart, ami trawl in the sam.- (linrfi.m, till' lnr«anl on.- at ill.- rate of .) miles an liour, and the other at the rate of seven miles ; Imw lonir Ix't'ore they will b*- toiretlu ? EXERCISE LXVII. INTKHIXr. r:il.-Mlati..ns in \,,\i-u->t are f-impli lied le the i,se..||l„. i.irnnil;.: I'linc. X '„ X Time ' Inter.'st -^ l'rineii)al Time Rate IINI I MH) y Interest /', X Time I0(» X Interest /^ X I'rincipal I and Tim, are "tlie other two. " In looking' for ,, /'/,»>■,;>.>/ and 'Jim,' are " the other two. " In looking: for Time, 1 'n „ri p,,/ niul .. are " the otli>-r luo. " In the following sums take notice that 2 X -;{ == \.u; ;f X :;; = 2I<» i X 7.^ =^ 2! 12 ."» X 7H =■ ;!(1.') Make calcnlations on tik- l)asis of 52 weeks to a year. What is till- interest on : 1. $U)0 for 2 years at (a) 5 ;, (/,) fil, (r) 7%. (,/) 8%. 2. On $300 for ;j years at (,,) 2%, (h) 3%, (c) 4%, (d) 7%. .^. On >^3r>0 for 4^. years at (-/) 2^%, (/,) ^%, (e) 4\%. 4. On $!.iO for 2 years n mos. at {„) :,%, {!,) li-, (c) 8X. &. On |3G0 for (i months at (,i) 2%, (//) 3%, (c) T;i. :«) fi. 7. j^, 9 ic. 11. IJ. l:!. II. 1.-.. 111. 17. is. i'.). :'o. 21. 2i 23. 24. 2;-!. 2(i. 27. 28. 2'.). 30. 31. 32. 33. 31. 3t;. •IT t>l . .•IK. ■M. 10. 41. 42. 43. 4t. (»ii $l,2".(» I'(.r4 lii<.inli> at KM 2%. C) .1%. (r) 7%. Oil $12.0(1 I'd- 3 iiic>iitli>< at («) ft ;, i/)i 'Ji., ((■) 10„. Oil |il I .Ml lur 2 iiiontlis at {) 6], (r) 9,'/. On !|i2.i lur 7.! (lavs uf (.ii 2'.''.,, (/<) 3 , (.-) 1%. <»ii i lur 7.! tlax." at (x) 2.j , (/)» 3 „, (ci >*>:,. On *t;.,')Oii for I tt; days at (<() 3 ,,. {Ii\ \%, {r) W'^. (»n s7.;il lur .'..■, (lay- a; I'M 2 ,, |/i| ."• ,. (r'l 10 „■ Oil J(l,3i I I'.ir I')il .livs at (./»!. i/-i I ,, 'I 7". <»ii .-?I,IIOO ir.iiii .Manli :;i,| I,. .\|.i\ i.itliaiuM I „ ..,, .> . On $I2.'> Ivoin .\|iril 2."»tli t.i S,-|.i. Mili at lu) 2.\ ,, i/<) 3 .. On i^\ If. ironi rdi. I. '.in. I>^-ili at (a) I ,, ih) .". .,,(«•) u . On S^03 fn.iii Oct. 31st, H-<7, to .Maicli 30tli, ls8S,at('M I ., I'm ■'> '6, I'M 7 . t i .".;<, cm'.»',. (./)2'i i. On ol l.ilO I'roni .\u'_'. .">lli io .lati. Isi ai CM ' ['i,, il>) 2', ,, w) I!: '/. On .ii.')!!!! I'or I Mars at cM 'i,/. (/m '> . f) ^^ ■• Oil .■^t;.')0 lor 2 y.'ars at (ai •') ,, ('>) li ,, C'l 7 ;, (•M :) ^. On i»;7.'>il.00 lor 2.1 years at I'M 2 ",, ili\ .'. ;;, ic) .") ,. c/( 7 ,, C'l '.• ';. On .§1,200 at ."< J for (l 7 ^^. (c| j< ,. On *l,ilOti from May 2.'nli to Dec. 30tli at CM '» ,, (''I »> :, (<•) •'",■ On $.'>00 from March Itli to Oct. 'Jl\\ at ('M4 ,;, ('m •"> -, I'l *'• ;. On *<100 from .Marcli 1st to Dec. istli at (a) ;'> ,, I'M ~ ,, ('I 10;;. Oii$>i.'i from .\i>ril 2nd to .Ian. Htli at I'M 2.1 ;, {li,:, ', (r| 1^, («/) 7;^. On jf2.')0 from Marrji Isl to Oi't. I'.iii at CM 2 „ (f>) 3 ,, (-•) 7'', {iH '.»%_ What Principal will yield : $1,000 a year <■• (u) 2%? (/») .V^,',? (-) S % ■.' |40 a moiitli r./ (.») .■.'/? (''> 'v'^V ('■) *^,V' $10 a week f" ('/) 2 '/.' {/>) 2.\%? (.) .•.';? $25 a wed; 6- c/) l^i-f {!>) lO;^'.' c i 2^;; ? $1,.')00 in 2 years («■ (.() ;;/? (//) ,■) ? c) 4 = '•' $700 in .V, years @ ((t) Bf^;? (6) ll,;'.' (c) 2.:^;? $150 a week («) (a) t'/J {l>) 5% ? ic) 1.1% ? IIow much must I invest at 1% to obtain a qp-irterly income at 5 ; V (h)•>\■'/^^! (c) 10% ? 4 3. I«. »7. »8. Mt. M). Til. ■j2. :3. 54. 56. 56. 57. 58. 59. CO. 61. 62. ♦V?. (54. • 16. M). Ii7. !-.8. tiP. 40 . In what liini" will -i-.'OO iiiiuMiiit t.. fiV) m (,|) 5% ? (6) 10% ? (<•) 2J:^? '■ 5' .OtK) uiuuiiiit to $1 .LiX) («) (i {, •.' ^„\ 4 /, •> '; *•'"♦' " " ♦<»0 " " $1,250 r..:{i%? f..; i%'' " " '• " *(1,0(H» yiel(l$5<)(,f) 10%? »50 '• f507(r,;4%? tWOO " f400(-r, ;{\%? f„)5%? $4(» " 40 cents (« 5% ? What Priii(i|.al will yield : ll.tKHJa yi-ar/ffi2^,%? (.»;6^%? („ \'2\%1 1400 a month .© 16% ? (a) 6%? (ii\ 8"/?° 140 a \M-fk f.,- 2]%? f-i 2J%? (,i 5%? $125 :i wevU Or. 5%? (i,, 12^% 7 $50 a wwk f», 2%? («r2^%? V 10% T $1.75 a wt'ok @ .'i% ? ^^ 4^/ ? @ 5^0/ y $450 a month @ 2%? @ ;5J%? („ 4^%? @ &»/, At what rati' must one invest $500 to jrive |25 in a vear? 70. 71. 72. 73. 74. 75. 76. 77. 78. 70. $800 " ' $1,2.50 • ' " " $0,000 '■ ' $1,000 " .1!s,ooo •' '• " " $500 " $78,000-' . .._„, At what rate will a sum of money donhle itself in 5 vears? 8 years? 10 years ? • " • In what time will a sum of more> 5% ? What Slim of money will yield 140 in 2 years? $1,000 in 4 years? $50 a month ? $5 every ;! month.s 7 $15 a week ? $100 in.'} months? •'?75 a week ? iDle itself at2%? 2^%? 4%? $210 in 2 years at 0%? $850 in 1 year at 2^%? $56.26 in 5 years at 2^% ? ^450 in 5 years at 6% ? $1,207.50 in .'i months at 2^7? $1,422 in 2* years at 5% ? After leavinj; $1.50.00 deposited in a hank at 4%, I received an intimation that my balance amounted to $174.72. How lonp did r have the money there ? If I deposited $2,000 in the bank at 4%. how much interest could I draw out quarterly ? v^um i A i.n.-.ee invests ^7,000 in a security paying 0%, ana $500 in another payin- 5,,,. How much interest will be available every ha.f-year? 41 80. A father wis'liKr' to ciulow liiH liuiiKlitcr xvitli an iiicoinc of $2,000 a yi-ar. lie limls a ^r<>' : — $8,000 at 5% ; 16,000 at 6i% ; .*i:.,000 at «%. Find my total animal income. 82. A money lender fhar>;«.'f< one shilling a week tor the loan of a soverei>»n. What rate of interest doefl he yet? 83. If I ixwseHH |.'5,.">(K) and wish to have a iiionthly ineonie of $22.00, at what rat*' nmst I invest the money? 84. What in the interest on $7')() from Nov. Uh to Jan. Kith at ('() 2J%? (M :!=:•> (c) 7% •/ (,/),s%? .s.'>. What princiiwl will yiehl a muiithlv income of ;*72.t)0 at (") 3%? (6) 4% ■■■('•) 8% ? St.!. At wli.it raif imist I invc-l sjD.OfXI to u.ve iiic 11 monthly income of S7-'> V 87. In what time will .•sl.oOO yield S;|.').0() at 2A%? 8H. What is thti interest on S7.'>.()0 at 21;, for :«) days ? S-.t. What is the interest on ;:«.').()(» at 4% for 02 days? i)0. What is the interest on .'^Hti at :)!.% for HS days? 91. At what rate nmst I invest $1,000 to give nie S4.').(K) a year? 'j2. What will be the amount of SCti') for :! years at »>%? 0.'>. If S-HO be (lilt at interest for 2 years „i A":, what will Ix; the amount ? 94. What will be the amniml if .•<2.'>0 be put at interest at >>% for :> year>^ '.' '.••J. Wliat will Ih> the an it of .^."lOO for 7 years at 4%? '.Mi. At wliat rale will a sum of money double itself at 2A%? '.•7. In what time will Ssl-Vi amount to sltH) at 2%? lis. What i.rincipal will ;five s2().(K» a week at 4°;? '.«». What principal will <;ive a monthly income oi SWX*) at 2%? at :?% ? KHI. Kind the interest on .^lO.dO for 2 months at 4%. 101. What is the inten'st of f2(X», f..r :! months at 2.1%? 102. What is the interest of .•*<«) for 4 months at ;ll%? id;!. What is the aiiioiint of $4(1 for 2 years and (> months at 6%? 104. What is the amount of $0(1 for 1 yeai and ii months at 8% ? 10.">. What is the interest of Sb") for 10 months at 12% ? 1(H). What is the intere.-t of .<(> lor 2 years and S months at (1%? 107. Wliat is the interest of $12 for 1 year and 11 months at .*<% ? 10«. What is tiie interest of |2.j for 2 years and 8 months at 0% ? 10i». What is the interest of |1 for 1 month at 7% ? 110. What is the interest of *!<>0 for :i years and x months at 0%? 111. In what time will i?4lK) amount to $.500 at 2%? 112. What jnincipa! will yield ii uh-iithly ii.c--nie of ^«> at .'!%? 11;;. What amount of money must I invest at ('/) 5% ; ('<) 8% ; in order to obtain a luonthly income of $40.(»()? 42 114. \t wlmt rail, nm.-t I i„v..>i l.s.iMHi i„ ,„,l,.r u, ul,|«i,. ..i. aiiiiiml mcoiiip .)f tl(Ki.(Xc.' II"'. Ill nhat tiih.- will a-uni.>f iiioiifv d..uh|.- it-,.|i at cm L'.'. ■ >l.):\V' lUi. Ill Wilut tillH- uill |!4(» yi.'i.l SL«.UI intflvst al 1.'. 117. What iiriiK-ipal will \ iel.l $.-.(Ht ,.v.tv » y.-aiH ai s " IIH. Il,.w n.nri, ,„„., | i„v..M at 4 , tn ^H a .i.-ni-annual v.r.;,r .,f $.:.>( I. ( HI' 11". Unw miiHi rn.i.t I inv.H i„ ^-.., a .,t.arl..rlv inn.iip. oi s- Aim, ,( | can gt'M'.y , lui r.iy i lev .' J:i<». What is till- iiit,.r,.si mm ^4i)r,() lur :.' inunih- at (. /.' EXERCISE LXVIII. ('(»\ri'()lM) INTKKKST. Find tlic CniiiiMnind Ininvst mi : I. I'lOO fur J years r-i (-i i 4 , ; , I,) r> ; (,., (j--. -'. f400 for -J ywiis (» (.() :. ; (/,; s J ;' {,■) 10°. 3. $l,0(m f,,r;! years (tji (,i) r. ; (/,, iij- . (,.) [ji '_ 4. $l,.".0(i for 2 years (()(. „.r 1 year O. („) 0; ; (A) ,s ,. i,.,..,,.,^ ,,^,,.,^^,,. ,|„^,,,,; _,, • J. W luu is tlic -liilVn nee bef,,,.,.,, the .-»,;,/. a,„l .he <■..»-,""""/ ntere^t nn $MHI i,,r::y.Mi>at 6„? 10. WhM is th, , lilferei.ee In'twe.-ii ihe .nn/.h ai„l the cmno / Merest oil ijJl.L'iMi f..r L' years al 5 ;? 11. lfa«-nnois|5^.on^^..,,.ail,.we,ltoaeeum,.lateate..nii,„un,iM.tere«t Iorl()y,.ar.sa. .i,e rale uf .-, , what w.,„l.l U- the total am..:,nt of m.Plley at the eii<[ ,,f the |)eri.,(l? 12. Iiiiii the .•on.i.o.11,,1 uiieresi ..i, $2,000 t„r L' veai- at (<(, • • (!.) n ' • (c)7,. ^ ' -■ >^>o, EXERCISE LXIX. i'|;i>i;nt wnimr .\,\i» i»iv(oi nt. I'lild th' I'r.'seiil Worth of : I sJK) due L' years hciiee (•' .'1%. s:;i."> due r. .cars lieu -e <>• -J.'."^. '■>. .■<7.") iu-e Oi !()';;. 4. .'s.VJS due ;; years hiiiee (" .t'^. o. .--4.S.').0J due ;> years hence f", ;! ,^. *>. :^I ,(».')(» due (J mouths heiiee (," 10%. 7. cK! due ."> inoiuhs in-nee f" 4v. 4:1 H. !!i.'>12 iltU' 21'.t .lll>;. l.'IKt' (-1 4 ^ tt. :* "lay.*" Iifiico (", 2)%. Kind tlu- I)i«iiiiiit >>ii : 1 . Sio (lilt- ill .'! luniitli- ('• I'',. 12. S14('».li)iluf in ■) (lays (■• .'> ,. 13. S22.»iH iliu- in 4 yt-ars (-/ 2%. 14. .SM>t> iar> '" 4 IS. If 1 ufif|)t sl.iKNtiii pii^ni.-nt Ml a.!.tit..f -l,2uiit ilo I allow '.' Ui. If 1 acct'pt S.-.0 in piiyiiii-ni nf .l.'l.l n( >."..();) ilu. Jl >'-:ir- n.'ni.-, what di;unt :il in pavini-nt oi a ilolit ..f >:;i>".. an.l .ill' a a .li- ■ 'int of .'> _. vv hen i- till- iifl>t "hii' " EXERCISE LXX. I'l.lICKNTAdKS AMI AVKKAdKS. 1. What is 2 (if I'/i >2(Kr.' i/.i >.-.ih)' i. 1 -I.T.'.n? c/i .-.',.".Mtr' •1 What is;; ul (,/is|.-.ir.' /')S42(I/ lr)s-7.")(i? 1./) -s.V. ' ;{. What is 1 ..1 (<'» >4.'>t>? (',)S4sti? ir)S7-V.? (.^(>7'>n..M) ■.' 4. Wiial is 2i nf 1-0 s22n.