^ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I 11.25 ■so ■^™ HiH j2.2 ut IM 2.0 Mil U 11.6 VQ ^> ^*>' ^J^ Hiotographic Sdences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14S80 (716) 872-4503 ^ ri>^ V <^ 4 k ^ ^ '9> CIHM Microfiche Series ({Monographs) ICIVIH Collection de microfiches (monographies) Canadian Institute for Historical Microreproductions / Institut Canadian de microreprouuctions historiques 1 Technical and Biblioflraphic Notes / Notes te The Institute has anemtpted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in th^; reproduction, or which may significantly change the usual method of filming, are checked below. Coloured covers/ Couvcrture de couleur r I Covers damaged/ Couverture andommagte Covers restored and/or laminated/ Couverture restaurie et/ou pellicula Cover title missing/ Le titre de couverture manque loured maps/ Caites geographiques en couleur I I Coloured maps/ n n n Coloured ink (i.e. other than blue or black)/ Encre de couleur (i.e. avae que bleue ou noire) Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur Bound with other material/ Relie avec d'autres documents Tight binding may cause shadows or distortion along interior margin/ La reliure serr^ peut causer de I'ombre ou de la distorsion le long de la marge interieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certaines pages blanches ajouties lors d'une restauration apparaissent dans le texte, mais, lorsque cela etait possible, ces pages n'ont pas ete f ilmees. r Additional comments;/ Commentaires supplementaires: This Item is filmed at the reduction ratio checked below/ Ce document est filme au taux de reduction indique ci-dessous. 10X 14X 18X 22X J 12X 16X 20X ind Bibliographic Notes / Notes techniques et bibliographiques best original s copy which ay alter any h may ilming, are L'Institut a microfilm^ le meilleur exemplaire qu'il lui a M possible de se procurer. Les details de cet exenr.plaire qui sont peut-«tre uniques du point de vue bibliographique, qui peuvent modifier une image reproduite. ou qui peuvent exigec -.••m! modification dans la methode normale de f ilmage sont indiquis ci-dessous. tilack)/ ou noire) □ Coloured pages/ Pages de couleur □ Pages damaged/ Pages endommag^s □ Pages restored and/or laminated/ Pages restaurees et/ou pellicultes Pages discoloured, stained or foxed/ Pages decolordas, tachetees ou piquees □ Pages detached/ Pages detaches 0Showthrough/ Transparence □ Quality of print varies/ Qualite inegale de I'impression □ Continuous pagination/ Pagination continue istortion e ou de la Includes mdextes)/ 1 Comprend un (des) index e may appear Title on header taken from:/ Le titre de I'en-tfite provient: ese have ajouttes j ritle page of issue/ i Page de titre de la livraison ns le texte, ges n'ont 1 Caotion of issue/ 1 Titre de depart de la livraison Masthead/ 1 Generique (oeriodioues) d<> la :ked below/ ndique ci-dessous, IHX 22X 26 X 30X u 20X 24 X 28 X ■JTV Th« copy filmed h«r« has bMn raproduead thanks to tha ganafosity of: Archives nationales de Quebec, Quibec, Quibec. La Tha imagas appearing hara ara tha bast quality possibia con^ Jaring tha condition and lagibility of tha original copy and in kaaping with tha filming contract spacifieations. Original copit \k in printtd papar covara ara filmad beginning with tha ftont cb^^ar and ending on the laat page with e printed or illuatratad limprea- sion, or tha beck cover when appropriate. All ether originel copies ere filmed beginning on the firct pege with e printed or illustre;r«d impree- sion, and ending on the ieat page with a printed or illustreted im|».ansion. The lest recorded freme on eech microf che shell contain tha symbol — ^ (meening "CON- TINUED"). or the symbol ▼ (meening "END"), whichever eppiies. Mops, pistes, charts, etc.. mey be filmed at different reduction retios. Those too lergc to be entirely included in one exposure ere filmed beginning in the upper left hend corner, left to right end top to bottom, as many frames es required. The following diegrems illustrate the method: Las plui del con film pep par deri d'in plet orig prei d'iiT led emp Un( derr ces: sym Les fiimt Lors repr( del' etd< dim illusi 1 2 4 5 uetd thanks L'axemplair* filmi fut rtproduit grflca k la g*n«ro«itA da: Archives nationaiet de Quebec, Quibec, Quebec. It quality I lagibility th tha I ara fllmad ding on :ad limpraa- ■ta. All ing on tha Impraa- a printad f^cha I "CON- •END"), Id at 'Qt to ba Imad . laft to 18 e« ata tha Lat imagas suivantaa ont «it« raproduites avac la plus grand soin, compta tanu da la condition at da la nottat* da I'axamplaira fllm4. ai %n eonformita avac laa conditions du contrat da filmaga. Laa axamoiairaa originaux dont la couvartura en papivir aat irnprim«a sor.! fiimis an commandant pa/ la pramiar plat at tn tarminant soit par la darniAra paga qui comporta una ampreinte d impraasion ou d 'Illustration, soit par la second plat, salon la cas. Tous las autras axemplairas originaux sont fiim^s tn commandant par la pramiAra paga qui comporta una ampreinte d impraasion ou d'iilustration mt en terminant par la darniAra paga qui comporta una telle amprainto. Un daa aymbolas suivants appnrahra sur la darniira image de cheque microfiche, selon le cas: la symbols — ^ signifie "A SUIVRE". le symbola V signifie "HN ". Les cartaa. planches, tableaux, etc., peuvent itre filmis k des taux dfi reduction diffirents. Lorsqua la document est trop grand pour fttre repraduit en un seul cliche, il ost film« A partir da I'angia supAriaur gauche, de gauche A drolte. *!.^* haut 9n bas. en prenant le nombre d'imagaa nicassaira. Les dia^.an.mas suivants illustrent la mAthoda. 1 2 3 4 5 6 R Edt ■'^'^^X PrI ^I..«,**- :;^SCHOOLJIELPS" SERIES. /y^^^ n J*- "'Vim ARITHMETIC EXERCISES FOR FIFTH BOOK CLASSES. BY ■ G. E. HENDERSON, Editor of " The Canadian Teacher" and " The Entrance." AND • £. W. BRUCE. M.A., Principal Huron Street Public School, Toronto. Price, 16 Cents ; Teachers' Edition, with Answers, 20 Cents. The EpycATiONAL Publishing Company, Toronto, JS98. 7l\ Entered accordingr to Act of the Parliament ot Canada, in the year one thousand eight hundred and ninety-cisht, by Geo. E. Henderson and E. W. Bkuce, at the Department of Agriculture. j PREFACE. ida, in the year one EO. E. (Ienderson ture. The authors of this series of Arith.netic " School Helps " offer „c apology to the s.hcol in.blie for the placing of tLr bcrs of the ser.es are prepared by teachers act i vely engaired jn the busy work of the schoolroom, and as tea 'herf ttev know the great difticulty that the average teacher en tJ^ZT^'u ''■•'"''' '""'' '•««Pe<-^tfully request a considera. t.on of thefoUowng points in connection with their series • s/;^R''"r'"l' ^^'•'^- ""'''' ''"P"*^ '^-'e passed the Second Reader the usual text books provide but verv scanty pract.ce .n the n.chanical operations. Pupils in^te^o^ beconung sw.f.er and n.ore accurate as thiy advance Z years frequently lose the speed and accuracy which they had acquired in the lower forn,s. To n.eet'ihis d fficu.^ the present series provides over en.,,. 'ncuuy nini^clf. This feature alone should commend the present series to every teacher of the subject. II. No Answers. I„ the Pupils' Edition no answers are provided; the Teachers' Edition alone con.aT„sl,e answers. v-wniauis me III. Saving in Time. The time of the teacher is too valu b, ,o be taken up in the d.ctation of ^^el'tr: wiThl t'V-'"" '"'' ^"^'^ P"P" -ay be provided with a set of exercises for himself. r V. Writing. The possession of these exercises bv th. fix n the pup,i s nm.d a thorough undemtondlnir of th7 technical terms of arithmetic. * *''* of r^HV '^"" V"**- ■^''° ?"■*'>■ "-"hanical operation.! IX. Book of Exercises. This seri,, :=„„.• 176832 designed to displace either the eTcTe "r^tr "I""'' ' " t«»vf T»,„ • icctciier or the authorize!' The Authors. i oronto, April, 1898. these exercises by the ndwriting— it prevents, oni dictation. Without giving formal Jcially constructed tJ nderatandlng: of the majority of the proh sn specially for thestj ply a re-arrangemeni] •roblems are not ar ss" fashion, but an refuUy graduated iij Jchanical operation'^ ided to be done at a] ;ing allowed as thtl s ability of his classJ !s is not in any sensd er or the authorizetij ow to teach ; this isj iadytotheteachersj h which to enforce! iRCISES IN ARITHMETIC FOR FIFTH CLASSES. 76832 68327 83276 32768 27683 76832 68327 83276 32768 27683 76832 68327 fHE Authors. 65984 69846 98466 84659 146698 165984 9846 18466 669 i6598 •984 9846 ADDITION TESTS. (2) 68327 83276 32768 27683 768.32 68327 83276 32768 27683 76832 68327 83276 69846 98466 84669 46598 66984 59846 98465 84659 46698 65984 59846 98466 (3) 83276 32768 27683 76832 68327 83276 32768 27683 76832 68327 83276 32768 98466 84659 46598 66984 69846 98465 84659 46598 65984 69846 98465 84f;59 32768 27683 76832 68327 83276 32768 27683 76832 68327 83276 32768 27683 84659 46598 65984 59846 98465 84669 46598 65984 69846 98465 84659 46698 (5) 27683 76832 68327 83276 32768 27683 76832 68327 83276 32768 27683 76832 (10) 46598 65981 69846 98465 84659 46598 65984 59846 98466 84669 46698 65984 6 V f 01) 07314 589(i2 73146 8J)fJ26 31467 96268 14673 62689 46731 25896 67314 68962 (16) 47963 79634 23456 78912 34667 89123 45678 91234 66789 12345 67891 23466 (12) 73146 89G2r> 31467 96258 14673 62589 46731 25896 67314 58962 73146 89625 (17) 25864 58642 34567 89123 46678 91234 66789 12345 67891 23466 78912 34567 ARITHMETIC. (13) 31467 96258 14673 02589 4t>731 25896 67314 58062 73146 89625 314(17 9(5258 (18) 69172 91725 45678 91234 56789 12;i45 67891 23456 78912 34567 89123 45678 (14) 14673 62589 46731 25896 67314 5S9()2 7.5146 89625 31467 9tJ258 14673 (J2589 (19) 67382 73826 56789 12346 67891 23456 78912 34567 89123 45678 91234 56789 (15) 46731 258m 67314 589(>2 73146 89626 31467 96268 14673 62689 46731 25896 (20) 97864 78649 67891 23456 78912 34567 89123 45678 91234 56789 12346 67891 Add 77777 ten times, oto : g, W W39*; (27) 08302 ; (28) 79218 , (29) 97143 ; (30) Add 888S8 teo times, etc • 27^. *' **^ ' ^*" "^ ■• <»») 21887 , (3i) 19478 ; (3?' 14) r,ii m iU )()2 4(i 125 67 68 73 89 •) i2 iti id 15 >1 iG 2 i7 3 8 4 9 (18) 46731 258!)6 67314 589i>3 73146 89625 31467 96258 14673 62689 40731 25896 (20) J>7864 78649 67891 2.^56 78912 34567 89123 45678 91234 66789 12346 67891 le line above, d the ten con- ; (23) 45783 ; ) 97143 ; (30) i) 19478 ; (3?^ MULTJPLICATIOX TESTS. • Add 99999 ton times, etc. : rnS ^^''*'' ' ^""'^ ®^' "'^ • ^'^^ ^^^'^8 ' (3«) 2r083; (40) SUBTRACTION TESTS. From oftcli of the following subtract 44444 ten times in I fivaT"" ^"""^ ""l *'^**, followins^ subtract 66006 ten consecu- tive tunes, and add, etc. : (11)079841 • (19, -fl^^^^ ^^ov I 804392; (14) 710829 ; (li) 87& ' ^ ' '*^^^'^' ^^^^ S»lJ: [S| l^^^^'*' <^'> "-iSOll ; (28) 1803197, (29) MULTIPLICATION TESTS. Multiply each of the following by 6 twelve t,m«« In iij\^«'(«!fergs! 8 ARITHMETIC. m) 37422; (In 427?8'.S'in*/'',"5J ' <26) 32076 13jM'fg^,^TmM^'5^fe"TS'.° ™«««io„: (31) (42TiS;74l) fJa"'. t«rS,!i^ ?I|^ (*•) "2"; 33642; (4r)3»249- M8)52m ^o^*Aif*> ^l*"; (46) f4S?«^.%'48r(ijnir3>^'^^^^ DIVISION TESTS. •^44; (3) ]642904V(M)P79ft^ /?x^?i ^2> 125173691440- 187760^7174016 ' ^^^ 166898255266792; (6) 23?oS54Tf7&&^^^^ *^-««-' (6) 299719- 8228428^4 ;fl2mm^ *l™«« •• dD 1580- 378624 ; (14) 4215527SS?«f ^?^^^^^^^ Divide each hyttS!^^^':^^) 4742468528504832. R35346548352,. (m SrHoToiQ^ooioo^'^f^^^ (16)6832- 529733792; (19) 20497^^^^^^^^^ 15373204- 919232. ^ ^ ^"4J' 606039645056 J (20) 23913873712- 157''o;^96 r"V24425m6^^^^^^^^ ^Ut.t'^^ ^' ^32: (21) (25) 47105388 • ?S SonVo^ ?oJ?S^^5 (24) 36637524; 0776 , (29) 109W%f (S^^^^^^^ (28) 9421-' (3^^^^Sf|^SS?S^ (31) 16003003; 96018048. ^ '^ 174264970; (34) 112021050; (35) MEASURES AND MULTIPLES. d 1. 2. 652789368 W»> «393G0616; (39)979184052; (40) 42'?U8Stf t3)^t?&^^^lfl • (40 1112652288; 2472560640 ; (46)^ 6lffllf°^Aif^L^^^^097^^^ J W 1978048512 ;\l9?20'^7r?^8^^^^0^4.^^^^^^^^^^ ^ I-HEASURES AND MULTIPLES. A. Find L.C M. of 545, 26487, 1853 and 11421 Kesolve 132288 nnd 107^9«,nf> *u • and find their L CM ^^^'' ^"""^^ ^^^"' 5 Resolve 34650 and 4^890 ,r,f« <.», • /*"" ^•^•«l. 1:f 3ti;f f • of I. *. I. and ., b/eue G.C.M. of l^. Find the sum of all the divisora of 810. B. Find the product of the foUowincr • 1- 9876543 and 336427, having a^rtial products. 10 ARITHMETIC. fi* tS ^"** ^^^-^*' ^^^^"^ ^ P^r^i^l products. 6. 135792408 and 384672968, havin, 4 partial products 7 tfrtr^T'' ^"^"^^ ^P-tiai products. ^ ""• 7. 9;7G54 and 39768, having 3 partial products. \if 'S ^'^?