(Ki' ('.) .<;.')ii.iMr.' in >44I).(hi? ,,/) ,-c,i1(..ih( .' f). What is:;: , ui i.ii >4:. (Ml? I'o .-.".(i.iiii? |,-| >•■,.-..( hi.' !./i >:i..tN)? i»l ;>;S.'i.(Xi '.' «. What p.T .vnl. is 1.(1 2 oi .•.'.' (/-i :;..t ..•' i.-|4 ui s? |./i 12. .1 liH/i. 1 ITi 1 • What iKTCfiii. ix i. four [M-r cciil. '.' y. Find th.' niiinhiTuI whirli ciKi i- :! p>'i cent.; r 1 t i- iL' [..r (•.•nl.; {c) 2.') is ."i per cunt. 10. What [KV cunt is („i !, of !, ? ('.) I of ! ' (-■) * ..1 ' "'1 of ; '.' 11. Find tiu' a\fiaue of (.0 4, 7, 8. !> ; l'.| 12. 2-.. :!4, 4s ; i,-i L".. 2(', ■".(•. •.»'. 12. If .\. lias ^ 1(1. (Ml, 1;. ,>;2.">.iHi, r. >:;(i, 2il the lu'.M, IS tiie iic\t. 1'. iIm next. 20 the niNt ; wiiat was my .iaily iiverajre'.' 14. The niinilx,T of boys a school increases froni l">t' t.. 2.sn : llnd the increase \n-r cent. 15. llie population of a city is l.-).(H)ll. When it has increase.i mm 4(»:; ; wliat will be the population'.' What when it has increased l'-) 75%. ]( 17 18 25. 26. 27. 28. 29. 30. 31. 32. 33. M. 35. 3«. 37. 38. 39. 40. 41. 42. 21. 22. 2,".. 24. How much i.s 5% of : ia)S7.^0, SSJyO, $<».20, $10.50? ('>) j;l50.00, 5^255.00, $8,400.00 ? (<■) 3 inilei^, 5 furlongf!, 75 yds.? (d) 25 lbs., 3.50 lbs., 5 tons? How imich is 2i% of : («)S7.00, $]0.(X), >;12.()0, $25.00? (/') $45.00, $(18.00, $96.00, $150.00 ? (/•) 20 gals. 5 quart,«. 160 pts. ? $5.00is20%of l.owimu'h? $6.W)is25%ofwhat? 3niile.sis;i:;^%of what? 27 is 45% of what number? 44 '• How mu< h percent, i.s : m l«)4 ceiil.< nf (iO centw •.' ('')36c. of .•S2.25? (e) 9c. of 75c. ? ('/)56c. of >;!.50? (<-) lie. of .•<.5,5.00? . What jier cent, is : 20. (a) I ft. () in., of 1 yd. 1 ft. ? (//) 3 yarcl>' (»f 1 p(,]V ? (c) 2 poles of 1 furloni;? (d\ 5 tents of 25 centa ? How much pt-r cent, is : (a) 7 mts. of ^ ^ ^' A certain tradesman ha.s a 7 lb. weight, which is i m. light • wlmt IS the iwrcentage of his gain " ^ ' * If I give only 198 Ihs. instead of 200, what percent^e do I gain ■> I sell c;ertain goods on commission ; on one transaction oTio I han,e .;/. on another of S55 I charge ,i%, and a third of $75 I cha^ 10^ How much do I get all together? ^ What part of a number is 25%? :wy> 40"/" V)"/'' "°"> What fraction of a number is 33^%?'°6/%•'" What part of a number is ]%? ,5°/-' 7.'"/" 1'>V/^ °-!7r»/ v ' ■i of a numljer is what per cent.? What per c^nt is („) --, ; (/,) ^., . ^,) j ^^^ ^ ^ number' Whatis;{J%of$100.' Of $40? ()f.S75' OfS85o »* ""™'^'- • Wliatjis 2^. % of $200 ? M 1 of $<}0 - ' " ' What is 3i% of $90? Of .$.50? of.^iy Of $150 > Of^tUO" What is ..% of ,100? Of,275? Of i«i«0 ? Of ,7.50 ? O^,900 ? 45 43. 44. 45. 46. 48. 49. 50. 51. 62. AVhat isi%of825()? OfiriKiO? OfSl.()()0? OIslUXMJ? OISS.'.UO? "What in i% ot $240? Of ^.S0? Of .s:52()? WhatiHi^%of S2? Of 87]? Of SI ? Of>!i? Of 812? Tea is f-ellinfr at 78 tentg a poiiiul, wliirli is an ailvancc i>i 4'. on former pric'e.>^ ; wliiit was tlie former price? A mercliant, in lu'cil nf money, sold goods for cash to the aiiioiintof $8,0()0, and thereby lost 10% ; wliat was the cost of tiie soods ? Five shares of stock were sold for 84S0, which was 4;; discount ; what was their par value? How much merchandise must a commission merchant sell, at a commission of .">%, ti' uain ."i-dO? The attendance of a certain school lias diminished by 40, which i." 10% of the number on the roll ; w hat was tlie number on the roll ? In a company, 14 men were killed, which was 20% of the company ; what w number in the company? In a spelling lesson, 24 words were misspelled, and these were 16% of the words in the lesson ; how many words in tlie lesson ? EXEBOXBE UCZI. INSUR.\NCE AND TAXES, ETC. 1. Find the amount of premium payable on a stock of $5,000, if insured for m% of its value, at 1.]%. 2. What premium must 1 pay to insure a hotise worth $8,000 for 3 years, at ^% per annum? 3. I own a houst^ worth 810,tK)0, and another worth 812,000. I wish to insure them for 75% of their value. What will be the premium payable at i}%? 4. A merchant possesses 88,0}«ts lt> pay a tax of 8 mills on the dollar. AVhat is the amount of the tax? 7. An estate worth 815,000 pays taxes to the extent of •"> mills on the dollar for school purpfises, and general taxes to the amount of 4% of the value of tlie estate. Find the entire amotmt of taxes paid by the estate. 8. A parish wishes to raise a tax of f5(X) for school jnirposes. if the total value of taxable property is 5;15er annum. He insures his stock and fixtures a. aimnmiuiuf U% to the extent of .S0% of their value, ami his store for .o , ..t its value. Find the total amount he pavs for insur- .nice and (axes. " What is the duty on 50() lbs. of tobacco at 7 cents per lb " What is the duty on 5(X» ,^.llons of wine at 7n cents per gallon V w ■! ;en;';;r'n::;" ' '"""^ " ^"^'■- ^""" ^■^"♦"'""■^ --''^ '^- «^ Find tlie total amount of duty pai.l on 500 yards of cloth worth 80 en 8 a yanl. (he ad valorem duty being 10%, and the specific duty M» cents jier yard. ■^ fM paid M/N.njfordn(yu,.voo,l> worth >:!:,.U(., lind the rate of What is the n,y income did 1 pavV ^;;;:j;;'r''''^ '"'■' ' '■="' '"f^-^--^;'-v...nchhadi iL™ ..s'r'r'" ''";■" "' '''''""" '""' "'^^' ^""^ '••"'P'^« «re MX.n as a .lozen, wluu percent, profit does the retailer make if .tr, :.;;;;; -:;";;s'7;t,"' •■'".■ ,"'- "--' - - ■-' <-^. I-!..!. !.„^i,.)ok, itU ,s .soid here at .•;il cent.>-, aiiowing 207 for duty fl-.d freight, an.i reckoning 2 cents as one penny ? 47 EXERCISE LXXIII. COM.AIISSIOX AND P.UOKERAGK. l'';i.'l llio Coinmisi^ion ,%. •4. $7,r.(»U('<;(<0i%, ;%;('•) .75%. Ti. W'liiit anioiiiit (if iiioiiey was invcf-tt'd when tlio b»•!)k('I■■^' charges ® i%c:iiiieto81.'.).00? 6. I cliarged S4M} brokeiaire at tho rate tpf •]% ; what was tlie amount involveil ? 7. f!<)l.1 S4(K>,(HMI worth of hojuh at a comiuission of 11% ; how much did I make ? S. An agent collect-s rents at a connnission of -4% ; lie earns S44(); how miu-h tloes he collect 7 0. 1 receive a consignment of wheat froni a customer, with instructions to si'li it 111 a commissi, ,n of 11% and invest the proceed.^ in |.ork, after deductin-; a new commission on tliis transaction at 2%. I sold the wlieat for S'2,'M) ; what was my total commission '.' EXERCISE I.XXIV. I'lIOFJT AMt L(»SS. 1 . If I huy an article for s4.(X) and sell it lor («) .S4.7."i, what is my gain percent.? What if I sell it for (/-), ■<.'.. .")(), 2. I I'liy an article for s.l.tXi and sell it for (<() >4.")(), what is the gain per out. ? What if 1 sell it for ('-) fr.'i.tX)? .'!. If I liny f:oo(ls for s7.(K). and wish to make L'.")% {irofit. how must I sell them? 4. I can l)uy a certain article at .V. ; if 1 sell it for (Is. :;d., what is my gain per cent. ? .'). Advance .•sS.OO hy t'M •_'(•% ; (/.) 2.">% ; (r) ;!(»", ; {,!) 40%. 6. If a iradesman marks hi-< prices ;{(>% above cost price and allows a customer 10% off his hill, what prolit does he make? 7. If h\ selling goods for .'SKiO I l,,se 20%, for how much must I sell thi'm to gain 2.')%? 8. If 4u yds. cloth 1k' sol.l for ,SH().(I0 and 2."»% profit is ma.le, how much did the elotii co-t '.' !». In -elling certain goods the manufacturer allows rm^ and 5% off for ca.-li ; how nuich per cent, does he actually take off ? 10. From .SI.-.0 take off 40%, !.->% and 5%, consecutivelv. II. Fn.in <:\m take off ;!0%, L'0% and 10%. 12. From y7.")0 take off :'.0%, 20% and 5%. it 48 13. If 10% b<' gaiiunJ by selling a piece of land for S.S2r>, wliat would I liavfc to f-ell it for to gain 12% ? 14. A gr6cer mixes 100 lbs. tea (<< 40c. a lb. with 120 © 4.V. lb., what must be sell the mixture for to gain (a) 15% ? (h) 20%? 15. A barrel of sugar contains 3l»t) lbs. ; if I buy it Oj 4} cents a lb. .ijid retail it at 5 cents, allowing 10 lbs. loss in weigliing, how much (n) actual profit do 1 make ; and (h) w hat percentage of profit ? 16. If I mix VA lbs. tobacco («; 75 centH a lb., with 15 lbs. fi tK) cent", how nuist I sell the mixture so as to makeaprofitof (a)2»»%?(6) 331 ? 17. If I loise 4% l)y selling goods for !?o2.80, what must I sell them for to gain M 10%? ('-)12%? 18. A person in India has a bill of jEoO to pay in England. If the rujiee is supposed to be worth 2s., but if the value of it has declined 40%, how many rupees must he send to cover his account ? 19. A merchant bought 30 bbls. of coal oil, each containing a!i average of 45 gallons. The loss through leakage in 10% of the barrels was 5% ; in 40% of their number 4% ; in the remainder 2%. If he paid 15 cents a gallon, at what muit he retail the oil per gallon so as to make a profit of 25%. 20. If 2% more is gained by selling an article for JfiUiS than fur $\(>'}, what wa.s the original]"cost ? 21. A grocer mixes .50 lbs. of tea worth .^ cents a lb., with 40 Ibw. worth 40 cents a lb. If he sells the mixture at 45 cents, what percentage of profit does he make '.' 22. If by selling an article lor ,'^5(i, 2% more is gained than by selling it for !*.>5, what did the article cost ? 23. If I mark my goods 40% above cost price and allow a cash discount of 10%, what i)ercenlage of profit do I make? 24. The cash discount of 5% on an article amounted to 45 cent- : what was the price of the article ? 25. If I received a discount of .'Si .25 on a bill of Sld.OO. what percentage was tiiken off ? 26. If I buy goods for JE400, and sell them at an advance of 12i°:, how much is my profit? 27. Take 4% off (a) 85 cents, (h) S\ .10, (<■) $2.50, (H) $15.00, (e) $17.50. 28. Take 6% off (a) 50 cents, (/.) .'?4.00, (c) $5.25, (rf) i^\.50, {>■) $25.00 . 29. Take ]% off (a) $1 ,000, (/-) $2,800, (e) $3,000, (rf) $50,000. 30. What is i% of (a)S5,000? (I>) $6,000? (c) $10,000? (d) !t;25,0K .i.S^'J, -'0%, 10%, 0%. 36. From $125 take off 20%, .")%, 2%. 30. From $72 take off 3:!:',%, 25%, 2%. 37. From $160 take off 20%, 10%, 2i%. 3H. From $85 take off 20%, 2%, 1%. 3!». A merchant marks hiw goods at an advance of 40% over cost, and allows 5% for cash when sellir.g. What actual profit does he make? 40. If I mark goods at 50% over cost price, and take off 25% for cash ; what percentage of profit do I make ? 