^. ^^" numbers is 6340380444Q4 nn^ 4S^9 ,.l"dlrhl^r^ '• ^"^ °^ ''^ ^^^^^r.t\Z' '''• ^hdr'^G bVS n' rf ^r^"- ^« 12121. and 1 1 mu™, ■ ' ^"^ *^^ ®*^her number. 11. The dnvmg wheels of a locomotive are ]7Wt in oir cumference and the trucks lO^ • «,!. .f ^- ! "^' the train move to'bJlnf^h^'a'a^SlrtkTJtt same relative position as at starting ? ^ ^^^ 12. A hall 60 ft. long is to be carpeted. It is found that by stretching the carpet lengthwise an^^^f !^ IL— FRACTIONS. Reduce to a simple fraction • 1. T~r-T^'^"f '■• Vi-H Hi/ Vi+^ KlA I X -—3 A* I lOJ-7,'', / «a + 18§f PRACTIOX PROBLEMS. 11 )389H494. and imbers is 8504- 9r is 12121, and imber. B 17^ ft. in cir- b distance must truck into the t is found that . any one of 4 -It the narrow- sen, what will III.- FRACTION PROBLEMS. A. 1. A man invests ^ of his fortune in land ^ of it in Wnt matdet «8 ^''^ debentures, and^lots lot S first ? • «Pe«"l«t»on ; what was his fortune V 12 ARITHMETIC. -t,j {^*-y »'.* '^"'^ ^ of their shares to D. who dies 5. Find what fraction must bo subtracted from 6, 8. 9. 10. Uof3^ 3^ of 2| of nodh 2,1 of 03 • + 32ii 31 of 44 IS of ' to make it equal to of ;{? of 31 of 12 v '' OU2 VhrrlmliS h/s Tnd {?/ -'h^""..! ^ ^^^ ^^ «^ of the work S 9ft • ? ^"'f ''^^ *^® remainder worSgTofetKrltrwo/^7'^^ *™^ ^^"^^ '*" I b'.ught I of 4.^ corJs of wood for ^ of 4 of asrt • what were 2 cords worth at the same rate M ^ ' What fraction divided^ by (^, + j\) - (3'-»|)x (.H^)will give^\ of -" of -II of 247? 6* llf A can do a work in one half the time B requirea • B can do it m two-thirds of the time C tl2 III PBACTIOX PROBLEMS. working together do it in 38 days, would it tnko each ono separately ? B. 13 How long X nf ^; • *k""? ""^ .T,"''^- ^^•^ «I'«"t $5 more than f of It in books ; $3 less thaa f of the remainder ^n clothing; and $1 more than'.-j of what still re mained in shoes ; after which he had left $5. What sum had ho at lirst ? *^ ^' ^mLhT^'in'''? "^""""^^ *^°^«' «"^ 5 c«W8 cost as "alue Ti 1'2'hoS: ^"^ '';'^^^^^ ^^^^ ^^^^ ' fi"r «39,6l,o; wirfsTiecoJt'f'rt^^^^^^^ "^ *" TV.- -ADDITION OF DECIMALS. Find the suni of 1.27.4183.079,0,79, .679, 814.73 and 6 2. 8..247153, .07, .0314, 1.3728, 71.7854! 26 9 31007 4. 4192. .384. .416, .1647. 31.8, 9.00417, 189 14763 5- .701, .0001, .000001, 7.8, .78, and. 0789 '• Add, without reducing to vulgar fractions :~ 6. .312, 9.4, and .23. 7. 16.73, 14.219, 5.817, 3.2678. 8. 8.97, 13.926, 5.4173. 6.812. 9. 16 7. 2.8166, 3.236467, 91.34. MULTIPLICATION OF 1>KCIMAL«. 15 3. 4. 10. 5.81, 1G.2;{45, 1U.10814, 2«U8%784. U. 7.r,, 1(5.234, 157.45ti7, l!).2468i, .57932 12. 73.72J, 11.342. 10.713, 10.034, 713.213437, 12.346678 V.-SLIBTRACTION OF DECIMALS. 1. Subtmct Jr).8704138 from 7(J8 'H47««'J „;^ ♦.; ■> s7r'7"::!,t "■■' '"" -"■ •' ''-*i rrsr- H (),)-it 19\7 1 \\ .V ."^ co!i303utivo y from a.UJJU2,>7 !iud add the six romdindors. From 834.1708:) tako 587.325. From 940.031 take 579.29853. 5. Find tho difference between 1708.9324 and 987 5978 6. Take 987.058432 from 1234.5078. 7. Take 1S.12345G7 from 97.91342 8. Subtract 79. 890 from 108.621734. VI.-MULTIPLICATION OF DECIHALS. Find tho product of : 1. 47.672 and 2.34. 2. 302.070 and .003. 3. .3060724 and 240.6. 4. 73009.6 and .005006. 5 2985.643 and 3.6872. f «4rif 'rf '"''"'^ "^^^'^^^ '^"^ P^^duct of : 0. 846.29 and 53.97 to three places. 7. 213.579 and 3.2164 to three placer . 8. 12345.6 and .9999 to tlxree places. 9. 98.610275 and 35.789 to three nlace, 10. 37.0007 and 4.071 to four places. H. 7.9384 and .6238 to four places. 16 ARITHMETIC. Ui] 12. 2.46846 and .96248 to f„ur pkcea. 13. 6.17 and 2.08 to four places. 14. .318 and .7432 to four places. 15. 3. 145 and 4. Ojf to four places. 16. 17.373 and 385.04397 to four places. 18 |;"^'r'^"""'^''«'^t°««t the value of«100x(1.03r 20* F ^d to th "'"'? "'"' ''" "^'"^ "^ «100x 1.035/. ^. * ind to the nearest cent the value of «100 x (1 .045)'> . VII -DIVISION OF DECIMALS. Divide to 3 places of decimals ; 1. 1.5708 by 28.645. 2. 28.64785 by .866. 3. 1.22475 by .707] 4. Divide .^9305 by 1.1612()2.> to 5 places. 5. Divide .5 by 1.15629 to 5 places. 6. Divide 339 by 1065 to 4 places. 7. Divide .150515 by .217146 to 4 places 8. 6. 931472 by . 2302585 to 3 places 9. 89,986 by 3,003882 to 3.placr 10. 250-3.141593 to 4 places. 11. 10-^.43429448to4place8. 12. . 1 --3. 14159265 to 6 places. 13. 2-J-4.60617018 to 8 pkces. 14. 93.723-29.4173 to 3 places. 16. .46-.il888i to 4 places. '• ailVacr^*^' ' by (3.14159). to L fourth DIVISION OF DECIMALS. 17 VIII. Reduce to simplo vulgar fractions : B. Reducing fractions to equivalent decimals. I. Why do i, I, }J, 3^ 1^^ reduce to finite decimals ? ^* ^nlSst ^' ^' ''^' '^' '■^'^"''® ^'^ P"'^ circulating deci- ^' Ti^"" ^' "^^ ^^' ^^ ''®'^"°® ^ °»^^ed circulating deci- '• ''prt1,nrdecTmV?^'^""'^^°^ ^^«^^- '^« fi-t« 6. What is the limit to the number of digits in the repe- ^' ^tfrcfJ*^''? ^^°'^*!' *»»«" without division write the decimals equivalent to |, f , ^, ^, ^ respeSti^J^ etuTvlitit^^'iT^'l^'r ^ ^^'^ ^--'» caUtyot^;rSt]^ed^^i±it?vl^^^^^^^^^ '^' ^h.*;flA/^J ^ ''^''^ "^^'''^ process) to a decimal • 18 ARITHMETIC. IX,-M,SCELLANEOUs^EXERC.SES ON Find the value correct to 5 dec. places of 4. i J . I 1 1 1 5^ l"*"5+g^+5^+6^-+5^ + - Find the value correct to 4 pi 6. 1+ + ^ ^ i 1x2 1x2x3 1x2x3x4' 7. i+i+-i.^-J__ 1 aces : 1 + ■ +. 1 1x3 1x3x6 1x3x5x7 + - - - 8. -+-i.+J_ J_ 5 3x53 oxo« 7x55^ 9. Reduce to a decimal 1 1 1 2+-I + + ^ l_ _ ^ 10 R. '!"' '^'''' 2X3X4X5" 2"^rxox6 •lu. Keduce to a decimal 2 + 5-i.^^^2x*X^ 2x4x6xr '' + $ + !- -4— ______ 3X6 3x6x7 3x5x7x9* ERCISES ON iXdXixoxG MISCELLANEOUS EXERCISES ON DECIMALS. 19 1- Simplify ^51_ofC00617^53^ , .007) • «3Ix.l7 " " " 2. Find thadifferonco betweenll'-^and ^""^^^^'^^^^ ^ of .345 72+ iJL 3. S™pUfy(.367-.26B)=^^ (.367)>-(.266)> I. 4. S.mpHfy^^ (086)3 +(.0U)» K^ (.08«)>-, 086,(.014) 6. Reduce to its simplest form : _(;05)4-(^25)a(^125)a -(.0375;* (-0375)3 -(.05)^(.012^^J^1^, 6. Express as a vulgar fraction the average of «. Prove that .48732= jieoai 9. Reduce to a simple quantity 2^of2^ 4£-2.83 0.8 of 3 1.136 1.6+2.629 2.25 10. Simplify 3.875X3.6-f5.63x^^^? 11 ^- ^ , 3.05 11. * md the simplest form of 12 J/^-^ + ^-^^+'^2)x(7.24574-2.634) J. ^uo 6 til Mil 20 iflllTHMETIC. nil If; m X-PERCENTAQE. '"""f > »2J/ of 4840 sq. yds. ; 8% of 3476 horse. ^ 40? Whli!? *'l'' " '"^■•' "»'' '■"'I h« "W ru«,d W/S. What does he receive now ? fc 4. A lawyer collected »2348, and charged 6 r for hi. ear v.ce.. How maoh money did he ^y o4r ? , '■ '^r„5t^^r„na'.^:%rr'' '- "'"°'^^= ^j- ''tett'vSl " *^?.- ""'"O " "% »' "« value, worth? i7 *^ *^"® •^"^"^® 3tock \ 8. Ten years ago tie population of a town was 3840 • if has increased 207 Wb.^f . ** '""^" ^^s 'jaw ; it tion? "^^ a I %:/ present popula- 9. What^number ^ncreasedV 18% of itself is equal to '"• ^''738?"*^''* diminished by 14^% of itself is equal 11. A farm was sold for fl!6370, which was I, ' n>,r« than It cost. Find the cost! /!^t '^ ' ^v -pupHs s^Ve'rtriThooi J"^^ " ''' ' ^^- --^ B. .t the Ttl ''"■T^'^.VT "^ ^« «*^«l 171% PERCENTAOE. 21 IE. M6%of f243?7% bus ; 37*% of 1728 X of 3475 horses, ad his salary raised ■god 5% forhisser- pay over ? -y , ; ed in value 125% ; 18 11% of its value; ods, and had 33^% the entire stock 3wn was 3840 ; it 3 present popula* itself is equal to of itself is equal was log;/ more 80% of the num- 8 172 ; how many i of the proceeds he gained 17^% 3. 8. 0. How m«„y fail t" I't, ? i^' ">* "■"•ffiJer pa«, W"ges / //^ " ^ increase per cent, in '• ^.Sr„rioi\'J^- &/<-»'- •>-' *-e -t Of for the dollar ) "^ ' '•""[J'^y "»-,<»V'e now sell A nwii who owned 3riy „f ' • ''' f ''. r .hare for «,7,Sw.X"'''"'-'° f'* <«^ "' W"/^ A'8 money L Wr T '^ ™'"* "' ""' "•»» ' '^^ cent. iri'.':,li4 ■^^"""' '^'» ^ »•"" m„ch per >«.0„,.,teh«whatperee?t.ofthree.fourth.! ' '■ '-rn^oterprrl&rno^h' «*% Pr-t.nd with no?riTor,ioS^:£/rtXf -^ ■"■ ".""»• ""o c. . ^^'^" y One number is double another- l9io/ * .u ^, and 163% of the smaller make sd ^4-^*^^ «"^**^«^ -/ 2. A bankrnpf. na--" 4-o. , , '^''^ ^^ ^«d their sum. X/** creditor Vece/vesi;- what'n«r .'' l'^^ r^""* ^^h*** a loses ? ' ^^**^ P®^ cent of that which he 12 22 ARITHMETIC. iili! ' "l^t" nrot\? 'a-nfe'Sf I? "' ^■' '"- 20% of C'8. ' ^^2/ of B's may equal ; their cla niR Tl„n ? i'""® ^'^ creditors 8147 of their value How many 0^/^'^'//^ 23|%%eJow realize ? ^ °- °*' ^^^^ « <^»d ^is creditors '• ^^oun?a\:rX"^^^^^^^ P^"i^ *-^ -«J the the selling pr^^^r ni.^1'^ *^? 8*4,?"^ ^ent. when cost per ouncTtroy ? ""'" ""^"'- ^^*^« ««"^« «« the 6. A dealer sells goods 617 below f h« «, i j . still gains 257 Fin/f hf i !, ™^rked price, and co8t|l.32ayard ^ "^«'^«d price of goods that '• ^^'Zt^ittTZ^O^^^^^ of . third month it was 2 7?«^ 'ww ^* ^^t ^"^^ «^ the ^ at the beginnL^of 'th^ime"^''^' "^^ ''^ ^^^P"^*^^-" 8. A sold a lot of goods to Tl n a- i , . and sold themto D fo'r lelT'^V^ *^^"o*« ^' 10%, and C5%. Wlmt d[d f hi ^^ '"^'^^ ^^' » Q A rv,o ' ■> M ,. *'^"*'^°i" the goods cost A? house ? "• "^"''' ""« tto cost of the "*■ tuTta L'lUnX:^ t" S""* "' «» advance of 25r inch "riioS . SS en&r'^ • T*? ""r"™ ^alf "l the cost price of trgt^^s*"'^)"""! *"'•'*• ^"-l eHtirrt^r.i'i'rjfrH™'-"- -'"■ FaphyatlSOmrk'each rSiSr^'^T™ T"- m arith., 66°/ in .r-m-n-- ^ ,"""'"*">» fOX history and &%"i|'ge"-:°iv'" F^'r' ""^ '" rate per cent, (of the a^cgate). "^ "•"«'' 11. »at5% of A's share >i B's may equal , which, if sold at reditors 81^% of sold at 17^% be- r at23|% beJow ! did his creditors id troy jjnd the per cent, when he same as the arked price, and rice of goods that ;he population of the end of the 8 the population i of them to C, A made 8%, B 8 cost A ? times as much ^ HX more for use would have the cost of the Ivance of 26%, leasure half an $37.24. Find nmar are valu- story and geo- te obtains 70% nation, 60% in I his average TRADE DISCOUNT. 23 12. A ^cer has 180 lbs. of tea, of which he sells 60 lbs. at dOc. a lb. and gams only 8%. He now raises the price so as to gam 20% on the whole outlay ; what does he now sell at per pound ? >,^^, XL— TRADE DISCOUNT. Find the buying price : 1. List price, $253, Trade discount, 10% oS./ /J 2. List price, $487, Trade 3. List price, $796, Trade ^.j4. List price, $496, Trade List price, $760, Trade List price, $690, Trade do. do. do. do. do. SXoff./.lX 15% off. J 20 a^d 5 off. 30anVl5 6ff. 10anl(i4off. 5 6 7. Invoice price, $1,000, Discount 10 auTSoff. « I 8. Invoice price, $1,728, do. 12| and 4 off. !{! ^ 9. Invoice price, $2,040. 90, do. 10, 5, and 3 off * / 1^ 10. Invoice price, $804.36, do. 20, 5, and 2^ off 11. Invoice price, $1,213.50, Discount 20, 10 fand 3i off 12. Invoice price, $673.20, do 2o,16j and 12^ off B. paid $798 for a bill of goods ; what was tJio cost ? 2. A nierchant paid $459 for a bill of goods after being allowed $81 discount. Find the rate of discount. ^-' 3. At what price must a suit of clothes which cost $12' be marked so that after a discount of 6% is allowed tliere may be a gain of $3.20. 4. A retailer bought a lot of carpet for 90c. a yard at a discount of 10°/. He rpcei'-vl a c.JCL J ^' t^ % «>y f „ I "" ," ,. , . ^'"^'^ ^ ^"^tftur uiscount of wu ' ^^'^ '^''''P®^ *=^''*> ^™ per yard? ifto/ '%^^u *^^«r"f® tetw^en 25% off, and 15 and iv/o ott, the marked pryxf being $1.20 ? ■'■^b ; i--Sif^. 24 ARITHMETIC. article of w.4 th/oalS prioe'S'^'^r ''™'' "'» 8. What r.t. „f ^- ""**?<''' PouncMor good weight J ^ }i?hSS.ta^1°™^XSl;1^''"«-™'' ». A grocer mixes a pint of wafkr W.vu SX-. WhattUl.Tote\^Kjl&^^ ''• gooS^^lTh:r;l^^^^^^^^ .^- --^-t -ark his *'• r^J^dt^'off'"'^'^"^^ '^^^^ 10, 12. A merchant gives a discount of 10°/ K„f , measure iinch too short • ^2 iiJ' f "^®f.* y*'*^ him the wme rate of aSn 3?J ^"^ount would allow 'ate of gam if jEhe measure was correct? .^•n-,rt«SS!j"tri^^^ .,.^i., ^i" '^jS™"""**/ of the sales for bad debU? . '" . ,. this red3dSfof Lfr'-Th^ ""T P^"™'- »» of the origU ^.re^UT rj STelij^"- '■ ^Srw^d'a'^^aS^i^l^'I.J"? «'«<->. • f '"°'-' » ,,-;;^ of 10% off the trade prkelof £4-' '"*" '?'»«>™t .;-i^*, /'.a the list priced,' ,';'""^^^J'"i'»f,«tlOZ less than SlingT"" " """ --' »i 1i-har^rortht COMMISSION. an advance of 30%, idthecostpriceof Ml 3 $7^1. ]^t to giving an '^or good weight ? nt^ji^ving one inch nth every gallon of w^m this enable him merchant mark his iscount of 33^% and 5% discount,and 10, 0%, but uses a yard iscount would allow leaaure was correct ? >h cost me $3.42 a itilJ make 20^ after debts? - .