41 . If 1 lose 5% by selling goods for ijao.OO, for how much should I have riold them to gain 10% '.' 42. If I buy goods for $.S.(M), and sell them for $9.00 ; what percentage of profit do I make? 43. A coat was marked SI"), but the clothier took off «% ; what wa« the amount of the deduction ? 44. A merchant bought 300 pineapples, but, on examination, fountl 16% of them spoiled ; how many were lost? 4.">. A grocer purchased a bag of coffee at 40 cents a pound ; at what price must he sell it a pound in order to gain 10% ? What must hv sell it at to gain 25% ? 4C.. If a piece of broadclotli, containing 30 yards, cost $5 a yard, for what must it be sold to gain 20% ? 47. X merchant finds that a lot of goods, which cost $60, is damaged he sells them at a loss of 15% ; what does he get for.them ? 48. The price of a book is 80 cents ; but, being sold to a friend, a diecoiuit is made of 20% ; what is paid for it? 4y. A grocer bought 10 barrels of Hour, at $5 a barrel ; what must they be sold for to gain 25%? 50. A piece of cloth, which cost $45, is somewhat damaged, and is sold at a discount of :r>i% ; what is received for it? 61. If a grocer buys sugar at 4'. cents a pound, and sells it at 5 cents; what % does he make ? 52. By selling goods at |2.()0 I gain »)2i% ; what selling price would have given me 70% profit ? 53. If I buy eggs at the rate of 12 cents for 15, and sell them at 10 cents a dozen, find my percentage of profit. 54. If 1 buy oranges at $1.")0 per hundred and sell them at 20 cents a dozen, what is my iiercenlage of profit? 65. How much water must be added to a gallon of wine in order to make a profit of 20% in selling the mixture at 10% over cost price ? 5t>. If I buy sugar at the rate of $4.50 per cwt., at what price per lb. must I sell it in order to gain 10%? And what percentage of profit should I make if I retailed it at 5 cents per lb.? .57. If I buy cigars at 6 cents each, and retail them at 3 for 25 cents, what percentage of profit do I make ? 4 i i\ 50 .")S. 5!'. (K). (il. «2. (i3. (;4. (>5. 5.10. 4 20, " •' 5.24. 3.75, " '• 4.50. 8.00, '• It.OO. 12.00. " " 10.00. 23.4:{, " •' Ml. 24. If I lose 10% by selling an article for tl.so, lor liow much filioiild I have sold it to gain (a) 15% ? {h) 25% ? If I lose 10% by selling an article for $5.s5, loi- \u<\\ much should I have sold it to gain («) 20% ? {!>) .50% ? If I lose 20% by selling an article for $:J.(i(l, fm bow much should I have sold it to gain (a) 5% ? (/<) 10% ? If I gain 15% by selling an article for $s()..tO, what selling price would have caused me a loss of 10%? What iiercentage of profit i.s made on the sale of the following ? (a) Purchase price $4.50, selling price $4.95. (b) " (c) " id) •• W " (/) •• (9) " {h) " What percentage of profit db I make in marking good.x ,^0% above cost price, and then d(>ducting for ca«h, (")5%? (A»)10%? (r) 15°' * id) 20%? What percentage of profit do I make in marking goods 40% abf)\e cost price, and then de) 5%? (r) 10 '' (>/> 20%? What per cent, is (n) 2A of 5 ? (/<) 3 of 10 ? ( c) 4'. of 45 ? (d) 3J of ;J2A ? («)4}of(«i? What per cent, is (a) 3 oz. of 4 lbs.? {!>) 2 oz. of 5 lbs? (c) 6 oz. of S oz.? (d) 15 oz. of 1 cwt.? (e) 150 grains of 5 lbs. (Av.) ? What per cent, is («) 3 pence of (i shillings ? (b) 4 J pence of s shillings? (c) 3i pence of .3s., 9d.? (d) 5 shillings of £3 ? What per cent, is (o) 5 inches of 5 yards ? (b) ti inches of 6 feet ? {c) 12 yards of 1 furlong? (d) 1.50 yards of 5 furlongs? (e) 80 yards of 2 miles? (/) 15 feet, ((inches, of .!() yards? (fi) 12 feet, 8 inches, of :V\ yards ? EXERCISE LXXV. STOCKS A\D SHARES. Find the face value of $4,200 worth of stock in the 3 per cents. ® 84. $(},320 " " " $12,740 " " " " $11,550 " " " " $13,780 " How muoh stock can be purchased for : $4,300 in the 2 per cents. ©86? $25,480 in the 4 per cents. @ 91 ? 2 4 6 6J 79. 91. 105. 106. M, <) 10. II. 12. I.'!. 14. 15 I'.t. 20. 21. 22. 2:;. 7 per eentp. 0^ 120 V •') per centfl. fn\ 120? 24. 2.5. 20. 27. 2«- :jo. $12,640 in tlie .'i per cvutf. Oi) 70 ' . £9,790 in the .3* per cent,«. (/',, 80 ? What income is obtained by investinj: : $41,.310 in the 4 per cents. (», 102? $7,035 in the 5 per cents, at lOo ? £5,625 in the 2;^ p ? I sold out ,*40,000 of 3 per cents. (TA 08 and invested the proceeds in company shares dr .56, paying 2% ; find the alteration in mv income I sold out So.OOO of 2.] per cents, at 101 and invested the proceed^ iii 7 per cents. (?) 2.50 ; what alteration was there in my income? If a 4% stock is at 112, how much money must I invest in it in order to obtain an income of £600 ? Which is better, 6 per cents, at ia5, or 7 per cents, at 122.1 ? Which is better, 2.1 per cents. @ 05 or the 10 per cents, at 360 and what would be the difference in the incoLie given by inve«tin" $34,200 in each ? A city issuing bon%. EXERCISE I.XXVI. DIVIt<10X INTO PKOPOHTIONAL PAHTS. I. Divide (JO in the proportion of 11 : 1». -• Divide 120 in the proiwrtion of 5 : 7. 3. Divide |78 among three boys accordinn to tlit-ir respective ages, which are 11, 13, l'>. 4. Divide $860 among A, Band f, s<. as to give A ;■ of BV share and C J of A's share. '». The length of the sides of a four-sided ligure are as 4, .">, 6, 8 ; tht- total length is 80 ft. <> in. ; find the length of each side. fi. The representation of :{ towns is according to population ; the lirst has 480.000 inhabitants, the next 120,000, the next :«)0,000 ; between them all they have 8 uienibers ; how many hsis each town ? 7. Of the population in a village i are Methodists, 4, Episcopalians, | Baptists, i Roman Catholics, and the remainder, 146 people, are not classi'ied. How many people are there in the village, and how many of each denomination ? 5. A bankrupt owes A 1?55, B |t)0, C §150, E $S:iO, F $400 ; he possesses $609 ; how much will each creditor receive, and how much does he get in the dollar ? II. In making a certain compound a chemist takes 4 parts of one salt to 3 parts of another and 5 parts of third ingredient. How many lbs. of each must he take to make up a total of (a) 40 lbs.? (i**) 48 lbs.? 10. Divide £19.10 into an equal number of sovereigns, half-sovereigns, crowns, half crowns, shillings and sixpences. 11. Divide £5.15.6 into an equal numl)er of half-sovereigns, crowns, shillings and sixpences. 12. A legacy was left to be divided among 4 i)eople in the proportion of 10, 9, 5 and 3 ; the share of the last named is £360. What is the amount of the legacy ? EXERCISE I.XXVII. PARTNEKSHIP. 1 . A. invests $4,000, B. $5,000 in a business ; at the end of the year the profits amount to $9,900 ; what is the share of each ? 2. Three men enter into partners! dp ; the first contributes $1,000, tlie second $1,500, and the third $1,800, and at the end of 6 months they take in a fourth partner with $2,000. If the profits for the whole year are $o,830, how ought the money to be divided ? 10. A. puts 4 cows into a pasture for .» monthn, B. puts in 5 for 4 montiif. V. puts in 2 for 3§ months. If the rent of the jMisture is SlS.fiO, how njuch ought each to contribute '.' Two men engage in a piece of work for wiiich they receive $(iS ; the tiret works 8 hours a day for 10 clays ; tiie second works 10 hours a day for 9 days. How much oujjlit eacli one to rtjceive ? A. and B. enter into partnership, .\. contributing S;{,500, H. $4,000; after tliree months they admit ('. with $;!,000 ; at the end of six months more A. witlidraws $1,000 and B. .■«2,000. Their total profits amountint; to .<<,70() by the end of the year, how ought they to divide them ? A. and B. rented a field for 12 months for £3.3.0. A. puts in 3 oxen for () months and 4 slieep for 4 months ; B. put* in fi oxen for f> months and 5 sheep for .! moiitlis. If tiie oxen consume twice as much as the sheep, how much ought each to contribute towards the rent ? If two jiersons purclia«e a house for .SlH.tKX), and agree to let it for 3 years at a monthly rental of .s")0, how much ought each one to receive for the entire period, A. having contributed $10,000 towards the purchase money? A. begins business with SI, 000 ; at the end of 3 months he admits B. into partnership witli .^WX) ; after another 2 luouths C. comes in with $1,000. If the profits at the end of ;i.5 months are .•fl,730, how- ought they to be divided ? If 3 men have joint ownership in a mine ; A. having 3 of it, B. i, and C. the rest ; liow ought they to share in the lo.«ses on the working expenses, which amounted in one year to $2,020 ? A., B. and ('. join their capitals, which are in tlie proportion of \, \ and } ; at the end of 4 -uonths A. withdraws half his capital, and t the end of 9 monthj more they divide their jjrofits, which amount to $5,025: what should esich receive? EXERCISE iJXXVm. .MKASURKMENT OF AREA. Find the area of rectangles with the following dimensions : 9. 5 meters, (J centim,, by r,T 5 feet by 4 feet. 6 feet by 7 feet. OJ feet by 7} feet. 3} feet by 2^ feet. 5 ft., G in. by 7 ft., 1(» in. 3 yds., 1 ft., in. by 2 yds. in. 15 yds.. 2 fr.. 10 in. by 5 8 in. 3 meters bv 4 met«iv. II). centim. .'< kilometei-s by 7(X) meter!-. Find the area of squares liav- ing sides of the t<,l!. wing lengtlis : 10 11. 12. 13. 14. ir>. (a) ft. (a) 9 ft fr C Jft. ;')12Jft. (''.) 15 ft (c) 3 yds 2yd: , 2 ft,. iin. (u) (> me,.'. • (ft) 70 meters. 8 meters, 25 centimeters. "i4 IS. 1!'. LM. •J4. 2fi. 2(1. The area of a mtaiiplo lieinjf .'>!».'. iVi-i, aixl iln- lfii»rtli :!."> feet : what i« the breixhli ? The area <.f a rettanjjle i> \M> «.quan' tc»'t, .Ml im hew ; llie bn>adth iH ;$ feet, ;! inches ; wluit is tlic lenifth? \Vliati«th»- length of the sides* ..f tliewiimn* havini: the fi.llowirin area« : (a)!>feet; (/.) 25 ft>.t ; (n Mi feet ; (./| KNi in.: (, i I ft., 1 12 in.; 0") 1(H) square meters? ta) ti feet, ;!i> hi.; (/<) 2 s«uiare yds.. 2 ft.. ."Mi in.; ir) I.ITHgqnare ydf., 7 ft.; (r/) 1 acre ; (c) 2A acres? A rectanjfnlar Held is '>() yards U>un and :!