^^ ice of an article by same per cent, oflf cash price is now find the rate per )d8 a purchaser is * further discount [ig a quantity, and ;his bill for cash at 10% less than fs 35c. on the shil- ves a discount «f e charges on the 25 A merchant marks his goods, so that he may allow a discount of 5%, and still make a profit of 15% Fhid the marked once of broadcloth that cost him M ^* iii i. ■Lit-. A storekeeper on March Ist. 1894* ' bought goods was allowed successive discounts of 33i% and 57 SerS'torT'^^^^^ ?^J'^'' after VhichtinTe iT^iol t ^^.f^'^Sed at 7% per annum. On June 1st; Im) ^ ^^' ^°^ "^"^^ '^ ^^« ^"^ J"^y lows teachers a second discount of 10% on all cash prices. A teacher paid «5.13 for a bookTwhat was the marked price ? . ^^ . / ^ 4 ^ /)'- 4 .T/J®, , ^cnunTo?dl^"'V^^^"*^Ks"^^« ^«« ^«^"«ed on ac- " " . • "x^^*" ^y ^^^ J * ^"''ther reduction of 124°/ f Z ^.^aV^ i^"* ^'^^'h- ^««^« that were originaliv/^ marked $6.40 were sold for $4.20 cash ; what rX^^' tion m the marked price was made li^u!. ^ n':TiT A merchant bought a quantity of cloth, and marked it at an advance of 25%, and in selling it used a yard gained altog:th'er^^?8rwhtr^^^^^^^^^^ ^ -"; XII.— COMMISSION.- A. i'hat is the commission for buying : $542 worth of goods, at 2% commission ? $56. 20 worth of goods, at 2J% ? $508 60 worfcli of goods, at 1^"/ ? 715 bbls. of flour at $4.80, at 3% ? ro ««-« 26 ARITHMETIC. 'if l& I Ji(!' .,^^ What is the commission for selling : ,6. 3,245 bus. wheat at $].08, at 1% commission? 7. A house and lot for $4,850, at 2^% ? 8. 420 acres at 018.50, at 2^% ? 9. A commission merchant sold 10,500 bus. of potatoes - comm'ss'ionl'' '" ' ^""^-^-^^^ ^^ 2% ; what was his 10. An agent sold 1,500 bus. of oats at 3Ge. a bus on a - commission of ]|%. Find his commission. ' ^ ^' trT^y^r '%"l''?^^"^ j?i^.^ consignment of apples . for ^1,756. W hat sum did he send his employer, his '•' commission being 2^% ? ,, . - 12. A commission merchant retained «5.85 from the pro - iT' T<^"V K ^'^^ ''^ ^'^2^ ^'^'^ «^ ^»"er at IGc. per ID. tf md the rate of commission chartred B. An agent's cominission for selling some land at 080 an sTonaTlf? ' h«^ ^»?ny,^cres did he sell, commis 2. $1,648.27 includes the 'price paid by an agent for s'o^f'ihegtdrr"^"" ^' '^^- ^^^^^ -« ^^« 3. A commission agent bought 13,450 bushels of wheat at /8c. abus_, and charged 1^% for buying. How much must his employer send him ?H p C hK » ^ 4. A broker received $11,560 to invest^in pork at Sc.' 1 did iTe bu% ^^ commission of 2%. How much pork ^' \SSr*?^^7?'''r'?^*^^^^^^'46<>; the agent paid $225 for freight and other expenses, and remit ^^^^f^^^^^^^e'^PWer $9,067.50. Find', the rkte of com - 6, An agent charges 2% for selling and 3% for guarantee- ing payment ; the sales amount to $875. Find the amount the agent receives. 1. s COMMISSION. 27 A commission merchant bought a lot, 50 ft. frontage, with the money he realized from sailing wheat at fWo i the net proceeds of the wheat, after deducting the commission, being «23,887.50. Find the prici per foot paid for the lot. ^ An agent sells 256 reapers for $125 each. He is to be ^ responsible for bad debts, which amount to 12A7 cf the entire sales, and is to receive 20% of the good sales for his commission. What are his net earnings ? A firm became insolvent and owed $4,050: their as- h^d'J'^"''^"^^ -^ ^?C^^^- ^^' ^'^*^ P«^ ««»t- of theirs lne« llT^ ^'^ *^"y pay. having allowed the as-^ Mgnee^^% on the amount distributed- for their ser- vices ( I received $4,100 from my agent, who had deduct- ed his commission at 6%, as proceeds of sale of goods ; what were the goods sold for 2 f PnX^r* ^i^' T a commission of ^%. a cargo of 1,200 tons of coal at $4.75 per ton ; he investel the net proceeds on a commission of 1% in lumber, at ??18 per M. How many feet of lumber did he buy i Yifpll^'^^fLi!^ ^''^- ""^^^^ ^^ ^1-40' 800 bus. / / Jlu^r ^J"^ ^^ ^"«- »<^ ^^-20, to his agent, who K soldthehrst at 20% gain, the second at 15% gdn! and the third at 4^% loss. The agent's commifsicm was d/ and the other charges were $83.44 • find the dealer e gain per cent. ? - ' 0. An agent sold a consignment of flour for $4,800, and nvested the proceeds (less his commission on both transactions) m the purchase of tea, receiving on the latter purchase 4% of the amount invested. His commission on both transactions being $300, find tne rate of commission on the sale of the flour. ' commission merchant received from A, 150 bbls. from B, and 225 bbls. from^'c ; finds on inspection that A's is 10% better than B flour he 28 3. ARITHMETIC. s»m m!st he remit to S* ^^ '=°"'"»»«<'»- Whatl III per pounS were re^fet^ ^^hfcheertr^ ""^^ Bion beine I y anri froi»i.i. ■ ""™»e, the commu ing to »8l2S(£T=H86|)!' """"""=«• ""«■. »»ount- *■ ^S^7'^"^™'""" ^"' " oo-'ignment of wheat t^iTz =sr:na" ;'iti^ihe «„:t~ »?he ».o„rf h"rt^^s;;!L'uS.;;r^^' """ "■»' ceedn hJ« L!« • • ,^ commission for seJIina ex- ceeos las commission for tuying bv 2R F;r.f fu Talue of the goods remitted to hfm ^ ' ^'""^ ^^® reserv nSTsuffident sn"t"^ his com„,i8aiona and commission of 27 Th/fnT i ^ P^^*'^>» ^n a «16.80; find the ai;J'of%!>tUr"°" "*^ bbl. forCstorar of ?he /^^t ^f^^'^ ««• « wheat, and $5a?9 for fref^ht"" H^''- ^J"^' ^" <^^^ $5.60 on a commit -,„ ^f ± ^^f^^ ?^ ^""^ ^^ a bus. on a comSion of 9^ i? ^^'^ T^^*^ *<= ^6° h. remit to hi^rp:;er?' ^ ^""•' ^'^*^''»°» ^^^ % LOSS AND GAIX. 9 10, 29 ^oSstr S^""*'^ *^''™? ^'^ ^ '^^^in rate of 217 wTthon; Tn ^ g"*^ranteed payment of sales, or -2/0 without any guarantee. His emnlcver accpnf^ the former method (which is better Zn^tSelatL^ by »2I owing to a bad debt of $84). If the totel ;rrt:f "^^ ^^^ ^^'^^ what^^he gu'^^ti toXdurhir^'^ ^^' ^^'""^ P"^^^ ^i*h instructions to aeauct ins commission of 2^ 7 anri imr^a^f *k aSt^;.'^"^ '' ^' ^ ^^'- '^ I^ "-o"o/ 'eig'h^ flour bo sow ^ hn T"'' f" ^125, at what must the nour bo sold a bbl. to make a clear profit of 157 ? tent wXinT^^\^^^-^ ^" ^'^^h ^"d better to his the pV^^^^^^^^^^ *° «^^! ^1^^ »^""«r *nd invest agLKJe s'slv ^^f «o«^»"?sion8. in tea. The cfse . fimffhl^'f """/if r"^^ ^« ^a^^les in each case , Und the value of the butter shipped if his t/S commission amounts to $38.90. ^ XIII. -LOSS AND GAIN. ^ ■Find the selling price : g- Jl. Cost $674, gain 12^%. ^'iV'-*' j2. Cost $713.40, gain IGffAJli; 3. Cost 11.024.16. gain 37if.,,j.,:, [4. Cost $1,250, loss 6%* ' ^7.^ -> |5. Cost $1,348.75, loss 4%.»"r ?■. ," } [6. 13 bbls. flour @ e5.30,"gain 30^^.f 1 7. 432 bus. oats® 31c., gain 25%^ jr^ » ,^ 8. 18 parlor sets @ $42.75, gain SS^^Z.'. 11 toT?? ^^"^"^^ ® ^22 per M., loss 6%. >79i 11, 19 bbls. sugar ® $7.50. gain 2%:^/U--Ji lii'ii 30 ARITHMETIC. 13. A grocer bougI,fc coffee at 4fto ^^ |oasof,2^./ ^i"dre*3e1?^J7ri^-^BoIdat| J4. A grocer sold goods to fh« ^ ?"««• i.- gained 16^'/. Vd ?!„ • 'J"'"""'^ «f «8.40, ani ^'-d.s would have sold S"^ '^^ ^^^^ ^hafc th! ^•^o;;ra^^fLr^^sp:^do.en,a„d ■«?md his gam per cent. , . {here i'"a "^Slor"! I^t."' ^.r"' '» »n !« quart, were^oIdfo/tLirlTm !"""■" «^'' ry,fc j'-- ^^^^^ Wl6%is lost when »n „»• ."^^ ' what.hou>d it be^,Tto"t?;^j;y^Yv *'-'^' 4 A sells a piano fn P „4. . '^^ ri>-"^ 1 did the pianS iost A ■! • • *'^ """« ««« A. Whaf . • '^f^^^^t^'- e^- ^^"« I'' «^- ^ ^^^ "^imFn "¥'''' ^ u*^ * ^^^^^ «^ '»nd '^t a profit of 60-\ ,. but the buyer becomes bankrupt, and pays only 76c. 3 y y ^ I 'o2 AHrrilMKTIC. What^per cent, does the speculat,, on the dollar, gain or lose ? loss j)er coat. ^ ^ ' *"" '"*' i^iyer XIV.-TAXES. , , Find the taxes on : 1. Assessed value $3,760, rate ] i% -. Assessed value ^,500, rate l|%' o. Assessed value $8,500, rate Uy 4. On $2,637 at 2c. on the $. 5. On $3,642 at He. on the $. 6. On $3,900 at 15 mills on the $ 7. On $6,300 at 17 mills on the $ 8. On $8,240 at 37^ mills on the $. , ^ZtTLfo!t^^l^'' -U-n the doUaJ 10 Th« f^* 1 f ^ ^^'^^^ assessed at $3 500 ? f m mUls o,. the Soita ^ ""°^ " ""» ""» i « the^pt borne by A whif pj^p'^l^ irf does a „„„p„y ^^^ propere^iallS^-r^;^' i What sura must be assessed on « school dWri^f J 1\ ..-k ■ic. TAXES. >nt. does the speculate^ yard, which in apongini per yard must he sell y of certain goo.l) for )er cent, and the iniyer' | ES. 33 5 mills on the dollaj 3essedat$3.600? I property of a villa J e raised at the rate * >d on a county havinj of $5,793,000; wh;^ 56 property is valueB^ ilding a schoolhousel .18 $2,242,000; whal IS assessed at $6,660 f a school district ti 175, and pay 6% foA 14. As income is $960. What tax does he pay t400 being exempted, and the rate 15 mills on tn'offi the doUar " ^'"^ ^^' '^ ^^ ""^ ^« "^i"- «« B. I. A tax of $24,750 is to ho levied ..n a town, the assessed valuation being 1.5 mills on the dollar ; what tox does a man pay on an income of $1,100, of which $400 18 exempted ? ^' ^n!r''fT'''i'^n"^^.r*'P.?f*y," assessed at $9,600, pays on the dollar J mills for township rates, Ufhr county rates, H for railway bonus and 2 J for school rate. How much does he pay in all 1 ■ '^"'ir ''^^^^ P*y^",^ an income tax of 16* mills on the dollar, and spending $3.37* per day oS an average IS able to save $1,230.87* per year (365 days). ^Find his gross income ? - *' -^ ^ "»J"'> ■«'ina The expense of coMtructing a bridge was $8,590 which was raised by a tax on the assessable property ofatown. Therateof taxation was 2c. on the $. ana the collector s commission was $160. Find the assessed value of the town property. '''is 177* amount received by a village for taxes is aIc ,? '**^.°^ taxation is 17i mills on the $. wi *^«, collector's charges 5% of the total taxes, vvnat IS the amount of the assessment ? A farmer pays $56.70 taxes on property worth $3,600 which IS assessed for f of its value. Find thHate. At a 16-mill rate, a man who has $400 of his salary exempt pays $5.60. What was his salary ? ^ A citizen, whose property is assessed for $5,235, pays on the dollar for interest and other charges on general citydebt6.763mills for interest and ^otherch^^^^^^ on Public and High Schools 3.486 mills, for Admin- "i£ •n''^'^"'^''^ 2 035 mills, for Free Libraiy rate >^P6 mOB, fpj- Street Locftl rate 3.373 mills, aid fop 34 ^ (If I ill m m 1 How much does 9. iO It ARITHMETIC. General Citj purposes 1.387 mills, he pay in all ? \m'Anr '^'''.T^'?, P'°P«^*^ amounting to V475,U00, and on a 3J null rate they raise «1 59fi after paying the collector's charges. What per cent of the taxes did the coUector receive f^''^^^'' °®»*- A man bou|?ht a farm for $4,500 : at the end of 3 he snenf L?R "^ ^^^ **''"*'• ' in another 3 mo s. lie spent^25 on improvements, and at the end of the year he sold the farm for $6,000. Find hkeai^ money being worth 5 per cent ' "°« ^" g»"»' XV.-INSURANCE. A. Find the premium of insurance on : 1. Policy $1,200, rate |%. 2. Policy $6,000, rate |%. • 3. Policy $3,600, rate 2J% for 3 years. 4. Policy $1,800, for 5 years, rate §% for each year. 5. Policy $660, at 90c. per $100 for 3 years 6. Policy $6,000, for 4 years, at 11% per annum. i. Policy$5,000, atl.17%. in A u M.. * " ^"^•' ^^' ^*^ '^'^ t «f Jfcs value / 10. A building was insured for $2,500 in one company at •f %, and for $3 000 m another company at IV/ Wuat was the total premium ? ^^ -'^' 12. A man insures a house worth $4,000. for 4 of its value, at 2% premium. If the ho'use 'be ditroyet INSURANCE. 30 ills. How much doen jperty amounting to e they raise $1,696, rges. What per cent, iceive 7 00 : at the end of 3 )n f of the purchaaed r ; in another 3 mo a. ts, and at the end of ',000. Find his gain, CE. 8. ' for each year. 3 years, per annum. worth $18,000 for § g 4,840 bus. wheat, I i of its value / ) in one company at ir company at 1^%. ure a house worth ears, the rate being t.OOO, for i of its ouse be destroyed. find the total loss sustained by the owner after one premium has been paid. B. 1. Fj»d the premium i«id to insure a house worth $7,690 Jor i of Its value, for 3 years, the rate being 97 of the policy for each year. 2. A factory valued at $17,000 is insured for | of its value in two companies, the first taking .if of the risk at ; % the second the remainder at |%. Find the tot^l amount of premium. 3. A vessel running between Oswego and Hamilton is in- sured for $12,360 at the rate of 13 % per month. To I«^?i*in!ti V^'^^V""' ""^ insurance amount from April 10th to November 10th ? 4. An insurance company took a risk of $9,600 at 2h7 and iT® r'A^f '^ '«-'"«"red h of it in another company at 'i/o. If the property be destroyed find the loss sus- tained by each company. ^' ^JTr^^u*'''''' * ^"^ **^ 31%, and re-insured § of it tliA^ «?LP''T' "?" Received exceeded the premium paid by $144. Find the amount of the riskf ^" \S5"«!fS?S'P^''*^''''"'^.^°'^ •^'325. for which he policy to $6,000 ; what extra premium will he be re- ^ quired to pay if the rate for the latter is i% greater ? I. For what sum musti insure my house worth $2,450 at renSum ?