(> yards wide ; what is the distance from corner to corner? .Another is 80 yards Ion); and m yards wide : what is the distaniv from corner to corner? Another is 1(V) meters Jon^r and 7.". meters wide ; what is the distance from corner to corner? < Tlie height of a square huildinu is To feet ; the length of the base in 40 feet ; wliat is tlie area of its four sid»'s ? Find the area of equilateral triangles with the followinjj: sides: (a) 1 in. ; (//) 4 in.; (c) (i in.; id) 12 in.; (,-) 1(1 in. Find the area of a riRht-angled triangle, tiie h vpothenusc of which is () in. long, and one of the sides "> in. Tiie area of any triangle can be found bv multiplying half its vertical height by the length of its base.' Kind the area of the following triar >8 : («) base (i in jrtical height 2 in (I,) " «) ■ .. " i '• (c) " 12 " '• H '• Find tlie area of the following figures • N A / 8.. ; / »» 12. N^ «• X 28. The diagonal of a square is 2.") meters ; what is the length of it.'* .sides ? What is the length wnen the diagonal is I ft."' 29. The diagonal of a square is 9 feet ; that of another square is 15 feet ; lind the difference in their areas. M U). ::i. •■14. ;«. o(l. ;{7. 39. Themdouf ii sqiian* in 12 inches \oini. How long muct the Hide <>i' a square be, tho area of which in four time!' att larjie? Another fix tinieN as largo? Twelve tinit-M an large? What is the area of a circle inscribed in a eqiiare, the wide of which ineahures 4 InilieM ? What is the ana of the eircniiiM'riU'd circle ? Kind how many yards of carpet, :!4 inrlies wide, will l)e required foi rooms, the dimennioriH of which rre : tf«) 20 feet by Hi feet ; (A) 2"» feet by 20 feet ; ((;) 12 feel l>y 10 feet ; \d) 12 feet, (l inches, by 10 feet ; I,' ) 1") feet, ft inches, by 12 feet ; (/ ) 1« ieet, t« inches, by Iti fe«'t. Find the exijcnse of cari,etin>{ a rttoni the dimennions of which are 12 feet by 10 fe«'t, uitli carjK-t :!•> inches wide, («. 75 cents per yard. Another room Hi feet by II feet, .1 inches, with lairiK't 27 in inches wide, the len>;th being 120 feet? Cost of cari)et jil.OO a yard. The costof carjietinga room 21 feet long, \!^ feet wide, with carpet (<»'. 50 cents a yard, w K!.').(Kt ; lind the widtli of the cari^t. How much will it cost to provide car|)et8 for rooms of the following dimensions, with carpet 27 inches wide, (n *'■() cents a yard :— (a) 12 feet by «» feet ; (b) i:> feet by 12 fe<»t ; (r) Hi feet, 8 inches by 14 feet, '■'> inches ; (} lengtli 10 feet ; width "4 Ieet inches wide, fr 15 cents a roll. (c) length 18 feet ; width 15 U-t-t wide* (si 20 cents a roll. (fi) length 18 feet ; widtli Iti feet ; height 12 feet ; paper 18 inches wide @ 25 cents a roll. {e) length 20 feet ; widtn IH feet ; height 12 feet ; paper 20 inches wide, ("; -HO cents a roll. (/■) length 18 feet; width U> feet ; height 12 feet; paper 18 inches wide, @ 20 cents a roll ; there are 3 windows, each 6 feet by 3 feet, *> inches, and two doors fi feet, (> inches by 3 feet, <> inches. if M *). 41. 42. 4:1. 44. 45. 46. 47. 48. 49. 50. 51. .-42. 64. F^nd the c.>Ht of jmintiiiK tlu- Hrior of a r.»„u IH fe«.t long lA fet-t wid..; the paint costH $l..V)a umllon. an.l ..„,. umllr.n in Hufilcient t.. cover 200 Hqiian> feet. Another r.K>in 20 feet lon«, Hi fe,-i wi.le ; (mint i-.«t^ $-2m a ^U.,,, How many Hquare.ile.. 4 inch.- H.,„an.. will U. m,uir,.d to cov.ra floor JO feet by l«i feet, an.l what will |,e flu- .ost fi 15 cent* each A «,uare court-yanl, 40 l-et square, i. to Ik- ,m.v.. anls ion^ an.l I.-.0 yards wi.le : what len^h must be added that the area may lie 7 acres ' A field :m yanls by 200 yards .-ontains ho« main acres V A field is one acre in extent; ..ne ..f Us .i.les is 121 yards l.>n- : w hat is the lenjrtli of the other '.' A piece of land .S.5 acn>s in .-xf-ni i. ,o Ik- s..ld at the rati, of $2.7.) p.>r square yard ; what is tiie value ? A piece .>f land 700 feet long wiis boujrht f.,r .S<«.Oa».00 at the rate ..f 60 cents per .square foot ; what was th." wi.lth of the land? Lun.ber is sold at a certain price - ,,^ thomnndr meaning a thousand square fet^t of lund^r 1 inch thick. What will f« the c.,«t of 1(X1 boards 12 feet \o^^^, I0 inches wi.le, 1 inch thick, at $1K..H> per thousand ? What will be the c<«t of 5.5 Iwards 10 iWt Lmp, I foot wide, 2 inches thick, at $22.00 per thousand ? For building a flat r.>ofed shed 25 fe.t long, l.i feet wide, 10 f.-et high, the lumber is quoted to me at $2<.per M what will the wood coet n,e? The floor is to be lai.l with 2 inch board.- ; the rest « ill be of one-inch boar.ls. There will l.e 2 windows. 4 feet bv <> feet k inches, each cosUng $1.50, and the door, whi.-h n.easures 6 feet bv 42 inches, will cost .fi.OO. are I. •I 1(1. 11. IL'. la. 14. !.■>. l«i. 17. l.H. 1«. ;t tei't, J feet, 2 t». i. 4 feet, ;; lift, l\ feet. Sfeet, 4^ f.-et, .1.25 ftH. ilow main Itriekc S inclici •20. EXERCISE UCXIX. .MKASl'KKMKNT oK SOLIIMTV. Und tlie ciihifcoiiifiiisoi' n. taiiirnlur^ .litl>'>»f which the «liii..ntii„ns iw followf) : ». 7 ft.. ;; ill.; ti ft., 1' in.; •"> II.. H in. "'. .t yard.k^, i yard, I.s inclic. • '. IK ytiitls. .'ivarilK, • feet, »i in. i'liii.'. 1 iiKliry wide,.'! iiichfs thick, uiji be required to build a wall 4ti it',.| |on,f, 10 iV.t hitfli, i i..,,t thick ■' How umny bricks of the satm- sizti for a wall. Km tVcr ...ug, 12 fwt high. <» imhew thick, and wlml will he i!i.> cunt f- --"..I'.'-a thousand? How many cubic yard.x oi earth can, be e.\cav:n.ti in.ni a plot of >frouiid 500 feet long, .'KMI tVet wide, by Koiiij; li. l.j.th ..f li feet / .■\ tank lOO feet long, .50 lect wiiK , f, f«..t (lct'|., ij- lijl-d with w^t. r ; liud its weifflit. (,\ cubic loot of water weighs I .hi .,/,.» A tank 100 feet long, fiO f«'ct wide. S iVet d. • f i- (ille.1 at the ra«e of 20 gallons per minute; how lonjr will ii to (ill/ (.\ pint -.f water weighs a pound and acinarter.i A piece of wooil, 1 foot tl inches Mpiare, conlam- :.'[ cubic feet ; huw thick is it? A piete of woor ti days can e.\cavate a caiial IftO yards long, ».5 feet wide, (i feet deeii. how manv davs of 10 hours each must 400 men work to excavate a canal LW \ardfi long. .'!0 feet wide and 8 feet deep? A vehsel 10 inches long, K inclies wide, li inches deep, is full of water; how many inches will the water be reduced if 1 pint is taken out? How many cubic inches of water can be jmt into a vessel 10 incheo long, inches wide, li inches deej., at th.- Iiottom of which is an iron ball 2 inches in diameter " What would b«' the weight of a cubic mile of water? How many dice \ inch edge .an b«' put into a box meiusiiring 10 inches, by 8 inches, by f> inches ? A tank 75 feet long, :{0 feet wide, contains ."lO tons of water ; how deep is it? What would b«' the wei^lit of the water if it wen> 12 feet deep ? How many gallons of water can be put in a tank 10 teet long 6 feet wide, 3 feet deep? If the water were 101 inches deep, how- many gallons would iliere be? 21. 4. 5. (i. i . H. It. 11. 12. 13. 14. 15. 17. 32. 3:5. 34. 35. 3. .-> + J- = 7. .") + 3 .r = 2 ./■ + '.». ■■i.c + it = 2.r + 13. 7 x+ 10 = (J.r + 12. 10 .V - 4 = \)x + ::. r> X ~ 7 - 4 X -o. 17 J- - 5 ^ ',) J- + ;>. V2x + ■.) = 4x + V.'>. X -t- _4 — ( ,. .<--7J = iH-:\i. 4.-; + 5 + 3 J=.2x + .•> + 1(1. lOr + 10 + 7.r=r^44. IK. lo-_^-=»L+* (i 8 .-{ 1!». '•+-? 15 + --^ ■1± + 5 3 o«. 5 2 10 L: + 5^=41. •^.+ £=13-5 :: 4 2 20. j: + H = * + _* + * 2 3 4 21. •l£ + 3x=.H + 2i ' 3 22. 4 ij- - 3) = 3 (a; + 4). 23. 7 (X 4- 5) = 5 (« + 7). 24. 10 (a- 4- 7) = 3 4- 5 (* - 3). 25. H2x + :',)-!] (3^+ 7) + ^. 2«i. 3'(5x + 2)-5(x + 3) = 54- fi X. •>7 :5 X 5 11 x ;} 2K. ^: + •'».(•« 4- 4) = :}<>. 20. 4 (x 4- 5) 4- (x + 10) = 90. 30. 3 (x + 5) = >K) 4- 7 (x 4- 5). 30. 3 (a 31. 7(x 4- 3) = 5 + 8(2x= 1). What number is that to which if you add (i. it is 4 times the original numl)er? What number is that to which if .v..ii add 20, it is .=> times the original numlx?r? To wliat number must wc add 78 to ^'i-t 1)1 ? What must one add to 8 ti> }:ct 5(>? If 500 Oc added to n time,-; a ccriain nuinlur the result is 833; what is the mimlxT ? Of what nuinher does the lourtli pan and the fifth pari added together make 180? If the eighth part of a luiinbr be taken from it, the result is 5ti ; what is the nundier? Ii IS be subtracted from the lift 1 1 part of a iiumWr, the result is s ; what is the numlHT? 5« MK The sixtli part of a ihiihIk-i i-xcitds its ninth part by 2; what ii' the number? 41. The fourth part ol h ntiiiiber excfwls its tenth part by 20; find the number. 42. From a certain number 10 is tai8? 44. The half and tlie quarter of a eertsiin number are tojjretlier 12 lefs than the number; wliat is tlie numbt^r? 4."«. What number is o less tlian its iialf, its tiiird and it« fourth added together ? 4ii. A farmer lias 1,5(K) sheep, but food for them for only 31 months; how many must he sell in order to make the food last S months '.' 47. A man has 2 fioeks of sheep of equal numbers. J le sells 39 of one rtock and?t3of the other, andfindsthat the first flock is now twice as large as the s«>cond : how many slieej) were there originally in each flock '.' 4.S. .\ merchant pays' four clerks .s:i2 between them ; the second gels .S2.00 more than the lirst, the third ?^J.(X) more than the second. the fourth .S4.00 more than the third; how much does each get'.' 4'.t. A boy spent 50 cents, then half what he had left, and had tK) cents over ; how nnich had he at first '.' .")(>. Two barrels contained together 440 pints ; after drawing from the tiist ', of its conteiUs, and from the second I. they held an equal (piamity ; how nuich was in each at lirst? ">]. What number is that to which if you add 14. tlie sum is 3 timeh the original number? 52. What number is that from the double of which if yon take 15 the remainder is 55. 5:>. Find a inimber such that the diffeiviice l)etwfen its fifth and >eventh parts is 2. 54. Find a number to the eighth part of which, if 3 be added, the result i^ half the original mnnber. 55. .V father's age is eleven times that of his son ; their united ages amount to 48; what is the age of each? 5('(. A father's age is 32 ; his .son's is 2: in how many years will the lather be 3 times as old a.« his son? 57. \ father's age is 60, his son's is 15 ; how many years ago wa.« the father 10 times as old as his son ? 