° ^®*'°^®'' ^ *^® ""^ ^*^' ^^^ value and $47,680 at the rate of f of 1%, so that in^ij of loss the owner may recover both the value of the property and the premium paid ? f f^ '^y 0. What will be the cost of insuring a ship worth $486,- ^ej ac oi/;, su that in case of loss the owner mav frS;;^»t' "' ">. d.ip..nd «,. amount paiS 86 ARITHMETIC. If I Will 10. A merchant bought 20,000 bushels of wheat and had lb insured for 4 of its coaf aHJL°/ ^ y»"«a«i ana naa of «i qfi A *.^ I I • ' i?^' P^y^^ff a premium to^afnVonh^loK fhe'Vhrr-^^ '^-" '' U. A dealer shipped 200 bbls. of apples to Livernool • «ie average cost of the apples wa. $3.76 a bbHi; what sum must he have the apples insured at fy premium to guard against all loss in S^»e of -hiD"^ wreck, his other expenses being $751 ^' 12. A company took a risk at 1|% ; re-insured 40% of it w ¥j xu ^^^ °^ *^® remainder at 1X7 What 13. A merchant had 450 bbls. of flour insured for 3 of Its value at 2i%, paying $45 prem^Sm At what price per bbl. must he sefl it to eain 2fi°/ nf fit; • cost as well as of the premium ^^Jf^^ of the prime 14. A cargo worth $2,250 is insured for 807 of its value - the premium paid was $24 ; find the Vate ' 15. An insurance company took a risk at 24°/ ^r.A insured a of the risk at 2°/ Thl •*'^' *"^ '®- XVI —DUTIES AND CUSTOflS. A. What is the specific duty on : 1. 12 chests of tea, net weight 785 lbs., at 9c. per lb. ? 2. 147 gals, of oil at 12c. per gal. ? 3. 59 pianos at $25 each ? , at 9c. per lb, ? bUtlES AIJD CUSTOMS. 37 P'ind the ad valorem duty ; Invoice ^1,650 at J 8%. Invoice, boots and shoes, $769.40 at Uy Invoice, jeweUery. $5,327.60 at 25% °* 1 On rf J"""' ^^ ^^°^"' *' «^-^^ P«' doz.. at 277 2* O I ,''"' ^^ "'""««^ ** •^.go a box, .^t 157 12. On a book, invoice price $4.60, at 15%. B. Vm irt'A^h: ptt /r "^ r^^^^- ---^ to duty and makes a S of 2?^^^ l- ^^u^l ^'*^°^«°» What do I pay f^Ah" booU'^ " '^^ ^^°^" ^"^^'^y- Find the duty at 10c. a lb and 19°/ -^ 1 *oirti1S^?afe^,f .•?'»'• of ?™«"-«h box i« »13.20. the duti l«?/' ruJ*,' ^'^- Th» freight gained by .„U„g Z7Xtt st^Zt T"" *" age. What wi thetf^oice Jr^"o-,tt^»'», ""'" of the goods. ' ^ *"® invoice price - J80. p«.,«., wr,.af ^i t^^^ 38 ARltHMEtlO. 9. 1 1 8. A duty on coffee at 12* % in baM of Ifimko invoiced at 15c. a lb wtli S? 77 fin f u K^°"' '"^^ allowed af d.y IT ' V^TT.bO, tare having been allowed at 4/. How many bags were there ? in^L^e'^'^lfii'^.rr// ^^"«' ^^^^ 30 bottles «„« K J ■^",®' ^^ ^'^^ ^een allowed for bieak Ta 1 ^'^ *" "^ ^*^"^«'" <»"ty of 20%Tthe frSa iJ 177 wir^^'^ni^^''^^^^- The whtle cost ufng 10 Jt I' . """ ^^^ '"^^^«« P"«^ P<^r bottle ?^ nnfi. ^^""^ surgical instruments is 257 and So- on the cases^ A case of instruments was inv feed at Ke in^stutjt^^^"^ '''-''^ ""^ ^^- --- P^^^^^^^ XVII —STOCKS AND INVESTMENTS. A. What is the market value of 1. 72 shares of stock at 80 ? ' i 2. 168 shares of bank stock at 75 ? 3. lar shares of mining stock at par? 4. 213 shares of stock at 112 ? 6. 350 shares of stock at lOSf ? 6. $3,600 in the 3 per cents at 94 ? 7. $4,000 in the 3J per cents at 98^ ? 8. $2,240 in the 6| per cents at 106| ? 10. 163 shares of stock at 7^% discount ? 2 t2 q^ WK^ «^ ''"''^ '^^ '^^^ »>«^«^ P*r ? ^. f-4,900 in the 6 per cents at 3|% above par ? What wUl it cost to purchase 13. 98 shares in the 5 per cents at 79|. brokerage i% ? i« ro'otr^: r ' '" ^^"^'^ ^^ ^^«i. brokerage i7 I ' 17. £2.600 r«lw.y stock .t par, brokmg. J% ? STOCKS AND INVESTMENTS. 39 VESTMENTS. i\'hat does a stockholder receive who sells jl8. 25 shares bank stock at JSl^, brokerage i% ? 119. 18 shares in the 10 per cents at 137g, brokerage i% ? ■20. 126 Telegraph Co. shares at 84, brokerage i% ? 21. «75,0eO-Central R.R. stock at 121^, brokerage |% ? n. 114,400 of 5% stock at 2\% discount, brokerage j"% ? Find the income from investing |23. $504 in the 6 per cents at 84. 124. $819 in the 7 per cents at 93f. $4,788 in the 3^ per cents at 105. j26. 11,868.50 in 6% stock at 101. j27. #4,147 in 4% stock at 72f, brokerage \%, J28. 16,720 in X\% stock at95|, brokerage i%. p9. $8,475.50 in the 3 per cents at 92, brokerage J%. [How much stock will 130. $4,200 buy in the 4 per cents at 75 ? [31. $2,983.60 buy in the 7 per cents at 117 ? 1 32. $1,878^75 buy in the 8 per cents at 125^ ? 33. £2 199 buy in the 3 per cents at 91^, brokerage |% ? 34. $3,741 buy in the 3^ per cents at 86|, brokerage i%? 35. 84,706 buy in the 6 per cents at 90§, brokerage J%°? I What per cent, is made by investing in the 1 36. 8 per cents at 120 ? 37. 5 per cents at 96 ? 38. 3^ per cents at 76 ? 39. 7 per cents at 93J, brokerage \ % ? 40. 7i per cents at 90^, brokerage ^°% ? 41. 9 per cents at 102|, brokerage \% % ^ow much stock must be sold in the 2. 8 per cents at 123 to produce $861 ? 3. 6 per cents at 112J to produce $843 75 ? 40 ARITHMETIC. 44. 5 per cents at 101 to produce $934.25 1 46. U.8 (10-40'8) at 83^ to produce $2,250 ? m^m^'''' '^'"''^ ''' '^i' ^••°''-««« i%. ^o produce What sum invested gives an income of 47. $320 in tire 8 per cents at 120 ? 48. |600 iu the 6 per cents at 85 ? 49. $2,600 in the 5% at 89|, brokerage iy ? 60. $672 in the ^% Ht G8, brokerage i%f B. i. A broker invests $5,924.50 in stock at 87 on iV ^nm mission ; what are his charges ? ^ J' "*" *^ *'°™- of 8% per annum, brokerage ^ % aiviaend | 7. What rate per cent, do I receive on my monev bv in rrdfvSenrf t%T^' ^^^'^-^^ ifpayin^a^^iT 8. What percent, is made by investing in 4^% stock at ^' ^hfn!nn*^^P"'l*'^ ,* ^^^ ^'^^^^ ^^ich pays 57 on the money invested ? *^ "'^ '^ 1. STOCKS AND INVESTMENTS. 41 What ia the price of a 6% stock payinj? 4*°/ on thA money invested, brokerage |% ? ' ^ *^ ^^" " '*'® Sold stock at a discount of 12A% and made Ifiiv «« my money ; at what rate of dil^Snt d7d I biy¥ " nvttmenV^a^ S.hf""' ^"^ P'^^^ ^^ ^"^«r«-t «" the I.e. ^SToMf^'''?x^^"V^-'' -''-»» P-d a yearly aiviuena of^/. Ue Bold out at 102|, and invested he proceeds ,n Michigan Central stock at m my- a^e [%!" SrseT^^' '^ ^'^^ *''^-^-' ^-^- M invested money in 3% consolidated stock at 95 *n^ •10 a y'e^J^i^^^ frfrhe^r: '^SoTry' fifty dollar shares did he purchase? "^'^ ^anj A retire.! farmer invests 40% of his caoitml ,*n ^lo, stock at 90 and the remainder in 4% sS at 95 hil ' ^e"^ds ?n « !!'' ^ P^! °'"^ ** ^8 and invested the pre oeing V.186, hnd how much 5% stock he had. A man invests $6,000 in 6°/ stock «f I9ft . „i. tt What must be the market value of 6% stock so thaf yield 6% on the investment ? ^ ^ofySw'^soM nirt^lo?*^^ fP^ '*°*^ after anumber Jly ^I! "** ** ^^' *"*^ f«»nd that I had made 42 ARITHMETIC. ( Mli Mii L6'^^ y m It to yield a yearly income of $794 after JaJini an income tax of 15 mills on the dolla^ STm^oH come being exempted from taxation ?' ^ ^ ""* 9. Havnig received a stock dividend of 8%. I find I arr iTwn'LrfiSrr' ''' -^^^-^ Wmfn/llid^S 10. A man having a certain sum of money to invesf 1i.d SlTuttult^ha^' Pun.hasi„g7% sSVtXd aeiaya untU it has risen to llo. What per ceAt \ his^mcome lessened by not purchasing^' th^Ll etck Xh L4r h«l"P'^''^%^^"«»^«d in ban] ^* 70/ ^"'^^^ 3^, J-^ o?^owr par and pays a dividend of 7/, may yield an income of $1,680 ? °*^**®"1 t,tTHo''''!f^*^^'^^"3%stook at 75; he .ell out at 80 and invests ^ of the proceeds in 3*? stocf jL^k*""* the remainder in 5% stock at li^f H the change in his income. ""par. jjinq XVIII.-SIMPLE INTEREST. A. f °jii! ^''^ "®*''^** ^®"* ^^° "°*P^e interest on 1 . $87o for 2^ years at 3% per annum. 2. $279.40 for 3 yrs. 2 mos. at 6%. «/ 3. $631.90 for 3 yrs. 73 days at 8%. 11. 12. 4. fl,400fromMay3rd,1897. toNov. 16th. 1897 atfi- it^ ^'"'"^ '^"»- ^^^^* ^«^^' ^ J-'^e ISfch. 1896, 7. On March 1st, 1896, Fred. Harris gavehia note fo, die* ^frifh""*"; Ti'^ interest at 6% perlnn^-mt^ pn^st-stt^t^drf^i^i-^^^^ the exact amount paid. ' ^ * °" SIMPLE INTEREST. 43 Find the rate when #2,676 amounts to $3,317 in 3 - years. v^i"** m o ■ TntrL*^!?n«?2n^^^i^"^*^ days is $58. 80; find the . interest on $650 for 2 years at the same rate. In what time will $3,200 amount to $3,820 at 7*% ? 1^- V*^ whi?l*TiT*!^ ^^'^^^ '^^ ^^ ^ ««rtain time at 9% : what would be the amount of $532 for the same time? The mterest on $1,805, loaned on May 14th at 5i°/ - numYste^^mT•'^r * ^^^^^^e^t 7% per an- num IS $385. What is the face of the mortgage ? $360 amounts to $400 in a certain time : what sum will amount to $400 in half the time ? /if y^^ " B. y 1,^00 at 7iA, and $1,000 at 6% : find the per cent he receives on the average. ^ '^ieOsTfnr 2^ "^ '""" ?*i"r«y »*^ » <'^in rate is $693.33 for Sycars and $640 80ifor SA^ears. Find the pnncipal and the rate per cent. ■■''^"' '*"" ^hTnlSvsr'' ""''*•'''" «1>S20 amount to $1,733.75 ^9n??» borrows I6& on April 10th, and on June- 7 22nd pays his debt with $5l0.20-y-At what rate ner A cent, per annum was he charged^Sl/fea^ ^ ^n/frp^'^*^ ^r"«/ ' ^ *"*^ ^- «« *^»fc nine months' mterest on A's share at 3W oer annum «inl months-interest on 'B's slie a^t 31%, and nSe months' mterest on C's share at .^^m^y aU^ '^«tfwif ''"• ^^'1*^ «*^" $2,210.10 if at the same rate the gam on $24,944. 10 for 1 year and 16 / 44 ARITBHBTIO. il»y« is t2,696.92 1 Wh»t i, ,1,. . . annum (1 ye«r=366 days) ? "" ■*" ^ ""'• H transaction? 'V did I gam or lose by th« on the f, and also 5rc?nn,i? ^'® .''*^"^ »<> ^^i m.f 10. Bought goods ate 4 r ""T/"^'*'^ as made n.y imSl\f .i^ViAr Ret"^'"' ?'^^^' est at 4% per annum, h^^loniiredfttdTgfver " XIX.IPARTIAL PAYMENTS. tofc^a^X^rlS-L^^^^^^^^ be equal! payment. ' "tnerwise it is added to the next ( ^^rnn.«4oO. Date, Mar. 3rd, 1896. Time. 2] ^''\m%: ^^' ''""^ ^''^'^ '' May 3rd, 1897. ^ v^.°''T'^'"'*"^M*'^- 3rd. 1898? Rate 6y P V*A'2^- I^*te. Oct. i2th 1895 ^1^', Paid -Oct. 12th, 1896.3i.00S'/'i^;il^r2Si.'a' *. JNote-fbOO. Date. May 5th, 1897. Time, 6 mos. BAXK DISCOUNT. 45 8 the rate per cent, pe^ iBt. 1895. Tune, sffpall; ^"'"am"^^ ^'^' ^'^^'' ^"8- 31«t» eiOO ; Oct. 2nd ^"'rZ 1%!' *^"^ ''' '"*'""^y <^'^^' 8^h- 1897) ? '''*^'iy;^-°^^' ^''*«' Oct. 1st, 1897. Time. 125 Jan. jgt, 18»7, $100 j June Jst. 1897 SUOO How much is due June Ist, 1898 l'lilto8y ^ort^ge.-f3,400. Date, Sept. 13th, 1894:* Rate ^"^kii^^"^ ?^^S ^®^^' ^^ ' J"ly 2nd, 1895 ^600; July 2nd, 1896, $1,000. "»awo, IW much discharged the mortgage on Jan. 2nd. pl!r*V^^^-?^V ^*^» J"n« 2nd, 1895. Rate 67 •7no^X 17th, 1895, $207.80 Oct. 6th 1895 How much redeemed the note on Oct. 7th 1896 ? P*"-!" ^V*^- ^**=«' June 30th, 1896 Rate 7*°/ $T^^'' '^'^^ '''*^' «200; June 30M97. V 7 "'H^!;.^''^ the mortgage on Jan. 31st, 1898 ? ?a,^'~?f^^- «??*«' ^^^- l^'^J^' 1896. Rate 67 $r08S-. f'£' }??.'' ,^nl^' Dec. 28th. 1896 1897 »5^fn^-«^^^.\^?^' «210.18; Ju^eCth 1»»7, $60.10 ; Sept. 2nd. 1897, $183 25 «ow much redeemed the note on Nov. 11 th 1897 ? XX.~BANK DISCOUNT. '^nJte?T"*''^"**^^P''°^*'^' '^^ ^^»« following >. ?i{^ 46 ARITHMETIC. X'l e 3. G. 4. Y Fiwe, $1,128.25, dated Feb IBth i«or * i^i'. Discounted immediately at 67 // ^'^°' ^ ^^H Face, $025, dated Jan 15th Ihoi * "o "^*''' counted Feb. Ist/m, atVr 'r^^' ^ ^'' ^' Face, S137.60. dated April Igt ]«Q« f . '' counted June 4th, ISjfe. at 87 P^^^"' ^ ™""- ^S Face, 8480. dated Feb. 6th 1897 L /^ ed on Sept. 15th, at 7% ^ > ^' ^' Diaoounb terest at 7% ^' ^'^^ ^^" "^^e bears i„| terest. ' ^' ^"note bears 6% iJ . B. per annum. Find the g^ " ' '"'''' »' ^ 2. A man got a M-days' note for mi ten t , I coat »1,200 cash iust a v«^r T f H? ''* "M worth 6%, find hiS „t^ " '"''"«• Money beiii ' (360 daytto the year? nlT™' ,""* "»» »' "l 3. A bm for ,263.«3fdat:d ?^X 'T- - ' ^^- -fiwa , the discount being at the! pe i Tl Th iTh Th Th ow ] l$3( vi,- L..;i 15fch, 1897, for 60 days I>ate, May 16th. Disj i-biB note bears in' EQUATION OP PAYMENTS AND ACCOUNTS. 47 rate of 9% per annum, and 45 cents bein^r charged for exchange, find the proceeds of the biil ^ ^d^r. \T^ «850. «nd give liim my note at 00 days ; what must be the face of the note to imv the exact sum, if discounted at 1]% per nUth 5 iJo7 f* nT, """'^^ ^ ^''"^ '"y note. Mar. 23rd on Maoist .?"^'' '" l''^' ^^^" discounted at1% on May 1st the proceeds may be $'490 ? ^«8^"' W?^''^^ t^"'' Sives me ^845 for a note of «8b0. When is the note due, interest 8% ? For what sum must a note be drawn on June Ist 1897 ffi at fto/^.^^'' ^ '^^' ^'^^« discounted on June A«tn, at «%, the proceeds will be f717 20 ? .^4oy^^kslhrtfor^^^^^^^ -« ^LttsT7(^Lnrai«er^^^^^^^ -^-^ <^-- ' ^ade Mai^Si,* ^^?^'" ^i«<^«»nt8 a note for $600, aiade May 10th, at 6 mos.. at the rate of 8°/ neVanl money /"' "^''' '^^ ^^^^ ^^ '^^^^ -^--^^n S |XXI.