5S. .V father is 3 times a." old as his son ; 10 years ago he wa.s 7 times as old; find their present ages. 59, .\. has $01, It. has $20 ; how nnich must A. give H. so as to have twice as nnich a.« B. ? i 'I t ! 60. 61. 02. (53. 64. 66. 6«i. 67. 08. 69. 70. 71. 72. imrt of which exceeds its tentli 74. m What number in that the nixth p&Tt by 40 ? Of what number is its half greater than its third by 6? Divide 140 into two parts so that the »,'reater may he equal to 5 times the lesser. Divide 200 into two parts so that :! tMnes the greater part may be equal to 7 times the lesser. Find a number such that the differiMue l)etween its fourth and its third is equal to its tweith. Find a number the different l)etween whose half and third parts exceeds its ninth part by 9. What number is r, leas than the sum of it- l.alf, ita third and its fourth ? A certain number of people had to raise a sum of money ; if each one gave $8 there was .«.=>0 too mm-h, while if each gave .'*7, there waa $10 too little ; how many persons were there ? Divide 4,8(>0 in the proportion of Ij', 2}, ;};|, 2^ The sum of the tenth and fifth parts of a certahi number exceeds ita twenty-fifth part by 13 ; find the number. The half, ti»e third and the fourtli of a certain number added together make 8 more than the number itself ; what is the number? Divide 21 into two parts, so that one part may be J of the other. $135 was raised by A., B., C. and D.; B. contributed $5 more than A., C. gave double what A. gav(>. and D. twicv what B. gave ; how much did each contribute ? A., B. and C. raised a certain sum of money ; A. gave one-third of it and $2 besides ; B. gave one-fourth of it and .'?8 ; C. gave one- sixtli and $10; how much did each contribute? A., B. and C. divide a certain number of sheep between them ; A. has 70 more than the fourth part of them ; B. has 140 more ha.s 112 more than the fifth part; how than the half, and C many does each get? 75. There is a number to the half of which if 10 be added, 4 times the new number is eight times greater than two-thirds of the original immber ; find the mimher. EXERCISE IXXXl. MliSCELLANEOl'S KXAMPLKS. 1 . Twenty-four labourers do a piece of work in 6 days ; thirty otiiei-s can do it in ."> days ; how long would tliev take all working together ? 2. After deducting 4}% discount, a certain sum of money amounted to 1613 ; how much was it at first? til 3. After paying t> d. in the t inei»uie-tax a man iiad £731 .1.3s. a year ; what was his gross income ? 4. A contractor undertalct* to dig a canal 5«)o meters long, 3.(i meters wide and 2.5 meters deep for j:5,000 ; He has 40 men at work, and they dig out a section 2b meters long daily. The earth is carted away in carts, which are 2 meters lonp, .8 meters wide, and .5 meters deep. There is a foreman who gets |2.00 a day ; each labourer gets 80 cents a day : each cart-load costs 2.') eent« to cart, away. What profit does the contractor mako? .'). A debt of $4,000 due on XovemlK-r 28, was settled on >Iay 28 lor J:!,800 ; what was the rate of di.«count given ? 0, How many steps of ■"•O inches does a man take in walking ('() 4i miles? (6) 7 miles? 7. If a man takes 0,!KX) steps in walking b miles, what is the length of his pace? 8. A clock which gains 14 seconds a day, is 2 minutes slow at noon on Monday ; what time will it indicate at noon the following Monday? Wlien will it indicate the right time? it. A man spends $10 less than a quarter of his money, and has left $;}5 more than half of it, what was the original sum ? 10. If the price of >, oz. In- $.4083, what is the priceof .001t)25 of a ton ? 11. If I borrowed from a friend ffiOO for 3 months, for how long should I lend him $4.50 in return? 12. If a man, travelling 10 hours a day. can finish a journey of 2,500 miles in 10 days, how many hours a day must he travel to cover .3,000 miles in 15 days ? 13. A ship has provisions for 80t) i)eople for li> days ; if 150 people more come on board, how long will the provisions last? N. If 15 pecks of potatoes .serve ft persons for 22 days, how long will S bushels serve 5 people ? I'>. If 12 horses can plough 21 aires in It days, how many hoi'ses will be required to plough 70 acres in 10 days ? 111. If 5 persons are boarded for 3 weeks for £17. 10s . how long should 14 persons be boarded for tjO guineas ? 17. If 6 men can dig a trench 220 yards long in 2\ days by working 12 hours a day, how many men will Ije required to dig a trench 440 yards long in 5 days, working 8 hours a day? 1^. If $3,500 be invested in the 3i% at it8, what is the annual income derived ? In. The 3J% are at IKt; ; how much nuist Ix' investetl to produce iin annual income of $1,400? L'ii. What is the price of stock when $8,300 can be purcha.sed for $7,470? --'I. If tea be bought at 2s. Ud. per lb., and sold tor 3s., <>d., what is the gain per cent. ? 1 > 02 -'2. I sold9(» cwt. ol lead for *21»>.0(), ami gained 1:.'.l% on tlie trans- action ; what did it i-ost me jwr cent. ? 2.3. If I own ,i,th of a lionse, worth $3^MX), and it iw insured for .ItlOr) of itH value, wiiat^wonhl i los^e if the lioui-e wa« hurned? '24. \i ejrjts can be bought at tlie rate of "i for 4 cents, how many must f give for 2") cents to gain 25% ? 2'». If gunpowder is composed of Hi parts of nitre, 14 of charcoal, and 10 of sulpliur, how niucli <>f each of these will Ih! required to make a ton of jH)wder ? 20. Two men run a race of a mile ; one of these gains .'> feet in every SO yards ; by how much will he beat the other ? 27. A cubic foot of water weight l,00t) o/. Find the weight of water in a tank measuring 4 feet, (i inche«, by :! feet, by 2 feet ; how man\ gallons does the tank contain ? (One gallon weighs 10 lbs.) 2s. A cistern is 24 feet, 8 inches long, and 12 feet, 9 inches wide ; Ikjw many gallons must be drawn off to lower the water 3 inches? 2!t. What length must Ik- cut off a straight plank 18 inches broad, 2 inches ti)ick, that the piece may contain 2 cubic feet? .■50. If (M) yards of carpet, 24 inches wide, cover a room 24 feet long, find the width of the room. How many yards will be needed if the room is 24 feet square ? ;J1. A can perform a piece of work in .") days, B in ti days, C in :\\ day,-: A and H work at it together for I day ; H then works alone for a day ; how long would C take to Hnish it? 32. A can do a piece of work in (> days, A and B together can do it in 4 days, V and C in .') days ; liow long will the work take if all three work together ? a;?. A tank is fdled by a pipe in ^^ hours ; another can fill it in 4 hours ; it can be emptied by a tap in 10 hours. How long will it take to fill the cistern if all three are open at the same time ? ;)4. If o men, or 4 women, or ti boys can do apiece of work in 24 dayt ; how long will 2 men, ;{ women and 10 hoys take to do the work all togetlicr ? :{5. If a bankrupt's assets are $4,080, and his creditors receive 24 cents on the dollar, what is the amount of his debts? How much will a creditor receive to whom the bankrupt owes $80.50? ;$«>. If 5 !uen can mow acres in 10 hours, and 8 otlier men can mow 12 acres in 20 hours, how many acres can they mow in 1(> hours all working together? ;J7. Divide $371 among A, B and C in such a manner that as often as A gets $4 B shall get $3, and for every $5 B has, gets $6. .38. If 48.0(X) copies of a 12 page paper be printed, each page being ;}() inches long and 22 inches wide, how many acres will the issue cover ? How many copies would it take to cover a square mile ? U3 •'>'.•. A eoldier being allowed 10 lbs. of bread a week, how many Ibe. were required for a regiment of fUO soldierH for the year 1896, and what would be the value at 14 cent^ for the 4 lb. loaf? 40. Montreal being 75 degrees west of (ireenwich, find Montreal time when Ix)n(lon time is (") 5 p.m. ; ('<) 8.30 a.m. ; (r) 10 a.m. ; (ff) noon ; (f) 10.80 p.m. ; (,/") midnight. 41. What time is it in Montreal when London time is (a) 8 a.m. ? ('<) midnight? (r) 4 i).ni. ? (rf) noon? 42. What is the time in St. Petersburg (.'iO degrees eact of (in!enwic;h), when Montreal time is {>i)H a.m.? (h) noon ? (r) 'j.SO p.m.? (d) 10 p.m.? 48. If 4 lbs. of tea are worth 8 of coffee, and 2^ coffee are worth 2 lbs. of chocolate, and 8 lbs. of chocolate are worth i barrel of flour, and flour is S4.r><) a barrel, what is the price of a pound of tea? 44. Divide 1,740 into three part«, such that 4 times the first part, may equal 5 times the sc^cond, and inches deep ; required the length of the edge of a cubical box of the same capacity. 59. If .32 pears are worth 50 apples, and 6 apples are worth 9 oranges, and 20 lemons are worth 27 oranges, and lemons cost 27 cents a dozen, what is the price of 64 pears ? (KJ. A and B rent a field for fllO ; A puts in 40 sheep and B 50, but at the end of 6 months they sell half their stock and C puts in 50 sheep ; how much ought they each to pay towards the rent at the end of a year? 61 . Divide $600 among three jierBons so that A shall have twice as much as B, and C twice as much as l)oth the others together? 62. A and B are partners, having each contributed |2,500 towards their business. At the end of :5 months iheir gain is $1,500, when A withdraws $1,000, and B advances another $500. At the end of another 3 months the profits are $1,200, and B withdraws $800 ; they continue 6 months longer in business, during which they gain 40% per annum on the capital invested. How ought they to divide this at the end of a year ? 63. What would be the difference in income produced by investing $6,175 in the 3% at 65, and in the 4% at 95? 64. If I buy $10,000 3 per cent, at 64, and when they have risen to 69 sell, and buy 3J \^er cent, at 92, what alteration takes place in m.\- income ? g5. If gold can be beaten out till its thickness is but ^ti'sbs of ««» inch, what surface could one cover with a (a) cubic inch of gold? (h) with a block of gold 3 inches by 2 inches* by ] inch? 66. A man whose weekly earnings are $25, lays by 15% of his weekly wage every fortnight ; how long will it be ere he has saved $150 ? 67. I own $44,000 four per cent, stock at 97-1 ; I sell out and invest the proceeds in 4J per cent, at 95 ; And the alteration in my income. 68. I buy a cask of wine containing 60 gallons for $180 ; I keep it for S years when I bottle it in quart bottles. What do j my wine cost me a dozen bottles, reckoning compound interest at 5%? 09. What length must be cut off a board o\ inches wide, that the area may contain a square foot ? If the board is 2J inches thick ; how much must be cut off to obtain half a cubic foot? 66 of room hv jtaint costs 20 feet i ceiitH 70. Find the cost of painting the walls and ceiH long, 16 feet wide, 10 feot and (J inches high ; i a pint, and a gallon covers 200 square feet. 71. What will be the cost of papering a room 16 feet long, 14 feet wide, 10 feet high, with paper IH inches wide, at 10 cents a single roll of 8 yards ? Charge for hanging the pajwr 15 cents a double roll. 72. The telephone poles along a certain road are placed H8 yards apart. If driving along the road I pass one every 20 seconds, how many miles an hour do I drive? 73. Keduce 4 furlongs, 7 3ards, to inches, and express the result as a decimal of a league. 74. A man is to receive $2.00 a day every day he works, and forfeit 50 cents every day he is idle. At tlie end of (tO days he received $95.00 ; how many days did he work ? 75. If the two sides of a right-angled triangle are respectively 40 feet and 50 feet, what is the lengtli of the hypothenuse ? "(>. Two ships start from Liverpool for Quel)ec, 2,6;i0 miles distant, at the same time. The lirst vessel can go 15 miles an liour, the st>"ond 16 ; if tlie first burns 200 tons of coal a day, and the second 250 tons, the price being $2.50 per ton, find their respective outlays for coal. 77. A clock takes 30 seconds to strike 6 ; how long will it take to strike 12? 7S. How long would a train 250 yards long take to go over a bridge 1,260 yards long at the rate of 20 miles an hour ? 79. Two pipes A and B can fill a cistern together in 2 hours ; two others C and D can fill it in 3 hours ; B and C together can fill it in 2J hours ; B and D can fill it in 2} hours ; how long would each pipe take separately ? 80. If .35 of an estate is wortli $4,900, what is the value of .45 of \ of the remainder ? 81. A invests $6,370 in 3 per cents at 91, B invests $6,060 in tiie 3} per cents at 101 ; find the difference in their incomes. 82. If a bankrupt owes $8,400 and pays $3,7.50, how much does his creditors receive in the dollar ? 8;5. If A and B can do a piece of work in 16 hours, B and C in i hoiu ?, and A and C can do it in 12 hours, find how long they w» i!d uike to do it all working together ? 84. If 5 men or 7 women could do a piece of work in 47 days, how long would 7 men and 9 women take to do it working together ? 85. If I buy eggs at 16 cents a score and sell them at 15 cents a dozen, find my gain per cent. 86. If $7.50 is the interest on $750 for 3 months, what is the interest on $800 for 7 months ? 66 88. oa 91. 92. 9:5. 94. 95. 9ti. 97. 98. 99. 100. 101. 102. A and B receive $12 for a certain piece of work. They work together for 9 hours ; then A leaves and B finishes the work in 7 hoursj; how'should they divide the money ? A and B eacli have a certain amount of money. If A gives Batliird of wl)at he has they will each have the pame amount, and if B gives A $4.00, A will have four times what B has ; how much have they each ? A and B can do a piece of work in 6 days, B and C in 7 days. A, B and C in 4 days ; how long would A and C take to do it? A bag contains a certain number of silver dollars, 3 times as many 00 cent pieces, half the number of quarters, and four times as many dimes ; the whole sum contained in the bag is $302.50 ; how many coins of each kind are there in the bag ? Wliat number bears the same ratio to 20 as 15 bears to 107 As 18 bears to 15 ? As 25 bears to 20? Two watches, one of which gains 15 seconds daily, while the other loses the same, are set right at noon on Sunday : when will there be a ilifference of half an hour?^ A and B together can reap a field in 6 days, working 10 houre a day ; A alone could do it in 15 days, working 7 hours a day ; how many hours a day would B have to work to do it in 16 days alone ? Find the present worth of (a) $918 due 4 years hence at 5% ; of (t) $1,105 due 3 J years hence at 3%. Find the difference between true discount and banker's discount on $710.50 for 3 months at 5%. 1 l)orrow $800 for 4 months at 8%. The interest is, however, deducted immediately ; find what rate I really pay. If 3 men, 5 women or 8 childn^u would do a piece of work in 53 hours, find how long 2 men, 3 women and 4 children together would take to do it. If 7 oxen are worth 64 sheep, and 3 sheep cost $12, what should be given for 56 oxen? A person buys coffee at 39 cents and 40cenfs ; he mixes them in the proportion of 5:4; what will he gain jKsr cent, by selling the mixture at 45 cents per lb.? Find the side r' a square, the area of whicl; equals 28 square feet, 64 inches ; of an. - which meatures 21 square feet, 1 inch. If I buy goods r $250, payable in 6 months, and immediately resell them for $L;45.00, do I gain or lose by the transaction, and, if so, how much ? Interest to be reckoned at 6%. If I buy goods at 15 cents per lb., and retail them at an advance of 20%, how much shall I make on investing in 450 Ibe. of the goods ? «7 103. A merchant boujjht 3 tons of iron at $25 a ton ; freight and duty amounted to 20% of tht? ci,!-! ; lie incurred |3() of other expenoes. For how mucli iimst he cell the iron to make a profit of 10%? 104. A and H went into lairtnership. A put in $9,000, nnd subnequently took i, (it the profits ; how much did 15 invest? 105. There if a circle the diameter of which is 4 iiiclies ; what is the diameter of a circle !» times as larjfe? Note.— The area.s of circles are to each other as the squares of their rcMiHJctive diameters. 100. Two sides of a rij^ht-aiiKled trianuie measure respectively, 6 inches and 8 inches ; what i.M the length of the hypotlienuHe? 107. There are two t^lobes ; the larger is 40 feet in diameter, and its cubic contents are (H.OOO times that of the smaller ; what ia the diameter of the smaller? 108. If till- diameter of the sun is 112 times a.s long as the diameter of the earth, how many kIoIh's like the earth would it take to make one the same si/e as the sun ? 10(1. What is the sum of ail the numbers from 1 to 50? From 1 to 100? From 100 to 200? 110. What is the sum of all the even numbers from 2 to itfi? From 8 to 44? U!. What number is that from which if you take » of its.If, the remain- der is 12? 1 12. A ship hax sprung a leak which admits .')00 j;allons of water a minute; it has a pumj) which can pump out 400 gallons a minute ; if 200,(HJ0 gallon.9 would suttice to sink the ship, lii>w many miles an liour must it make in (inU'r to just reach land, 303 miles distant, at the moment of sinking? li:'). In a certain battle one-tenth of the army was wounded, one. twentieth was killed, one- miles down a stream in an hour, and 3i miles against it ; what is the rate of the stream ? At what per cent, in advance of cost nmst I mark goods so as to gain 15% after deducting 10% from the marked price? If I mark goods at $1.% and gain 3.5% .on my outlay after "giving a cash discount of 10?;, wliat did the goods cost me? A and B can do a piece of work in 4 days, B and C in 3 days, A ami C in ;« days. How long would A, B und V take to do the work together ? How many feet in 1.50 must a road 2 miles long rise to be carried from a plain to a hill .")0() feet high ? If the rise in a grade 7,000 feet long is 3 in 450, lu.w much higlier is one end of the grade than the other '.' Divide $1.35 into 5 parts, so 'that each part may be 6 cents more than the other. If by marking goods at $2, ^,=5 I gain 12j%, what deduction can I make in order to gain 10%? If a 3% stock is at OSf, and the 3A% at m;\, which would be theb«'st to buy? If the value of gold be Ki times that of silver, aner \v«-k T If .'.L' meters are i-qiiai to ;5.'» vanU, how many mettTsare } of J o( a mile? Kediice 4|(l to the decimal of hiiif a crown, and 78 ikl to the decimal of £.■>. If the valuiUion roll in a villa>,'e U' $140,000, what mu.-t be the rate of taxation in order to raise ?4!H)? Add together ? of lialf a crown, J of eight shillings and ; of agninea, and reduce the result to ^he decimal of X2.2. How many sovireiKus will weigh 1 lb. Avoirdupois if 1,800 sovereigns wei^'h 40 lbs. Troy? Ciliiilating a en.ses average •'?40 i)er week. If the prolits from his sales amount to fl(»,0O0, what is his not annual profit? If 1 own ..'i oi ii of a ship and sell ..'!.") of my share tor ?i:{, 12.">, what proportion of the ship do I still own, and what is the total value of tli«' ship at ihe same rate? A man has an income of $.i,0tX) a year ; an income tax of 2A cents in the dollar is established, and at the same time the duty on cigars, of which he u.st'S 1,(K)0 in the course of the year, is placed at two cents each ; how much does he lose in his annual income by the change? If S oi the numlxT of boys in a sciiool exceed one half their number by 1.5, how many boys are there in the school ? What is the cost of lighting a room with 5 ga-s-burners, each con- suming 12 cubic inches of gas every .'SO seconds, for one week during 6 hours eac) \ening, ga.s being w >rtli 00 cents per thousand cubic feet? If 1 cwt. of an article cost $4.50, at what price per ton must it be sold so as to gain 15%? If a sheet of paper 5 feet, 3 inches long, and 18 wide be cut into strips 1 inch wide, how many such sheets will !io required to reach 100 miles? 70 162. lfi:5. 154 155 ]5«. 167. 15.S. 16!l. ]fM). 161. 162. Kill. 164. 165. 106. 167. 168. 1«!!». 170. If an ounce (.f mik is suHlcient to make a thread 110 yanls long, wliat would 1)6 the weitrht of a thread of cilk long enough to jro rountl the eartli— 25,000 mjleg ? A man bouffht 5 barrelH of roul oil, containin>r '<.n an averaire 45 KallonHeach at 12 centra Rallon ; he lout 6% by leakajre ; at what price nnist he Hell the remainder per gallon bo an to Kain 15% 7 H men workinn 16 days can mow a Held l.