^E0UATION OF PAYHENTS AND ACCOUNTS. A. te interest on what sum for 1 day equals I The int. on f 100 for 4 days ? The int. on $50 for 10 days ? The int. on $130 for 12 days ? The int. on $225 for 16 days ? The int, on #350 for 27 days ? ' 3w many days' use of $50 equals the use of $800 for 1 day ? 48 A^ilTHMETIO. 7. $70 equals the use of |1,260 for 1 day ? 8 080 equals the use of $37.50 for 64 days ? $62.60 equals the use of $87.50 for 30 days ? 10. $52.26 equals the use of $60.16 for 25 days ? 11. I loaned Mr. Smith $300 for 4 months- for hn»l many months should he loan me $^o"io balll^^e'td '"' %zrz irnrth":? ^^ ^^ « ^'^-^ ^« ^^^ -I , ,13. A loaned me $."50 for six mos., $70 for 5 mos • howl much money loaned A for 1 month would Wance'S 14. I loaned A $100 for 2 mos., $75 for 3 mos and toO ^°' 1 r°^ ,' ^^'^ '""^h «h*uld A iS^'iie fof? month to balance the favor 't 15. A person owes another $20 in six mos «5n i« a ^ and ft()0 in 19 »v,^„ **",'" "'^moBMiWHiin o mos , B. 2. I owe $1,700 to be paid down «1 Sno ;« oa ^ $1,700 in 40 davs FnrK 'P^oOOm 20 dava uadl 3. Find the equated time of $50 due in 2 mo« sun • 5 mos., and $30 in 7 mos * • **^ '"I 5. Fmd the equated date of payment On t , . I »r 1 day ? r 64 days ? \ for 30 days ? 6 for 25 days ? • 4 months; for howl me $200 to balance the 00 is equal to the uae| , 670 for 5 mos. ; howl inth would balance the r5 for 3 mos., and |oO aid A loan me for l| »x mos., #50 in 8 mos, j time may all h^ paid o either party ? ' >lIow8 : 8100 immedi- le balance in (j mos her? . !l,o00in20davs uadl ny days must my note I y be paid in one pay ue in 2 mos. , ^0 inj : of «360 due in 60| in 30 days. >nt. On Jan, Ist al ►ws^$500 due in 601 iu 30 days. wholesale house as worth on 30 days' EQUATION OF PAYMENTS AND ACCOUNTS. 49 equated time of payment ^ *^*"^ ^^^ balance this account, allowing interc «""J 6% ? ' Harry Cuipman. 1897 lay 1 . |fay 15. Line 12. Cr. m , II 1897 SOdys eOdys fiOO lOlO iJune 15. By cash « 91000 500 fnfaccouSr ''' '"" '"^ '''' P'^^"-"^ «f '^^e follow- Herbeut H. Burgess. Cr. 1888 Mne 10 Jily 15. |"g ?0 Bpt. 1.. Tomd8e@30dav8 4o days 60 days 30 days << PoundedyearI 6 Jiin^ t, ' ^ ^'"'^ "* ^^ P«' *»•• <'°»P yearly 7 S. % ^"''^ "* '^ P^' ^"^ <'««'?• half-yearly 10. f2,000forrye!r?®irrr' "'"^- ^"*''"^^- 11 JiPft^^ !''y®*^^®^5^Peran.,comp. yearly. i U. m> for 16 months ® 10% per an. , oomp. q„./J 16. A man deposits »lno in a Savings' Bank at th. » or^it „„ jin 2nd I AT,?'','"' «"« l«^to bl > INTEREST. COMPOUND INTEREST. B. 61 per annum, compourdtteea^^^^^ ^."t'^* «% A money dealer borrowed «2^J^ . „ ""^ ^'*«*^"- a /% per annurTcomp.^^^ f years 6 mos. . 6/ per annum, comp. Ltf^Sv fS'T,?- '^ °"<^ ^'^ A farmer mortgaeed his f.ZfL f ""* ^" «*"»• 1894. at 6% pS^;,i,u^ ^^™Lfe^ f .750 on Feb. 1st, amount of moneHas ^Zl^tAf'^^'^^' ^hat mortgage on Aug. IsrisSe^ noli ^ dwcharge the . paid m the meantime ? ' "''*'^*^ ^»^n« been I A man borrowed 34,000 at dv r. yearly. In two vearBVi? 'f P®*" annum, payable What was each payment^InC at^"/ P^yn-enf. pmd approximately in howT -^ ^^^ *"**""» ' money will doubJitlelf at isTZr^" a sum of A man puts «.?50 in o . "^ ^ "^ annum. " n">g of the year is emfLi J^^^'^'i™*'^*^ begin- P« annum, iSSlSS^Sr"? ■""*" ^''** *^ ■ •!»,■»• 62 11. ARITHMBTIO. A lent a sum of money for 2 years at 10^ d annum, compounded yearly. B lent an equal su for the same time at 10% per annum, coSp. ha| yearly. B gamed 220.25 more than A. Find tH sum each lent. i'l; ^vli M ill I XXIII-PRESENT WORTH AND TRUfij DISCOUNT, Find the true present worth of : Ci^ 1. $840 due 2 years hence, money worth 6%. ^ '^V- i 2. ^,026 due 3 years hence, money worth 7%.^5r^' 'I 3. 01,375 due 2^ years hence, money worth 4%di/ ^i 4. $918 due 4 years hence, money worth B %- ° W n ^ ■ 5. $1,120 due 16 mos. hence, money worth 5%.^ Find the true discount on : 6. $572.50 due in 2 years, 5 mos., money worth 6%. 7. $9^0.60 due in 3 yrs., 4 mos., money worth 6%° 8. $1,820 due in 6 yrs., money worth 5%. 9. $416.30 due in 3^ years, money worth 3|%. 10. $636 due in 9 months, money worth 8%. 11. Find the P.W. of a note for $962, payable in year, money being worth 4%. , 12. What sum will discharge a debt of $1,003.50 to paid in 8 mos., if money is worth 6% ? ( What is the T.D allowed on a note for $2,070. payable 19 mos. hence, money worth 5% ? A merchant bought goods amounting to $618 ol credit of 4 mos. ; the discount o^r is 4% for cash money 18 worth 9%. how much cheaper can he get I goods by paying cash ? ' A man rent* a farm for 2 years, at $.141 per annJ the rent to be paid at the end of each year. Mo) being worth 5% per annum, comp. int.; find •um would now pay the 2 years' rent. 13 14 16 PARTNERSHIP. 6a or ^2, payable in A owes B $400 due in 1 vear •qn.-k a • n and $200 due in 3 yeara 'S^hLf -. ^"?,''' ^ y^*"' cancel thA Lv.*. ^ "**' ®"™ P*'*! "ow would Sterest? *^'' ™°""^ ^"'^'^ ^^ i>«' «n . comp A Kentleman has two sons aged 18 and 19 resnecHv^l,, What sums must be deposited in ^K^^KJu^ c^dit now. so that eacS'^wm^e' e?ve%2jc^ Xn 2T XXIV- PARTNERSHIP. A. Vulel''^^ inrestr«fi^^^^^^ '^ ^^ ^^^ divide a gain 7|l%fb^e:n'th^em""^^ '"'^ ^ ISu"T.r"^'y purchase a house, the one paving T?.^. ^ the purchase money, and ihe other £ 728^ They rent the house for «132.75 a vear Ww' I of this ought each to have ?^ What part Bh^uld get f ' ^'^' ^"^ "^"°^ °^ *"« gain l|nrcfpS37f l«/^A^i:t;,' s-«.: biSs j""'" ""^' "P^^^ ^^^ »--- P-t i^o'the hshfres^of oniT ' P»^"«"hip ; their respective did invest ? *" ^- ^^"^ «»"ch hw00f^r^«f^^ ''' i'tf^- ^ P"<:« into the business 54 ARITHMBTIO. 9, 11 12, Rosa rented a house for one vear tnr m^an i. xi. lose^ «1,620 benig received as insurance ? i?. °™S^ ^' ' "»'»»toe"t wa. »2,600 , find ttey"ita J MVi""' ""r^ ?' «f •»?«. hy which B. 1. A begins business with a canital nt Sk'i onn *i. o nios B is admitted as partner wil IS.' 1'' -^ ™rk«i. which ™ 3 to r '-h"^ i^nS"2^inS and at the ««*! «f a ^ ^^V . , ,P"'' ^^ *wy at first •uu ac ine end of 4 months withdrew $300. B puf PARTXERSHIP. 65 I for which they are to head for 12 days the d the third 80 head for ay? r for f 360; at the end armer as a co tenant ; ey admit Patterson, before the year is up. 1 pay ? ylost; f ofitbelong- 3 D. What did each nsurance ? nerahip, their money »o8., 4 mos.. and 3* were $460, $600, and lent was $2,500 ; find of $1,575, by which for his share of the bdid M contribute to 1 of $3,200 ; after 3 «fith $2 400 ; after 3 1,600. What fraction ave ? A puts in 6 horsea eeks, C 50 cows for ned as 3 oxen, and each pay ? ece of work for $60. bion to their ability I to the time each T much did each re- > to carry on a mer- put in $900 at first Irew $300. B put in $600 at first and at the end of 4 months put in $300 more. They gained $3,000 ; find A's share. Three persons, A, Band C, trade together, having a jomt capital of $4,700. A's money is in the business 6 mos., B's for 8 mos., and C's for 10 mos. Each receives $600 as his share of the profit ; how much of the capital did each contribute ? A »nd B engage in busineas, A contributing $7,500. B $4,500. The gross receipts for the first year were ?7eW °^ ^'"*^^^ ^^ ^'*^ ^^^^ ^"^ insurance, and 14f % for other expenses ; of the balance B received a certain sum for managing the business, and the rest was divided in proportion to the capital invested As share was $1,260 j find B's allowance as man- pger. A person m his will bequeathed all his property to his three children as follows : ^ to John, ^ to James, and ^ to Mary. If his property was valued at $7,488 how much should Mary get ? At the beginning of a year. A, B and C formed a part- nership, contributing $1,2(10, $1,600, $2,000, re- spectively. A acted as book-keeper at a salary of «»4b, aiid B as manager on a salary of half as much again, both salaries to be increased in proportion as the business increased. After 2 mos. C added $1,000 to his capital, after 4 mos B added $500 to his, and in 6 months' time A added $300 io his. The total gain for the year was $9,026.00 ; find the share of each. 9. A and B engage in trade, A invests $6,000, and at the JUIJX ° ^^^- withdraws a certain sum. B jnvests «4,000, and at the end of 7 mos. $6,000 more. At the end of the year A's gain ia $5,800 and B's $7,800 ; find the amount A withdrew. 10. A and B form a partnership, A supplying 25% more «n^ * ^""^ ^' -^^ ^^^^ '^^^ "^ ^^® y**'^ A withdraws t)0% of his capital, and B withdraws 40% of his. At the end of 2 years there is a gain of $3,383 50 to bo aivided \ how much does each receive I 56 ARITHMETIC. XXV.-EXCHANQE. _. A. Find the cost of a draft in 3. Mobile „„ New T„.t ZmM^^^Z:^ 4. Toronto on New York for Si 500 JilJ^ Find the coat of a bUI of exoKage in *■ ^f" ^"'■'' °n I^ndon for £330 (£1 ^ti SU) 7. W innipeg on Liverpool for £420 10s «1 IL a-l. 8. ^-Orleans on Glasgow for £600 ^/iirs^jf'^^- | ';^^:fr^jrae1r;^.-rf-"-" VanooJ '"■ ICae'tut^i'-^V'^'**-** franc, ^rt^'^tSTrafe^or" if »»-"«»» Berlin per 4 marks !' *" °' «ohange being 96J cents "• S'"^'^^«-?»^^"S°'e/?4°i!r ,. *''"™'"l>ecost,brokeragtj|/ • '^'" ***^- What did I?eoeive: bVoke^e'i%f *°- ' EXCHANGE. 57 ige on Paris for 1 725 broker, a bill of ex- [remium on the old par. When sterling exchange is luoted at 9, means that £l=:|8g of U-U^. ^^^^^^ '^ • ^™rfy the legal par of exchange between this country and Great Britain was $4.44* for £1. th^ S Lrp^rS^J." ^-''^ ''' ^' ^ind -hat increase per cent, the present value is on the old ^iToolfor l9fi0°^ ^ jO-day bill of exchange on Liver- pool for £960, exchange being quoted at 9* (or par). ':^ili::t9f ^ '^"^"'■'^" ^" ^--^^ ^- ^'720. "i^l'e^rnge atf4^^ exchange on Dublin for £816, ?x:Lrgrt'io ?''™'"'-''" ^'^^ ^^ ^«"^'^^ ^-«2,2oo I' ""^rS^OreriJanle^^lV^^'^-^^ ^^ '' '^^^'^^- ^ht draft LW'*^^ ^" Baltimore for $2,750. I sold ine dratt at i/ premium, and with discount off of &y per annum. What did I receive ? '^ ^or 87 So^riof f- ^^"^^.^ * 60-^*y '^r^ft on Toronto woo *l . ¥ ?"count, rate of interest 5%. What was the cost of the draft ? I ■ )^r ^ 475 Ti"; "^^ ^ ?30 deceived ff J^ J^ ^"""^ T""^ "'^"^ ^^"^^ ^« have roceived If he had ordered remittance through Lon- beTn'^luT-,!?^ exchange at Hamburg onTond^n oeing 11^ guilders for £\, and a^ L""-|7n -- Mn" London / ^'°^^"^«« ^^"g li% ^<'r r;mittance from ^h«'^?®"*'^'i*"™"^* «"^« *<> I*ari.s with $6,000, which ha changes for French money at the rate of 19|Tent! 58 ARITHMETIC. M for 1 franc. He spends 830 francs in France andl thence goes to Vienna where he exchange? what h spends 500 florins m Vienna, and then goes to En J and, where he exchanges his money, gefting Is 8d for a florin. His outlay in England sl-TRinJ How much American mon^y has heffif li% l? J «r^t"K "' y«r^"^«r. British Columbia, owes $4,000 in New York ; exchange on New York isl premium; but exchar^eon Chicago is lndon on Lisbon was ISO pence for 5 ml^es • Jh of L,8bonon Hamburg was"^ 5 milrees for 18 mark 1 Hejhose th. circuitous exchange. What was his ^' ^ew Yntw""^ of exchange between London and J^r^of'el^htge^ ^"™"'"- ^'««^ ^^^ calculate'the ^or iri^* ^'" °^ ^'^^^^^^^ «" P*"« ««« ^e bought for $1,500 currency, exchange being at the rate o $1 for 5.25 franca, and gold being Jt a premium o 6 niSCELLANEOUS EXERCISES. XXVL— ANALYSIS AND CANCELLATION.! ^" ^ieiih 14^S/ K ^""^' ? ^".-n^^^*** '^"d 2 in. thick.j weign 144 lbs., how much wi 1 13 weiah each fil ft long, 4 in. broad and 3 in. thick ? ^ ' ^ ' f ANALYSIS AND CANCELLATION. 59 ANCELLATION. If the property of a city is valued at $16,000,000, and a man who owns property assessed at $6,400 nays 8120 taxes, what is the total tax levied ? . ^in ^^'P.^^^"?^ occupies 40c. ft.; what will it cost to ,* . 2^^H/^- ^"""S' ^ ^^- ^^^« a^d 5 ft. deep, with coal at $5.25 a ton ? . i . i"' If $80.25 pay for 8J tons of coal, what will 7 of a ton cost? ' If i of f of 3J yds. of cloth cost ,", of f of $4S, what fraction of a dollar will § of ^ of Vf of I yard Lt / If 8 men can saw 240 cords of wood in 36 days each U hours long, how many men can saw 90 cords in 6 days, each 9 hours long ? If 600 bricks, 8 in long and 2 in wide, are required for a walk 100 ft long and 4 ft. wide, how many bricks are required for a walk 20 ft. long and 6 ft wide ? & ^• The pound Avoir, contains 7,000 grs. Troy, and 960 sovereigns weigh 20 lbs. Troy ; find the number of sovereigns coined from an ounce Avoir. A block of stone 5' x 3' 9" x 2' 6" weighs 7,500 lbs. (\ 12 sTo7e\^^?x1'"6'%'Pf ' ^' ^ "^"•^ ^' '"^^ ^^^ ■ Reduce to simplest form 1 5 X 18 X 21 X 24 X 27 X 30 X 33 .16 X 19 X 22 X 25 X 28 X 31 X 34* If I6/5 cords of wood last as long as 11^^ tons of coal. ofTo'^dT ^"""^ ^""""^ "^'^ ^^^^ *" ^^""^ *^ ^^* "^""^^^ |ind the value of : t\ f 25 21 a H h^3 16 35 ff '^ 871 2f 81,^1 — X — X — X y 371 98J 2f 128 n 15 :iM 60 14 16. ^of2| 3 of I 2}ofjf AofGg ARTTHMETIC. 