-^OO vardn lonjj, and 200 yanlH wide ; what will b«' the leiiRth of the Held" which is l.W vartls wide and which 4 men can mow in 12 days? If I woman and 2 lioyH can do a piece of work in 12 days, how long a time will .3 women and 4 boys take to do a piece of work .T times ai« large, the rateM of the work done by the woman and that done by the boy being a« 6 to :{ ? In what time will $450 amount to $5< his goods with two prices, one for cash and the other for 6 months credit; if the credit price of an article is I4..50 what should be the cash price, monev lieing reckoned at H% '' \Miat amount of stock in the 3i% at 70 can b*> bought fnr$n,100, and wliat IS the actual interest obtained on the investment? ti I invest |l.-,,855 in the U at 94?, what annual income shall I derive? What is the best stock to invest in, the 3 per cents at 89. or the 3* jier cents at !»8? Find the yearly income obtained bv investing j;5,040 in the 4 r^er cents at 126 ? I purchase |6,720 worth of 4 per cents at 96 ; after they have risen to .'/ I .«ell out and invest the proceeds in the 2^ per cents at 67,", ; find the alteration in my income. If I receive 4<% interest by investing in a :t% stock, find the price at which 1 purcha.st'd. Wliat sum woukl the Government save annuallv on Post Office f5.u iiigs Hank deposit.s, wliich average 3 million dollars a vear, by reducnig the rate of interest from 3% to 2i%? If I b.iv .JliO yards of velvet for |450, and °sell 200 vards for $2.00 a yard, and the rest, which is damaged, for 50 cents a yard, what do I gam or lose per cent.? If I can buy goods for $17.00 a cwt. and sell them for 20 cents a lb., what do I gain per cent.? 71 171. If 1 gain $4.50 on an artirlp whicli <-mt me f -UOO, liow much it thftt per cent ? 172. In how n)any jfars will |4.'><) ainomit i<> ^A\*-'} at 5%? 173. \ man offers for sale a lur-'-at an advanc*- of 50', ov*r coet ; he ai-wi>tM lO'^ U'HHthaii lit- urivrtiiallyaskfdaiul t Uiih niakw $.')2.50 ; how much did the horne <uine i ine ftir a port 1,")(H) mileH distant; the tirgl vessel averaj^'H 1- miles an hour, and arrive- in port 2ft hour-i l)efor»' the other ; liiitl the rate of sipeeti of t'n- slower vesBel. 176. How long will a i)roct'si-i(,ii ti(Ki yards lonji tak<> t<. i>;if> through a Htreei 1 mile lonj;, it tlicy proceed at the rale of :'. cteps each 2 Heponds, each step Ix'tntJ 2 feet lone" 177. The populati'.ii of the entire earth U-iiifj \Ji*\) million.* and allowing one !i<[uare yai I for each i)erson w hat wmild Ih' the space occui)ied bv • le ealire iiumlx-r it they i-onl:. is inches thick, and 2 feet wide ; ifapieii! t 'niaining :i culiic feet he cut off, what length will be '"ft " 17(1. \ ^l.^rts from X j.'oing towanls \ . walking; at the rate of 4 miles an hour ; t\\ > hour- later !'■ starts from Y, walking towards X, at the rate of 'M miles an hour ; he meets A after walking :! hours : what is the distance from A to H ? IHO. A train goes at the rate of 40 n i' - j,v. hour towards a certain town ; if it had travelled 15 nii'i - >ii In rr ! longer to reacii its destir, i ■.; : i" M»; the first wi .s4days : they then have only f . ,1 to wlio!ii they give |20 ,-^ .-ce? i/eaer nuuitjer added to same ntnnber of cents jht lb. Two men agret> to '■ t. i ] \ of the lesser shall ennal tlO. 183. What number of lbs. of tea, at il will cost $42.2.")? 184. A recumgular cistern, o feet long, 2 feet and 11 inches wide, contains i:;; cubic feet of water ; what is (a) the depth of the water? (b) wliat is its weight ? 185. A pound of tea and 5 Ib^. of sugar cost 75 cents ; if the tea were to rise 10% and the sugar 4% they would cost 81 cents ; find the price of each per lb. ? 186. If a hill rises 1 foot in 18, and the total length of a road from the foot to the top is li''r miles, required, the height of the hill. 72 187. il 188. 189. 1911. l!M. 192. 19.'). 194. 19.-.. liHi. 197. 198. 199. 200. 201. 202. 20;!. 204. The circmnference of the earth in the latitude of Montreal is 15,264 imles ; find tiie distance between two succesf-ive degrees of longitude and the apace passed over by the ."^un in his apparent dailv motion in a minute, assuming that the daily revolution takes exactly 24 hours. A piece of gold 2 inches square and \ inch thick is hammered out till it covers a surfac of 9 square yards ; find its tliicknes.-. Divide ;?} into two part«, so tliat one may be 3\ times greater than the other. What is the alteration in income by transferring $10,000 from the S per cents at 90, to the 4 per cents at 108%? It is desired to cut off an acre from a piece of land 50 yards wide ; what lengtii must In* cut off? I low many yards square is an acre ? What per cent is (a) 8 of 12, (h) 8 of 30, (r) 40 of .500, ((/) ,% of 00 ? A barrel of coal oil hud 45 gallons in it, 0% leaked out, how much was left ? A grocer uses a pound weight, which is 5.7(! drams too light ; find his gain per cent, from this. The population of a city being 64,4r.O, and it having increaf>ed 10% siicce-ssively during two years, find what it wua two vears ago. The numlier of children wh.. attended school on .Moiidav wa.« 55 Tuesday .56, Wednesday 60, Thursday 52, Friday 58, Saturday 60 '; find the average daily attendance. Two ijersons start from a certain point at the same time, one going ectively 1,100, (100, 2,000, 1,4(H'; Imw manv men should be quartered in each village? What per cent, is („) \ of J ? (/,) j „f i •> (,.) _'., of | •.• What is the length of a case 2 feet wide luidllH inches deep, whicli will contain exactly 864 boxes 4 inches long, .3 inches wide, and U inches deep? If 15.men or 40 boys can do a piece of work in 12 davs of 10 hours eacli. in how many days of 8 hours each would 10 meii and 12 boys d I a piece of work 5 times as large ? 2t)5. 20«. 207 208. 209. A publisher wishes to obtain ^3.7.") for eacli lopy of a work ; at what price must lie mark it so as to be able to a!I<.w a discount of 25%? The capacities of two culies are resi)ectively 1 cubic foot, 1,647 cubic inches and l.S.il cubic inches ; find tlie differeme Iwt ween the length of their edjfcs. If a storeroom is oO feet lonjr, 24 feet wide and 18 feet high, how many boxes eacli measuring 3 feet, by 2 feet, by 18 indies, can bo stored in it, leaviuf; a gangway of 4 feet in the centre the whole length of the room? A metre being ;>!>.;}7 inches, how many kilometers are there in 100 miles ? A sovereign weighing i-xaetly 12:?. 27447 grains, find the weight of a million in gold. 210. The German mark being equivalent to Iljd, and a sovereign being taken as $4.87, tind the value in dollars of 1,000 marks. 211. The Hussian rouble being worth .3s. 2d , what is the value in dollars of 10 roubles ? (£ 1 = $4.87. ) 212. Foolscap paper meju^ures Ki.i inches by 13} inches ; if a ream of it weighs 10 lbs., what would be the weight of paiH-r required to cover (a) an acre ? (//) a s(inare mile V 213. What is the present annual value of a lease having 37 years to run, of the net annual rental of $1,0(K). interest being reckoned at 6%? 214. Which is the l)etter investment, the 2] per cents at S3',, or the 3} {)er cents at 108| ? What interest do they yield? 215. If a cubic foot of gold weighs 1,210 lbs., and a cubic foot of lead 710 lbs., how much per cent =8 the former heavier than the latter? Of two candidates for rarlianieiit, the one who is supported by ,"3 of the cun. per yard and will last 10 years, while another 2 feet, (I inches wide and costing?l.."iOa yard will last 12 years, which is the more protitai)le to buy? 2r». A man rows 1.1 miles down a stream in 20 minutes, but without the current it would have taken hiiti half ;ui iiour ; find the rate of the current. 220. If a ship \)0 eijtirely lost, of whicii ; belonged to A and \ to B, find their respective l.»^res if the ship was insured for |oO,0(H>, it being worth i?80,0. 74 What Hum must I bequeath to a friend in order that lie may receive *l,2tX) after paying a legacy duty of 10% ? A contractor sends in a tender for building a bridge for $.55,000, payable when finished, that in, in two years ; another offers to build It for $48,000, but asks to l)e paid at the end of every :? months. iind the difference in the ten.ed in (.ermany), and Centigrade (used in France, and all over the world in the world of science). In the first the interval from the freezing point to the lx)iling point is divided into 180 degrees, freezing point being 32, boiling point 212 ; in the second freezing point is 0, boiling point 80 '; the third freezing point is 0, boiling point 10!). (a) If a Fahrenheit tliermometer shows W)°, express the same temperature Reaumur and Uentigrade. (6) 50 Centigrade is how much Fahrenheit ? (c) 45 Centigrade is how much iieaumur? (d) 10 below f.ero Fahrenheit is how much Ktaumur and how much C/cntigrade . ^ul ^ioy'"'^?o*'T,.t^''';"''"S/!!:»'^'' centigrade in terms of Fahrenheit : iiu , 4U , .SO , 10 — 10^ — 40 . J^ •* 236. '237. 23!>. 240. 241 242. 243, 244. 245. 246. 247. 248. 24;t. 25(). 251. 252. 253. 254. 255. 256. 2.36 cubic meters are how many cubic ceiitiiiicterB? 5.5 kilf)graiiime8 are liow many grammes* ? If a fallier iH 48 and hi.s Hon is 11', in how many years will the father be twice a« old aw hiH son ? A father is 50, his son is 10 ; how many years a;ro waij the father times as old as his .son ? How inanv vears ajro wa." he 20 times as old? in 6 days, workin;; 14 hours a day. A can earn SIS more than if he worked 10 hours a day ; (ind how nmcli he earns an hour. . If a man .spends 11.7.') a day he will run into debt |01..'5 in the course of a year ; how nnu-ii ought lie to spend to just keep out of debt" Divide 100 into three parts, so that the second part is .') ni<.re than half the first, and ilie third more tiian iialf the second. Divide 824 into t^iree parts whicii are ii,< ;! to 2 to 5. The difference in tlie area of two square.-' is l,02.i inches, the side of the greater is I(».") ; required the length of the shorter. A piece of land of tlie shape of a trapezium is 140 yards ; )ng, and the ends are ISO yards and itU yards lonjr resixjctively ; required its area. If the side of a .square measures 12 inciies, what is tlie length of the diagonal ? What is the area oi an equilateral triangle, the sidi of which measures 12 inches? The radius of the circle circumscribing a regular he.sagon is 10 inches, wiiat is the area oi the hexagon ? What is the area if the radius is 20 inclies? Wiiat is the area of globes having diameters respectively of " inoiies, 5 inches, ti inches, 1 foot ? What principal will yield the same interest at M as ?.!,4C)0 d<«.« at 4i%? An invoice witii 8% off, amounts to $874 ; what was the original amount of the invoice? If an account ..f £.54 was ]»aid in France with l,;}t)0 francs 80 centimes, what is the value c,f the franc in English money, and the sovereign in French money? If $4.87 is equal to jEl, what nnist be sent to Kiigla id to settle a debt of £45.10? From 1804 to 18;t4 the national debt of (Jreat Britain wa> reduced from 777 millions to .")87 millions ; find the reduction per cent. (lunpowder tming composed of 1.') (larts saltpetre, 2 jiarts sulphur. 3 parts charcoal, find the quantity of each of these to malte I! cwt. of powder ; what p<'rcent4Vge of each ingredient is used? The sum of 3 numlx-rs is ;!,411 ; the second is 120 greater than the first, the third 120 greater than the second ; what are the numbers? li 76 257. Three persons gtibscribe $15 towards a charity ; the second gives $1.50 more tlian the first, tiie third $3.00 more than the first ; how much does each one give ? 258. A carter carries 36 owt. 21 miles fc- A, 20 cwt. 24 miles for B, 12 cwt. 16 miles for C, and 28 cwt. 20 miles for D. The total charges are $159.01. Find how much each one has to pay. 259. Three men buy a factory ; the first contributes $0,000; the second $3,000, the third $5,500. If the net profits for a year amount to 15%, how nmch ought each man to receive ? 260. The exterior diameter of a hollow globe is 14 inches, the interior diameter is 13.75 inches; what is (a) the outer area, and (6) the cubic capacity of the hollow ? METRIC SYSTEM. 1. Reduce 4 metres to («> centimetres, (6) millimetres. 2. " 3 metres, 25 centimetres to millimetres. 3. " 4 dekametres to (a) centipietres, (6) luillimetres. 4. " 3 kilometres, 14 metres to centimetres. 5. " 567,8.50 mm. to ((f) metres, to (6) kilom. 6. " 3,500,000 mm. to km. 7. " 35! ',000 cm. to (a) metres, {?') km. 8. " 1,000,000 cm. to km. 9. ■ 15 grams to («) centigrams, (6) milligrams. 10. " 4.5,000 grams to (a) decigrams, (6) milligrams. 11. " 3 kilograms to grams. 12. " 51 kilograms, 5 grams to grams. 13. •' 2,500 litres to hektolitres. 14. " 20 hektolitres to litres. 15. " 2 hektolitres to decilitres. 16. " 17 kilolitres to millilitres. 17. " 50 hektares to ares. 18. " 50,000 ares to hektares. 19. Multiply .35 grams by (a) 25, (h) 1.50, (r) 1,000. 20. " 4.50 grams by {«) 45, {(>) .550, (c) 2,.500. 21. " 25 mm. by (a) 75, (b) l,.50O, (c) 25,000. 22. How many milligrams are there in 25 cubic centimeters of water? 23. How many cubic centimeters are there in a metre ? 24. How many cubic centimeters are there in a rectangular solid, measuring 2 meters, by 20 centimeters, by 5 milliniet«rs? 25. How many square meters are there in a hectare ? 26. How many square centimeters in a square, the side of which measures 4 J meters? 77 TABLES AND FORMULAE. WEIGHT. AVOIRDUPOIr*. For all Common Goods. Ifi Drams make 1 Ounce (oz.) 1() Ounces - - 14 Pounds - - 25 Pounds - - 4 Quarters - - 20 Hundredweight 1 Ton. Hence 1 Ton = 2,000 lbs. 1 Pound (lb.) 1 Stone. 1 Quarter. 1 Hundredweight (cut.) TROY. For Gold, Silver, and Jewellery, and in PhiJowphical Experiments. 24 Grains make 1 Pennyweight (difl.) 20 Pennyweight."* - 1 Ounce. 12 Ounces - - - 1 Pound. TJie II,. Ar. conlaln.i 7,000 gvK. Trotj. Al'OTnEC.\KIES. For mixing and preparing Medical Prescriptions. 20 Grains make 1 Scruple. .S Scruples - - • - 1 Dram. S Drams - - - 1 Ounce. 12 Ounces - - - l Poimd. Thi gr., oz. and lb. arr thr Kinii ns in Troy weight. LENGTH. 4 Inches make 12 Inches - :'. Feet (i Feet fii Yards - 40 Poles (220 yds.) 8 Furlongs (i, 760 yds .3 Miles - 2\ Inches - 4 Nails 4 Quarters .'S Quarters » 1 Hard. 1 Foot. 1 Yani. i Fathom. I Hod, Pole, or Perch. 1 Furlong. 1 Mile. I fjeague. I Nail. 1 Quarter. 1 Yard. 1 Ell. I Cloth M. W i lif: i\ 78 SURFACE. 144 .Square Inches make 1 Square Foot. 9 Square Feet - - 1 Square Yard. 30 J Square Yards - - 1 Sq. Rod, Pole, or Perch {P.) 40 Perches - - . i Rood {J{.) 4 Hoods (4,840 *!. yds.) 1 Acre (A.) 640 Acres - - . i Square Mile. SOLIDITY. 1,72« Cubic Inches make 1 Cubic Foot. 27 Cubic Feet - - 1 Cubic Yard. CAPACITY. 4 Gills or Noggins make 1 Pint. 2 Pints 4 Quarts Quart. 1 (lallon. 1 Pock. , 1 Bushel. 1 (iuarter. 1 Load. 1 Sack. 1 Chaldron. 1 Coal ) Measure. 2 Gallons - 4 Pecks 8 Hushels - o Quarters 3 Bushels 12 Sacks A Barrel of Beer contains 3(» (iallons. A HoKshead - - ,-)4 Gallons. A Hoj,'shead of Wine ti.'} CJallons. A Pipe - - - 2 Hogshead. TIME. 60 Seconds make 1 .^linute. 7 Davs make 1 Week 60 Minutes - - 1 Hour. 4 Weeks - - i Lunar Month. 24 Hours - - 1 Day. 3(i5 Days - - i Year The Year is ai.so divided into 12 Months, called Calendar Months which contain unequal numbers of Days — ' January - - ;U May - - - 31 February - - 28 June - - - ;{0 -March - - 31 July - - . 31 April - - - .TO August - - 31 ..^^. Of these all contain 31 Days, except February, which hi'^28, and th^ mentioned in the following rhyme, which have 30 : Thirty days have September, April, June and November. Every Fourth Year contains 366 Days, and is called Leap-Year • and in such a year February has 29 Days ; but 1.500, 1700, 1800, 1900 are not Leap-Years. September - - 30 October - - - 31 November - - 30 December - - 31 79 •ENGLISH MONEY. 4 Farthings (/) make 1 Penny 01). 12 Pence make I Shilling (,). 20 ShilMngs make 1 Pound (jE). 0««fiirthing, two farthings or a half-pt-nny, and three farthings are denoted by i, i, and i, meaning one-fourth, one-half, and lhrce-fourth» resjjec'tively of a penny. .1 Florin = 2 Shillings. A Sovereign = 20 Shillings. A Crown = 5 Shillings. .1 Guinea = 21 Shillings. n •I ft V o The Metric System is so called from the French word mitre (derived from the (Jreek metron, 'measure'), the name given to a line of a certain length (39-37 inches, rather more than a yard), which was fixed upon in 1799 by the French Legislature as the standard imit of linear measure, and which was at that time supposed to be the ten-millionth part of the distance from the Fxiuator to the Pole. It has been since found, however, that the measurement of the Earth's circumference then made was not quite correct. .\ml, consequently, the Metre, as originally determined by that measurement, is really an arbitrary length, like the English imperial yard. IK. The Metric System has four principal units, all ^ depending on the metre. 1. The Metre (;i«^ '" "" """' System, with their respective unUi. I. MEASURES OF LENGTH OR LINEAR MEASURE. The unit of Linear Measure is the .V.^r.-39-37 inches or 328 feet, ine unu ^o-i-ns in =.3-'>801t ft.=r0036 j/d«. ) or 109 vard (more correctly 39 3<08 tn.=.i -^^T' J 10 millimetres make 1 cenV"*!^^" 10 centimetres 10 decimetres 10 metres 10 dekametres 10 hectometres 10 kilometres 1 decimetre. 1 iretre. 1 dekametre. 1 hectometre. 1 kilometre. 1 tnyriornetre. 10 kUomeircB • —^ , • wi«r to reduce from one denomination to another, the pSs to the right or left a. the case-may reqmre II. MEASURES OF WEIGHT. The unit of weigh.t is the Gram^^^i grain., nearly. 10 milligrams make 1 centigram. 10 centigrams 10 decigrams 10 grams 10 dekagrams 10 hectograms 10 kilograms 1 decigram. 1 gram. 1 dekagram. 1 hectogram. 1 kilogram. 1 myriogram. Til. MEASURES OF CAPACITY. The unit of Capacty i. the Li,, or cubic decimetre=r,l-02T cubic i,ehes=V7« pint. ^^ ^^_^^ ^^^^^^ ^ ^^^^.^^^ 10 decilitres '" ^ htre. 10 litres " 1 dekahtre. 10 dekalitres " 1 hectolitre. 10 hectolitres " 1 kilolitre. The hectolitre=100 litres=176 pint.-2-2 gallons, or 2} bushels, nearly. . , . » . « • iaKlP« ffive a more accurate list of the equivalenis of ,„e ^^iicrsrrr^ i- -- «< ^-"•o --»- •""-" ver$a. i^'^ti 81 MEASURES OF LENGTH. Millimetre = •0TO37 inch. Centimetre — •3!):i7 " Decimetre = •nft;?7 inches or •328W foot. Metre = 30-37O7!t inche-s or 3-28(tSf» feet. or IW.m yard. Dekametre = 10-9.3<).TJ yards. or l'i»SS42 pole. IncI) -« •02.>4 metre. Foot = •3(k:,) Yard = •914:W Pole = 5 02^)1 metres Chain (4 p.) = 20ilti4 Furlong (10 p.) = 201M<)44 Mile or 1«01.'-3149 10093 kilom. MEASURES OF WEKiHT. Gram = •5C)438 dr. or 03527 ounce Avoirdupois. or 10-43284 grains. or (V- .01 dwt. Hectogram = 3"o_'7.>9 ounces Avoirdupois or 3-21507 ounces Troy. Kilogram =. 35"2739 ounces Avoirdupois or 2 •204(5 pounds Avoirdupois or 2-6792 pounds Troy. or 02204 hundred-weight. Grain = ■064S gmrr,. Pennyweight = 1-55.-.I." Ounce Troy = 3l ?0-i" gvaii). Pound Troy = 373-24195 " Dram == 1-77184 :^T-amp. Ounce Avoirdupois == 28-349.5-1 g-.-.-.E. Pound Avoirdupois = 453-.")9265 ' Stone (14 lb::) = 0-.3.T03 kiloKian).«. Quarter (2.5 lbs.) = U.3,S9S 82 1 j. i MEASURES OF CAPACITY. Centilitre = -07043 gill. Decilitre = 17607 [)int. Litre — 1-7007 " or -88038 quart. or -22005) gal. Dekalitre -» 2-20096 " Hectolitre = 22 0090 " or 2-7.M208 buH. or -343901 gr. Pint = -5<4755 litre. Quart - 113610 " Gallon - 4-64041 litres. HuKhel = 3 ■(i323;i dekalitres, or 36-3233 litrt;-. Quarter = 2-9a586 hectolitres or 29-0586 dekalitre or 2«.K)-586 litres. ■ INTEREST. Interest ^ ^""^'P«' ^ % X Time 100 Interest rrincipui — •>'/' J /o X Time Time 100 X I nterest X Principal 100 X Interest Rate {°/\ = "'tt'rewi «aie Wo) - Ti^^ ^ Principal Circumference of Circle (r = radiusX T - 3-1416^ MEASUREMENT OF AREA. Rectangle = Length > Breadth Triangle = ^^ "" Ver ticalHeighf Parallelogram = Base x Vertical Height Circle = r'^ y, -k Surface of Globe = 4r- x t Surface of Cylinder = 2r x ;r x Height MEASUREMENT OK SOLIDS. Recfangiilar Solid - Length x Breadth x Height Contents of Glebe == ^^\^ - Contents of Cylinder = ,- x tt x Height ANSWERS. The Answers are published in separate fern., and can be obtained by teachers only, from the Publisher or Author direct. Price -'5 cent. per copy, post free. ^ K*