6? of 2J 5}ofl| ifufVr* 5^of3| 2/ffOf3^y 8/7 of 3 8 tY4^ of 16 XXVIL—RATIO AND PROPORTION. 1. Divide 35 in the proportion of 2 to 3 B. D|yide^»284 among A. B and C. i„ the proportion „, part of hia capital, bo that the ratio was 2 to 3 IT ^' ^o^?.\\'^'^'*'''' i"l^ *r P^^t«' ^h««e areas are as 9 the farm ^ ^^ *^® number of acres in 8. Gunpowder is composed of nitre, charcoal and sulphur phiSrriir^^^^^^^^^^^ ^^^ placed by water that the ratio may be r.JlTl 10. Dmde «iri.60 into parts proportional to i," Y. | 11. A debt of $88 is paid in $5 bills |2 bills and ftAni S^HndVo .T' <^-minatioX^g ^?^^S tiO 4, 7 and 10 ; how many were there of ea^h ? stiAitiya 61 XXVIII.-SHARINQ. n the proportion of 1. A bankrupt owes four creditors hs follows : A §2,600 B «3,30O, C «4,200. and D $4,000 ; his property is worth f 10,500 ; what does each creditor receive ? 2. Divide $105 among three boys, A, B and C, so that B 8 share may be half as much again as A's, and C's a third as much again as A's and B's together. 3. Divide |825 among two boys that the simple interest on one share for 3 years at 4^% will be equal to the simple interest on the other share for 2^ years at 5%. 4. A, B and caught a certain number of fish ; when A's fish and B's are put together they make 110 ; B's and C's 130; A's and C's 120. ]f the fish be shared equally among them, what is the share of each ? 5. 9. A farmer shared his farm among his three sons ; to the youngest he gave 80 acres, to the eldest * of the whole, and to the second | an much as to both the others. How many acres did the farm contain ? The sum of $1,416 is to be divided among 16 men, 20 women and 30 children, in such a manner that a man and a child shall together receive as much as two women, and ail the women together shall receive $480. Find the amount received by each man, wo- man and child respectively. If lo men, 19 women, and 25 boys earn $15,190.44 in a year (309 working days) ; and if a woman earns f of what a man earns, and a boy f of what a woman earns, what is the daily earning of each ? A, B and C do a piece of work and are paid $73.60 for it. The money is divided according to their effi- ciency and the time each worked ; A's efficiency is to B's as 2 to 3, and B's to C's as 4 to 5 : A worked 6 days, B 7 days, and C 8 days. How should the money be divided ? What does each man, woman and child get when 62 J lM I III m m i 1 ARITHMETIC. and 2 w„„.e„ .„ n.uS .iTiud™?"'' " ' '"'""'"i iw. A man divided ltl'7 qja , . I are 16, 18 and KrB^Tn "? ^'' ?-«^"«' ^^"-« «««J three years afterwards he li^^fn^T'^? !^° their agis: «um. and again Xr 3 /e^ S ^'"J^"^ "^ «^"«1 each son receive altogether ? ' ""^ "'"''^ ^'^ u XXIX- WORKING PROBLEns. 1. A can chop 4 cords of wonri ;« q j t> much in 3 days as A in 4 da?s ff/ ^ ^ ^^«P - pie'ceS'wo^l^ fnTo^days'''^Tff *°?^^«' ^^'^ ^^ - and work on it for 4^: . n\7 "^^^rtake the job B finish the w.)rk in fcs^ IfV"''?^l"^ ^ *"^' the whole work by himse?/?; -^n / *'''"^'^ ^*^« •• ">ere may be a gai] "'• '^'iSu^'SwLr;!^* P»">-: 17 bushel, of water; what ia the strength of S^txIS^S T'l t„re at li rglf §?&°XVlr-*''"''l toTfSo?'^?.fi "' ">■=?•"" »-! water contoi., redilTh\trei"g\h"r6S";? 7,!?'h"'"" '"."'f'^ 'll must be added tS i„or.!tiI si?i„?rt"??J|'r''"' XXXI-INVOLVINQ SUH AND DIFFER- fciNCE« '• ''^rfln&rutr '•"«• •»- "■- <«*— I 2. The sum of two numbers in ftrtAQ . *i, • ,.«. I 7a% , fi„a the produerot^heTul^H.l!:.''"' "*"""'l •J. ■'^no sum of two numbers IS 7ft9 1 „ j ^i. • ,. 1267. FtadthediSn'o^^'be'S^'utL''*""' I 6 •At.n.Z.' ^""'"'"'yan'th'reofeaoh? ^ ' 8- Ataueleotion, A and B were the only caudidate. "nd their differenol INVOLVING SUM AND DIFFERENCE. 65 The total number of votes polled wan fiw« i elected by 772. How man/vldTr B J ^ "" B was elected by a mSoritv ofTw ">° ««ndidate8, feated candwfte J^Sf'e ?°°" ""'"^ ™"' "'"^ *« '^- ai^4ifete»it"t.r&--- 5:f^uXrt^e7.»e^•LtL-ss K r. r J?J be^i^ftltf I?T length of the farm io ion . j ** , "^"*?' " *"6 ho.\.n;t::-rsih'2Lt^r^^^^^ one man works 7v« aI V ^'''l/^ """"^'^ $252, and UouldJhll'ney^'edr^de'^^^ '''''' the other, how fern ^\h7T^""^'''t ^^'^ ' their common fac Iters \:k xifr^niXsr "'^^- ^-« ^- rowing in stmts ^ ^""''- ^'"^ ^'« ^^^^ ^^ M S hZg h^" f ^^«"»'22J miles in 3 hourn but (stream. ^ ^°"'' '" ^"^ "P" ^'^^^ the rate of the IpaHis' m'nfM\'^ """^ ^^"^ '■" «^"l -«ter. Com- ing up a^teeal ^r-T « """^ ""'^^ h'« ^*teof row- fan hoSr ^ ""^'"^ ^°^'« ^t the rate of 2^ miles tiSs 'Ld unV"'*"'" 1i?*^^^« ^«^" * stream in 30 66 ARITHMETIC. 17. I I 16. Two trams respectively 165 yds. and 109 yds. Ion] going in opposite directions, pass each other in 9se onds ; when moving in the same direction the oi passes the other in 45 seconds. Find their rates i miles per hour. Two trains, moving on parallel tracks, and beid respectiveJy 132 yds. and 99 yds. long, pass ea other in 6f seconds. When moving in the san direction the one passes the other in 47 J second Find their rates per hour. 18. The duty on imported axes is $1.80 per dozen, ad SIX ad valorem. The whole duty paid on a lot i axes was $45, the specific duty being $19.80 mo than the ad valorem. Find the number of axes id ported. XXXII. -SOLAR AND STANDARD TIMeJ 1. How are solar and standard times reckoned ? 2. Where is the zero zone ? How wide is it ? What ni« idian lines bound the east and west sides ? 3. Name the centre meridians of the time Eones betwa 5210 w. and 1421" VV. longitude. By what lo names are some of these zones known ? 4. WheT it is 2 p.m. at Greenwich, find standard tin at 75"W. ; 90''W. ; lOl^W. ; 106«>W. ; 113*"W. 5. When it is 11. 15 a m. at New York, 73J0W., find standard times at Washington, 77oW. ; Toronto W. ; San Francisco, 122|"W.; Chicago, 88°W. ; i ifax, 631-W.; Glasgow, 4i°W.j Limerick, 8h°^ Hamburg 10° E. <>• When it is 7.30 a.m. solar time at Winnipeg, fl7°| W , find the solar times at places : 44*'W • 1201 W. ; 56°45' W. ; 30" E. ; 4''30^E. ; 12oi5 'E. 7. When it is 7.15 a.m. true time at Rio Janeiro 42°l| find the longitude of places whose true timts i 5.30. a m.; 2.45 am ; G a.m.; 10 a.m : 11.30 a.i 2.45 p.m.; 10.03 a.m. i yds. and 109 yds. lonj , pass each other in Qse same direction the oii nds. Find their rates i TANDARD TIMEl (1.: 10 a.m : 11.30 a.i CLOCK PROBLEMS. gy What i. the real time^ .t Winnipeg 9ns/W. »t 10.19 What i. the tone time at Borton TriO'W. .t 2.43 r ^'"^ the longitude of the Falkland 1- xno'« ,w^ v • I 6 a.m. there, when it is 1 « r« Tn "^^^^ " '^ la longitude of Which is VfiP" ** ^' ^^ ^^' *»»« * Wha"ttthe?fZ'aW"t' ^"^ ^^^ '2» 3(y E Kome ? ' ** ^^^"^^ ^h«^ it « 9.13 a.m. at ^ebec is 7r 18' W. and Vienna 16» 24' T^' i v ^ When it is 2 D m af v,!^ ^ , ■^- longitude, time at Quebec.^ ' '*''^*' ^"^ ^^^ ^^ndard tng'^o^Vst'fe'^T? '^S* ^'«" St. Petemburg whenw&itb^^Sv^efa^tthn^^^ transmission. XXIIL-CLOCK PROBLEns. Between 9'„"i!ioTJ^.^ ^*",^'» -ectly opposite- Af^KoVr- """""' -between 4 and 6* ^^ Be"t?rnra,""i^re:.'^aSr, -^ ■"-" ^ 68 ARITHMETIC. 6. ^ :en will the minute hand be midway between thj i°Ji%K^"«'*' *"?TT^^''. ^^"""^ ^^- *^t«r 4 o'clock! And the figure III after 5 o'clock ? And the figur 11. after 6 o clock ? ° 6. At what time between 4 and 5 o'clock are the hand ^ of a clock (1) coincident ? (2) 2 spaces apart ? ] 7- At what two times between 3 and 4 are the handj , equally distant from the figure 111. ? ] d. When first after 7 o'clock will the hour hand be mid way between the ligure V. and the minute hand ? 9. What is the time when § of the time past noon is £ the time till midnight ? ^^ ^^* S>vwlV''^/''^r''.™'*^^\*r^^^^^^ '-> hour hand) moving 5% too fast, and the minute ii .d 107 tof slow Jn 15 minutes (true time) .hey will ' ^ together How many minutes measured on the fa ot a clock are they apart now ? ^^* WW W*"??**'.?^ ^w^^ '?^^^ °^ *^« ^^^ ^M When first after 3 will the miuute hand be half-wajf between the second hand and the hour hand ? XXIV._ON ALGEBRAIC FORMULAE. 1. The^-q"are of 2345 is 5499025. Find the square o| ^' '^456T"^ °^ ^^^'^ " 20857489. Find the s-ua- ■ o| 3. Find the sum of the squares of 9998 and 1CJ02. i ^* ^9488*''^ product (1) of 1003 and 997 ; ('.'^ %i2 an '• '■is^i";%r?^ri.^r5itdt ^" "• "- "" -J 6. Find the valueof(H.4+42 + 43 + 4*+46)(4-n- al. find the value of (6* -63+62 -6+1) (6+n ' 7. Simplify (275)3-0 25)3. (276)2 + (276) (125) +(125)2: )e midway between thJ IV. after 4 o'clock! clock ? And the figurJ 5 o'clock are the haiidsl 2 spaces apart 'i i and 4 are the hands! ■elll. ? the hour hand be midj d the minute hand ? t'jne past noon is ^^^^ d igulariy, i c; hour hanJ minute ii ;.d 10% to] time) jhey will 8 measured on the fa >tate on the same axis.! uute hand be half-wajl the hour h»nd ? C FORMUL>e. . Find the square oj Find the s^ua* -■• oi SQUARE BOOT. a76)g+(124 }«. 69 Simplify J*md the value of m2./3\2./_7 \2 . o/owo '• Find the value of M + iS' j.629 ■ bk , ,^e . Simplify «+i)x(;w:-if + ■»" i^Vp- puce to their simplest forms : ^±ii.8+16+32+64+ 128 ^ + '^ +12+2ii:48+96+m* J±6+28+72 + 4^+ 3024 + 241 92 ^+8+24+96^676+4032^:32256' XXXV.-SOUARE ROOT M the square root of • 127449. 984064. 22420225. [0676. f 0.481729. to five decimal places. ■1 to three places of decimals. ARITHMETIC. 8. . 5 to six dec. places. 9. ."^ to four dec. plares. 10. .Ot*7195' SE-l to six dec. places. 11. &i tj *lve doc= places. 12. 13 1 .x> five places of decimals. ''*• Ml '^-^ five places. 14. .047619-r 1.190476. 15. Find within one inch the side of a square whose area is 6 acres. A square field, containing 16 acres 401 sq. yds., has] a walk around it outside. 12 ft. in width. Find the| area of the walk in yards. 17. A rectangular field, whose length is three times itsl breadth, contains 6 acres 900 yds.; find its breadth] 18. The L CM. of two numbers is 10(»,793 ; their G.C.L M. is 17 ; their difference 1,224. Find the numbers.! The side of a square field is 48 rods ; find the length! of the side of a square field containing 2^ times ail much land. f The product of the sum of two numberb by their dif ference is 27.426,663. The smaller number is 2,061, Find the larger. XXXVI Find the cube root of : 1. 1953125. 2. 429172935¥>07. 3. 62712728? ','. 4. 107689002u. 6. 102503.232. 6. 179697.069288. ?. 483.736625. 8. .636056. 9. .697864103. CUBE ROOT. RECTANGLES. 71 >f a square whose area! 10. 32^ to three decimals. 11. ^ to four decimal places. MENSURATION. XXXVII.-RECTANQLES. A. A rectangle measures 48 ft. by 30 ft. ; find the area nf a square which has the same perimeter T\f A half-acre lot is 10 rods long. A 5-strand wire W 18 put around it How mu?h wire at 5c. pir lb wSl be required if 2 yards cost 3 cents ? ^ ^d Jl ii^ w'jf '! fu "■ \l^^ ^^^»- ^id^ ^* ^^^ end, and J4 in. wide at the other, and 16 ft. long ? If It cost 111.20 for paper for a room 25' 3" long 19' f ri^' '^^ ^K ^^^* ^h«»» *h« paper is I yn'ide find the cost of the paper per linear yJl No allowance for doors and windows). ^ What is the cost of boards, at $1 for 50 so feet to make a closed box 7'. ]0" long,' 3' 8" wideband ^ 6" thfck^ dimensions), the boards being 1 inch ' ^ath* 2^^r!5 ""^ gravelling, at ]2ic. per square yard, a path 2 yards wide, runumg around the iiiside of a square field containing 40 acres. Vv ^"In" *^ ^^'■™ ^^ * rectangle. 300 miles long by JW mUes broad, supports a population of 20,000,- support one person. SThe ?ooS§ ' '^-^^ P'' yard ; find the^idth ' ^FfoaTlT^PT r^" ^^^^^ P^"" ^'«'^«"^«r » Portion of road 100 miles loug and 94^ to. wiae. Find the whole amount paid. 72 ARITHMETIC. 1 H i (1 jotI ' m W miff '^^.P^*^*^"!?^ y^.^^^l'^ «f * 'oo™ 30i ft. v.r§V ^ 11- '^''^«' ^2 ft. high, at 18c. per square Itt^Z^^^'^'^^T^''' openings); find also the cost of carpeting such a room with carpet 27 in. wide and coating $1.80 per yard. . / ' B. '^ 1. flow many feet of lumber will be required to enclose a building 60^ ft. long, 40^ ft. wide,^22 ft high Ind each side of the roof 24 J ft., alWing 523Tft for winlti"' '"^ ''''^^^ "" deductions ^for dSors aJld 2. Find the cost of the material required to fence 2* ^S^^nTr^'l^'^^'f ^. "''^^ ^hi*^^' « 2x4 rail at the top and 6 strands of wire. The posts cost 12* cents each, the lumber $14 a thousand, and the wire 4' per pound. (A pound of wire stretches one rod) >^*'!J1i,^''J containing i of an acre is 4 rods wide Fmd the total cost of tlie material for a picket 7ence J'Tt'^f mch pickets 2" wide and 3' long, p aced tid? fi r K"°r^ ^^^"' ^°^ ^° inchT;ase 14" wide the lumber being worth $16 per M ; posts 8 3 from centre to centre at 13c. each ; nails $1 15 ^rVas?\o1*^^'^-f ' ^^ * ^.^''tangular piece of land fe'nVh 'of r 's£ ^^- ''' — ^^<^ the 6. A speculator bought a section of land, each side U miles long, at $37.25 an acre. FindtheTost * ina W ^r^f r* ^^ ^°'^^r S * «*1"*^« field ^'^"fcain- mg 10 acres, by means of a wire fence, when the wire costs 60a perrod theposts, which ar'e let Jo ft apart, 8c. each, and the work 40c. per rod. ^' ^ftn 'o*!!' -^^"^"^ * frontage of 80 rods, and a depth of ?ent. ' '" ^^""^^ ^"""^ ^-^^ P«^ *«'«• ^i^d the 8. The area of each of the larger walls of a room is 330 sq- tt. , the area of each of the other walls is 220 iq. rpet 27 in. widt I'BIANOLES. 73 9. 10. ft. ; the area of the floor is 384 an ft- ah • of the area of walls fl^r !i ^" ?' -^"owing A many yards of paZr 18^-Jr" ^"'^ ^'"^^^«' ^ow covei the waW^ ' ^^' '''^*^' ^^« ^«q"ired to VdThTi^arrtS I? ^- -^^"f -^ 135 ft. at a cost of 22?c n^r i! ^f V** ^'^TV'^ ^'^^^ gravel of the courtyard kcCSZ^'fKV *']^ ^'^^ remainder l^liorh::S\Z^rS^gtJ^'^ '^ ^^- -<^e was expense would have S U6 2(r"^^:!l^T' '^'"^ of the room. «4b.20. Find the length ''• intif by^^r^Te't" ^VJi.' ^' ^^« ^^^^ wore in such casiL 234 L va'rdi '^^t'^^^^g^^ would the original Rectangle ^' ^ ' ^'"^ *^^ ^^^"^ «f ' ''* tirh?t:L\ri78tyd;%7 '^- ^"^^"g^^ i* times its cover 'its wallsfUaS' wfll^^^"' .\^'- ^ ^"- ^^^^ '« . with carpet 27 in wMe In^ ?*' ^^^^^^^^"^ ^^^^ fl««r 1 ^ A i. M "®» ^"^ costmg $1.76 ner var/1 i 14. A piece of 1^^^' ^ ' ^^ """"" ™"^ ""»»• ' of iMd of tKame^„.H '*\"«'^J'"'P'"' "' » ""P XXXVIII.-TRIANQLES. A. "'l.S^^-^^alfthei.>duct sum), base into the »nd 28 their 74 ARITHMETIC. find hypotenuse, find hyi-otenuse. Find the areas of the following triangles :— 1. B'(8e20ft., height 9 ft. 2. Base 45 ft., height 36 ft. 3. Base 7 yds. 1 ft., height 4 yds. 2 ft. 4. Base 9 yds. 2 ft. 6 in., height 7 yds. 1 ft. 5 in Find the areas of triangles -whose sides are 5. 68 in., 77 in., 75 in. 6. 65 ft., 65 ft., 112 ft. 7. 26 in., 28 ii)., 30 in. 8. 24 yds., 25 yds., 26 yds. 9. 319, 444 and 455. 10. 17, 63 and 73. In right angled triangles whcie 11. Base=8 ft., perpendicular =6 ft. 12. Base=40 ft., pi ;v3ndicnlar=9 f 13. Base = 15 ft., perpendicular = 112 ft. , find hypotenuse. 14. Perpendicular =13 ft., hypotenuse =86 ft., find base. 16. Ba8e=16yds.,hyp Lc;iuise=17yds..findporpei 'icular. 16. Hypotenuse = 9.72 ft. , perpendicular = 8. 6 ft. , find the base. 17. The sides of a triangle are 25, 39 .uid 56 ft. respec- tively ; find its area. 18. The sides of a triangular fit (,re and G75 yds. ; the field is ri ed . the rent. B. 1. A footpath goes up the side and then along the end of a rectangular field 432 yards by 390 yards. What distance will be saved by cutting right across in the direction of the diagonal ? 2. The sides of a triangle are 13, 14 and 15 ft.; find the perpendicular length of the 14 ft. side from the angle opposite ; also find the area of each of the two parts into which the triangle is divided. 3. Find the length of the diagonal of a quad 14' x 6' x 2'. 5 yds., 396 yas. fll an acre, find RIGHT PAKALLELOPIPED AND PBI8M. 76 6 7. 8. 4. Two ships sail away from the same port nt the same time, one due north at 8 miles per hou., and the other due east at 6 miles per hour. How far apart are they In 14 hours? /^^ 6. A square field conteining 27^ acres has a diagonal path across it. What is the length of the patli in yards ? The base of an isosceles triangle is 20 ft., and each of the two equal sides is 15^ ft. What is the altitude of thetriH.s:|Ie? A man ca:. alk the length of the diagonal of a rec- tengular^id containing 6 acres, whose sides are as 5 to 12, m S' minutes ; find his rate of walking in miles per h Find the perimeter * a right-angled triangle whose area is 270 sq. ft., the base 16 feet. 9. The sides of a triangle are 40, 45 and 60 feet, respec- tively. Find the length of the perpendicular from the vertex to the side 45 feet. lU. The diagonals of a rhombus are 8 in. and 10 in., res- pectively. Find the area. 11. The top of a ladder reaches to the top of a wall when Its foot is at a distance of 10 ft. from the bottom of the wall, but if the foot of the ladder be drawn 4 ft farther from the wall, the top of the ladder will reach a point 2 ft. below the top of the wall. Find the length of the ladder. There is a garden-plot in the form of a trapezoid, whose two parallel sides are 40 yds. and 50 yds. res- pectively, the other sides being, respecHvely, 30 yds. and 24 yds. Show that the perpendicular distance between the parallel sides is ^f ^j j. XXXIX.— RIGHT PARALLELOPIPED AND PRISM. 12 mi I14'x6'x2'. Find the number of cubic ft. and in. in a cube 1. Whose length is 2 ft. 10 in. 76 ARITHMETIC. 2. Whose length is 3 ft. 4 in. 3. Whose length is 1 yd., 2. ft., 8 in. Find the number of cubic ft. and solid in. in a rectangular 4. Dimensions, 2 ft. 4 in., 3 ft. 6 in., 4 ft., 8 in. 5. Dimensions, 2 ft. 7 in., 4 ft. 6 in., 6 ft. 9 in. 6. Area of base, 4 ft. square, height 4 ft. 3 in. 7. Area of base, 12 sq. ft. 80 sq. in., height 31 in. Find the no. of cubic ft. and in. in a prism. 8. Base 5 sq. ft., height 2 ft. 6 in. 9. Base 6 ft. by 9 ft., height 3 ft, 3 in. 10. Base 6'4" x 6"2"; height 41". 11. Sides of the base 7, 16, 20 in. height 3 ft. 9 in. 12. Sides of the base 13, 40, 51 in. height 4 ft. 10 in. 13. Itain falling uniformly for 5 hours on a roof whose horizontal dimensions are 10 yards by 15 feet, fiUs a tank o ft 3 m by 2 ft 6 in., and 4 ft. deep. Find the depth of the rain-fall per hour. 14. An orchard is 24J rods long, and 15^ rods wide. At 1# cents per cubic ft., what will it cost to dig a ditch around it 3 ft. 9 in. wide, and 4 ft. deep ? 15. A reservoir is 25 ft 6 in. long and 12 ft. 4 in. wide ; find how many cubic feet of water must be drawn off to make the surface sink 1 foot. 16. Each edge of a cube is diminished by I of itself. ^ what fraction of itself is the volume diminish- B. 1 Find the surface and volume of a rectangular soUd. 4 ft'wide^ ^*" '*" *^'^ ^"^^ ^**- ^°"8 ^ 5 wh'chisia'"" ''^"'"^'^ t«angle,each Jde 3. A box with a lid is made of plank IJ in thick; the ex- BIOUT PAKALLKLOPIPICn AND PRISM. 77 ternal dimensions of f ho box aro 3'6" x 2'6" x 1 '9 ", fiiul exactly how many H()uare feet of planking aro used iu the construction. 4. A bed of gravel 4J ft. in depth extends over the whole of a field of yjj acres ; tind the value of the gravel at 10 cents per cubic yard. 6. Find the weight of a stack of bricks 10 ft. high, ft. wide, and 3 ft. thick, supposing a brick to be 9 m. long, 4^ in. wide, and 3 in thick, and to weigh 5 pounds. 6. A cistern is 19 ft. in. long and (i ft 9 in. wide ; find through how many inches the surface will sink if 620 gallons of water aro drawn olf. 7. Find to the nearest gallon the volume of a quod meas- uring 262.5 in. by 126 876 in. by 50 in. 8. A square plot of ground that conbiins -4^0 of an acre 18 covered with cord wood (4 ft. long) to an average height of 12 ft. What is the wood worth at 84.12 a cord ? 9. Find the number of cubic ft. in a hewn log. 12 in. square at one end, and y| in. square at the other, the length being 27 ft 10. If 1^8 men excavate a square basin whose side is 1,000 yds., and which is 30 yds deep, in 9 raos., how many men will be required to excavate a square basm whose side is 2,000 yds., and which is 40 yds. deep, in 12 months. 11. When the temperature of a cube o£ zinc is raMed from 32°F. to 212°F. each dimension h th(ireby increased 3%. Find the percentage of increase in the bulk. 12. A rectangular solid 4^ ft. long, 3J ft broad and 11 in. thick, is increased 11 in in thickness. By how much must the breadth be diminished, so that the solid may retain the same bulk as before ? 13. How many bricks 9 in. io r, ^ in. broad and 4 in., thick will be required to build a wall 45 ft. lone 17 ft. high, and 4 ft. thick, supposing the mortar to increase the volume of each brick 6^% ? '!■ ■rj 78 ARITHMETIC. XL— ON THE CIRCLE. A. Note : (1) c=7rD. (2) Area=ic x i d. (3) Area=7rR2. In the following samples 7r=3^. ^^' ^^^<5<;*»e circumference, having given (I) Diameter = ft. (2) Diameter =61 yds. (3) Diameter =8 yds. 2 ft 4 m (4) Radius = 10 ft. (5) Radius =3| yds. (6) Radius=2yd8. 1ft. 9in. * ^' 15. Find the area ofthe circle whose— (7)Radius= 7 ft (8) Radius =6 yds. 2 ft. (9) Radius =8 ft. 9 in. (10) Diameter=8| in. (11) Diameter=6 ft. 6 in. (12) piameter=3 yds. 1 ft, 7 in. (13) Circumference =11 feet. (14) Circumference =75 feet. (15) Circumfer- ence =11 ft. 8 in. 16. What will the wire cost for a fence five wires hieh around a circular fish-pond, 60 ft. in diameter. 100 yds. of wire costing ^1.25 ? ^"' ^^aL^^^ ^V^^^ **^ *^® '**^^"8 of a ^heel which makes 0,400 revolutions in going 13 miles. 18. The radius of a carriage wheel is 15 in. ; how miTV""^^ ^iU the wheel make in travelling one ^^' ^fi^]^\^^J'St^''^^^^.'>^rcyMchsuhatenda an angle ot db at the centre of a circle whose radius is 25 in. 20. Over what fraction of an acre can a cow, which is tethered with a rope 63 ft. long, graze ? B. In the following examples, 7r=3.1416. 1. Find the difference between the area of a rectangle 27 It. by ^j ft., and a circle whose circumference is the same as the perimetor of the rectangle. 2. The radius of a circle is 6 ft ; find the radim of another circle of twice the area ON THE CIRCLE. 79 3. The diameter of a circle is 36 in. ; find the radius of another circle of one-fifth the area. 4. A road runs around a circular pond ; the outer circum- ference is 280 ft. , and the inner 210 ft. Find the breadth and area of the road. 5. A road runs around a circular pond ; the outer circum- ference is 440 yards, and the width of the road is 20 yards. Find the area of the road. 6. The area of a circle is equal to that of a rectangle which is 512 ft. by 200 feet ; find the circumference of the circle. y. Find the side of a square which is equal to the area of a circle of 160 ft. diameter. 8. Find the perimeter of a semicircle whose area is 645 sq. feet. 9. A circle is 11 ft. in circumference ; find the area of a square inscribed in it. 10. A circle is T8.6t inches in circumference find the area of a square described about it, 11. Two wheelsi of a carriage are 3 ft. 9 in. and 4 ft 8 in.. respeciively, in diameter. How far will the carriage have gone when one wheel has gained 12 revolutions on the other ? 12. Find the diameter of a circle whose area is equal to the sum of the areas of two circles, whose diameters are 12 in. and 16 in., respectively. 13. The diameter of a circular plate of lead is 13 inches. From this is cut out a circular plate of radius 6 inches, and the remainder of the lead is moulded into the form of a circular plate with one-fourth of the former thickness. Find the diameter of this plate 14. Three equal circles of radius of 3 ft. each touch one another externally ; find the area of the space en- closed by the arcs between the touching points. 15. A circular shrubbery is surrounded by a road of uni- form breadth, the inner side of the road measuring 66 rods in circumference, and the outer side 77. How much ground does the road cover ? II 80 ARITHMETIC. 16. Find the cost of making a circular bicycle path 24 ft wide, the inside distance to be a half-mile, at 35c' per square yd. 17. Find the area of a circular annulus contained between twj circles, whose diameters are respectively 100 and XLI.— THE CYLINDER. Note -Surfacer^perim. of base x h. +twice area of base. Volume=areaof basexh. A. Find the area of the curved surface of a cylinder 1. Height 8 in., circum. of base 12 ft. 2. Height 2 ft. 6 in., circum. of base 6 ft. 3. Height 1 ft. 10 in., circum. of base 4 ft. 6 in. 4. Height 30 ft., radius of base 8 in., 7^=3.1416. Find the area of the whole surface 6. Height 4 ft., radius 2 ft. 6. Height 5 ft., radius 3 ft. 6 in. 7. Height 5 ft. G in., circumference 20 ft. Find the volume 8. Radius 2 ft., height 7 feet. 9. Radius 30 in., height 4 ft, 3 in. 10. Diameter 10 ft. 8 in., height 76 J in. 11. How many cub ft. of earth must be dug out to make a well 30 feet deep and 3 ft. in diamete? ? * fit *^' Whlf ^^ * 7,!" '^ ^ ^^- ^ ^"^ *"^ i^ depth 40 feet. What was the cost of excavating it at Tn average of «i2.70 per cub. yard ? 1 ^ *" ^^' Sr '} P\:t "^P^'"^^i"g ^ cylindrical marble B. ^* ^g'h ^^fn W Z^?.^ ^ cylindrical shell 2 in. thick, and 10 in! ^ ' "'''"' °^ ^^^ °"^'' ^^^'^'^ ^ing THE CONE AND PYRAMID. 81 f Circular cistern, 8 ft. in diameter and 9 ft. in depth 18 filled with water to the height of 6 ft. How many gal. of water are m the cistern ? (A cub. ft. of water weighs 1,000 oz. , and a gallon 10 lbs. ). 3. How many cords are there in a cylindrical log 20 ft long and 3 ft. 6 in. in. diameter ? 4. Water is flowing at the rate of 10 miles per hour through a pipe 14 in. in diameter, into a rectangular reservoir 187 yds. by 96 yds. In what time will the surface be raised one inch ? 5. A cubic ft. of water weighs 62.426 lbs., and a gal. of water weighs 10 lbs Howmany gal. will a cylindri- cal cistern of 5 ft. diameter by 4 ft. deep hold ? A circular cistern is to contain 66 bbls., and to be 6 ft. deep. Find the diameter of the excavation, allowing for a brick lining 5 m. thick. (1 bbl.-3U eal • 1 cubic ft. = 24§4 quai ts). ^ ^ ^ ' ^ Two vessels, one in the form of a cube, and the other in the form of a cylinder, together hold 715?, gal. of water. The diameter of the cylinder is 16in^, and the depth of the side 30 in. If a gal. weighs 10 lbs cube^ '• '^^ °'-' ^"^ ^^^ dimensLs of the Ascertain the cost, at $35.10 per ton of 2,000 lbs., of ab4 yards of iron piping 25 in. internal diameter and * in. thick, assuming the specific gravity of iron to be 7.7., and a c. ft. of water to weigh 62^ lbs., and 6. XLIL—THE CONE AND PYRAMID. NoTE.~-^urface=Kper. of base X8.h.)+ area of base. V olume = ^ (area of base x p. h. ) A. . Find the arAA. of n. .t ^-vaA anrf"'>'^ ~f - 1. Slant height 27 in., circumference of base 53 in. 2. Slant height 3 ft. 2 in., circumference 67 in 82 ARITHMETIC. 3. Slant height 24 in., radius of base 1 ft. 9 in. 4. Slant height 2 ft. 8 in., diameter of base 5 ft. 8 in. Find the area of the whole surface 5. Slant height 4 ft. , radius of base 24 in. 6. Slant height 5 ft. 3 in., diameter of base 6.4 ft. 7. Slant height 72 in., circumference of base 8 ft. Find the volume of a cone 8. Height 4 ft, radius of base 2 ft. 9. Height 5 ft., radius of base 42 in. 10. Diameter of base 8.4 ft., height 5.3 ft. 11. Circumference of base 12 ft., height 5 ft. Find the volume of the square pyramid 12. Base 3 ft. square, height 4 ft 13. Base 7 ft. 6 in. square, height 8 ft 14. Base 14 sq. ft 96 sq. in., height 3 ft. 9 in. Find the volume of the triangular pyramids 15. Sides of base 3, 4, 5 ft., height 7 ft. J 6. Sides of base 7, 9, 11 ft, height 4 ft. 17. Sides of base 6, 6, 6 ft, height 6 ft 18. Sides of base 13, 14, 15 ft., height 16 ft. B. 1. Find the contents of a cone whose altitude is 27 ft. and radius of base 10 ft. » ^/ re., ^' ^Wlin^fn .""fi ^S^^^^^'^f ^ co«e i« 20 in., and its neight 18 m. ; find its volume. ^' '^iBsTe^n ^^r-f TT.^y\^''^ «ide of which volume. ^'^^*'' 3 ft 9in.j find its ** '^i'A W?«f °^ ^Anf^\ '''^"l*' ^^"«' ^^««« «la"t height IS 41 feet, 13 40 feet ; find the volume. * "i — ■ ' . ■' ; '"^"^as *& in. wiae win be reauired to make a coni«ii tent 15 ft wide and 1 ft, hiTlOy maSngr''*' ^"^ '"' ^''^^ ^' *"^«d i»» »« tht ^HE SPHBBE. 83 ft. 8 in. 4 ft. ft. is 27 ft., I., and its < of which ; find itfl nt height required ligh, 10% a, in the 6. Find the volume of a cone the radius oi whose base is 16 in. , and whose slant height is 5 ft. 5 in 7. Find the volume of a cone whose altitude is 2 ff li in., and slant height 3 ft. 1 in. ' ^^ 8. The faces of a pyramid on a square are equilateral tolu Je!" ' '^" "'^^ '^ '^^ ^^«^"« 90 ft^find 'the '■ ^by m'^^^finl^T™'**, '« ^ ^«^?«8l« ^hi«h « 24 ft. rlJ? hu°^ *^® volume, each of the edges which meet at the vertex being 30 ft la The^ °tI:?^J'^^r^"*'«V^<'h side of which L'l3T'^Ftd\r vol^^^^^^^^^ ^' *"^ «^^« °^ ^»^«^- XLriI._THE SPHERE. . NoTB.-Surface=4 wr'^ - volume = J 7rR8. A. In the following n—^. Find the surface area of a sphere 1. Radius 3^ ft. 2. Radius lOJ in. 3. Diamoter 8 ft. 2 in. 4. Circumference 11 feet. Find the volume of a sphere 6. Radius 4 inches. 6. Radius 7 inches. 7. Radius 7 in., and surface 616 aq. in 8. Diameter 11 incites. 9. Diameter 31.5 feet. 10. Circumference 8 ft. 8 in, B. In the following 7r = 3.i4i6. 1. How much gunpowder m\\ be required to fill a ho!low 84 ARITHMETIC. a ^' ^^rdib'irr'J^Sf * -^l" ^^ ^''^^ ^ i"- i» diameter if a cub m. of gold weighs 11.194 ounces. The surface of a sphere is equal to half that of a richt circular cone ; the radius of the base of the cone if 1 sphere"^ its height V3 feet. Find the volume of the *• ""ne'sslflln^ch "fi"/..^"' '^ ^^*™^*^' ^"^ i*« thick- ness 18 i inch ; find the volume of the shell The inner radius of a spherical shell is 5 inches and th^ejhickness of the shell is H inches ; find ite v^i^ we'girisO lbs!* ' ^ ^ '"^^^ ^""' °^ '^'^ "^^^1 Tl 1 1 I. ^^ poiitentsare poured into a cylindri- Tlr^t f.u^""'^ '^'^^^^^^ '«diSs is 14 in. : find the depth of the water in the cylinder 8. The diameter of the base of a cone is 4 in and it« x'nchThictnP^^'l^ '^''' "^ * spherical sfSl of one nch thickness the external diameter of which is 4 m. Find the height of the cone. ^mcn is 4 9. If a sphere, whose diameter ia 4 feet, is submerged in ^^' Ink o^fTe^S '' "!?" '^^^ *^ «" * hemispherical suppheVbVatpe%t832Tal 'of" % -«tern\hich (1 c! ft. = ellal!). "* P®"" ""'""te XLIV.—QENERAL PROBLEHS. 1. A number of men and yvcu.^n «ftrr.«j 4ioo „ j._ S^?1"'"I «^-25 and each "woman If. 50 '' g^S therel,een b more men and 7 more womin the whole of the pow- diameter if fc of a right le cone is 1 lume of the its thick- 11. inches and ind its vol se external the metal BS, is filled a cylindri- ; find the 1., and its ell of one ivhich is 4 aerged in neter, the 11 it cause isphericaJ rn which r minute ►0. Had he whole GENERAL PROBLEMS. gg of each. "^'^'oi'nen. Find the actual number digit, i. divisible by 9 •^^^^'^ ""e sum o£ it, 7.44 time^a^ liaS 11 ?s Z'^"' "'"'° ?" "''S'" «.ew ii jirIl X'oi" ™:;°/ <" po"-"^ °* •-" mill. „n .„ "•'•"«>«* ^% yearly ; the tales are 16 mills on an assessment o( «12.460 and kurA- "pent each year on reimin.wi.Vl' ^ "W^^o is do», the invLment^n °' ""*"" steps pef „!„., <,:"^i"inTtheL^^h' TZo^i^,:" e. Ex^Uin how to find the vulgar fraction which e^'iial, nrs. oeiore A. Fmd the distance from P to O A number of 2 digits is multiplied by 3 and th« n.^ A has 8 bottles and B 2 Kettles of wine At ^ I GENERAL PROBLEMS. 87 Troy, and froy, how in to do a in average len do re- ay 'a work. > complete elp of 17 much less B part of as than )w many 9 minute the hour lire of 16 gal. cost- 7 selling » bus. for and the sre there f 17 per ining 37 » weigh eight of iron rod minute bk other. thick ; What is ing the same a« length) that can be construoied with either kind of bnck ? 21. How many days are there in four hundred consecu* tive years ? 22. When is a number exactly divisible by 2 ? by 4 ? bv Jj5^y6?by8?byl0? by 11? by 13? by 25? bj 23. The quantity of saline matter in sea-water is .036 of the whole weight, and of this weight .061 is magnesia 1' ind the number of grains of magnesia in a cubic foot 2 (K» lbs ?^''* 8"PP<»"ig 32 cub. ft. of it to weigh 24. Equal weights of gold and silver are in volume as 20 to 1 ; and equal volumes are in value as 1284 to 36 A certain volume is composed of equal weights cf gold and silver ; find how many times more valuable the same volume would be were it composed whol y ^^' 'Sf3«*'^°^l?129 is 102696641; find the square of 101293 without going through the operation of squanng. *^ ^^' tifhJ^'J^r ?,°»?e8 do^n stream in 40 minutes; without the aid of the stream it would take him an hour ; how long will it take him to return against the stream ? 6~«»w »- "« 27. A certain kind of brass is made by fusing together old braw^ refined copper and zinc, in the proportion of AJ, 6o and24; how much lefined copper must be teken to produce 170 lbs. of the brass, after allowing 28. At an election in a constituency in which the number of votes was 1800, the votes polled by the candidate, were in the ratio of 7 to 5, and the successful candi date was elected by a majority of 240. J'ind the number who did not vote. ;■ ~, iT'^--"i-"'~6'*^'^> oxygen ana iiyuroKen, in the proportion of 89.9 to 11.1 ; what weight is there of each m a cub. yard of water (a cub. ft. of water weighs 1000 ounces) ? ..^* . 88 ARITHMETIC. 33. 34. iafn of 157 ^ ! S' * ^'''" •"^.^^^' '^^ ''^ *hem at a gain ot 15/ and the remanider at a loss of 107 foTff Xe^Jl ^'^^^ ^'''' ^- --^ <^id 4fy ^^* torTlo^h^*^K"'-^^.^^"*<^' he can sell it at once of f20 n?id ^'- \ ^^ ''T"^ ^* "P ^«^ « ""«• »t a cost ±le adopts the former course; money being worth oriT^y-soIin'r™^^ '^" ""°' '^ '''^^^"^^ 32. A bankrupt who is paying 37Jc. on the dollar divides IZZtt)''-'''-'' '''''' -' -l-tdohisdeb?: If 3 men or 5 boys «in io a piece of work in 17 days in how many day. . ul men and 3 boys do a Se of work three tm.rs fl^! ^-reat ? /a uu a piece 8lirn^jM'''nr' i'-i^J'*^. ^^^'^^0 ^*^- «f lumber at his ga^n! ' ' *'^*^ '^ ** ^^''^ P«' <^- Find 35. A merchant bought HOO bbls. of flour at 86.25 per bb . ; on a credit of 8 mos. He sold it at 86 50 per bbl on a credit of 4 mos. Find his cash gain monev being worth 12% ** ' ™°^«y t md the ratio of A's speed to B's "• morit m1 °1 ""?. t'u»* r"-' «■ ■»«»y «"" 30 OKVERAL PROBLEMS. gg inches per yard ' ^ ^® K^'^s "nly 34 he gain J'«5 on thV^t'e tillLttT^* ^'^ ^^^^' '' ''• ont'l^xJ^e^e'^Sor J^^^^^^^^ one,sixth now, and What is the eq^uatei time? ^' ^^"^" '^'^^ ^« P^^d- 48. One-sixth of a deb taTdue ?6 d """ " ' "°-- due now; and the balance x^n^^''^'^' """^'^^^^ '' equated time f payment. ^^'- *^'"^ *>^e A workman was hived for 45 davs at ftl an , ^ every day he worked, but withThf * ^^^.- '^^^ ^°' for every (Uy he was id 1p 1,1 *^^«/ond»twn, that On the whole heZdei^^7V'' ^^^^^^^ 27 cents, he work ? ^ '^•'** ^ ^«'«^ n^any days did 50. Divide$980amonff4mpn ir» on the supposition that ?man doe? '"^ ^0 children, men or 6 children ^^ "^"^'^ as 3 wo- ployed? ^^ '*'*^ 5 ^°^ n»any men were em- 49. '> IMAGE EVALUATION TEST TARGET {MIS) '7- /. // t «* ■6r 11.25 Z. Big ^" lit lU u 140 1.4 .Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14S80 (716)872-4503 iV s\ ^. ^\ was '':;j^^-^ 90 ARITnaiETIO. 62. A map w drawn on a scale of 8 mUea to an inch • on tftw map a township measures HJg in. by li in • how many acres does it contain ? ^* ' °' ^* "*' ' ^""^ 53. How many exact divisors has the number 6336 1 fh«^."^" r"*". I'u* perpendicular walls 16 ft. high, the diameter of the room being 28 ft The ceilS^ 8 a hemisphencal dome ; find th* cost of plaaterinf the whole surface at 17ic. per sq. ft, n=d, ^ tjf ?nf "** '^'^"T ^"a® ^"- diameter, is meltedand cast mto a conical mould, the base of which is J8 k» m diameter. Find the height of the Tne ^ ""' LunT^fc^'yn^' Vf "^ ^i^^^^S'^'^O an acre, and by selling It m allotments finds the valve increased acre'S^himJf^'H^ °^^" ^^^' ""^ "^'^ ^^ acres for himself. How many acres did he buy ? ?«L .^ ^^^ ^''^^ ^V P*'**' ""^^h th*t the simple in- le eouaftrilT" ^"', ^-^f "' ^' ^^ ?«' annuCi^y 6 vZ« L <»! o^ """P^^ '"*^*"''' *^" **»« <>th«' P»rt for o years at SJ % per annum. ^* «R"So'?*'lVf "' two kinds of flour, the superior at MO fcn ill ^''^ *^",-°^^"Li?* ^ P«' »»W. 'He sold *^' fn ft^'^^i*" ^ll"^*! ^^'^^'^ ^^"^^ 1» 1896. to be paid ^dtrn'^fcftv interest at 6% per amium till Sue, «rf flS ?« * ,^ P®"" ^t""""™ *"^ P*^d- The note wa^ amount ""^ "^""^ ^®' ^^^^ ' ^"^ *^« «"<'t 62. Three persons. A, B and C, trade together, having a i mos^'^B^sl**'^^-. ^> r"«y^i^ '^^ b»«i"«»« •^ ak^U »r'" Ti ^ ' ^? "^^■- ^«h receives dre^h'cS.&' ''^ P'^"^- ^^^ --^ -Pi^^ OBNERAI. PROBLEMS. 91 63. A grocer reteCing sugar at the rate of 22 lbs for «i makes a profit of 11*°/ if „ ili t ^^^ *' ^A per annum, brokerage being ^% "^viaend of J897, 1600 worth at 30 days' credit. Feb 25 189?' ^h aTlf da;^ cfedftni^dlt f'^*'^' f^ inter^t should^ be^^^lj^^r.-^^^^^^^ 66. A person sets out to walk from A to R af fi,« -^ . 5 mUes an hour. When heTad tmfeJled Ji mill' i.17r rr'*''"^ by a coach fronrATwhthla^ S f^r^V**^ afc starting. At a distance of lU miles from B he met the coach returning f < on B. whSe 1? had^stopped 30 minutes. What is^he Uistin^Xi' "''• tVoXare STeeo' Th" °' '^ '^^^"^-^ -<« - is 1 9Qfi . J ®P- ^^® number in the regiment squ;?eV "'""^ "^'" """^ ^" ^^« front We ^' of Jf,;"*;!" iS*''* J'P,? P°^^ 31 inches during 12 hrs hou^ n?^>^ ''"'I ^\ ^°^" '« inches during ]i Jet S?l?.^ ''*^*' ^^'^ ^°"S ^"^ i<^ teke the snaS to get to the top of a pole 35 feet high ? teSrt'J?.*' ;fn\"^^"^ ''"'i'^^" g^^« "««« a pound Z^^ll. \ ^"^ ^®*''y' »"^ in selling them a Sound ^nn^^*' * ^'- t'^^ J'ghfc.and gains |l9 by hi^Ts honesty Fmd what he paid for the goodT ^ ^*"' tt^of 'n vh!'""' o*''""' *"^. ^^^'^^ *° ^^'hool at the rate of 11 yds. m 9 sec, and is 1 min late Jthl had walked at the rateof 22 yds. inTs U he wouM 71. A man in harrowing a field walks 26 miles in a day. i X r 92 73. 74. 76. 76. ( i ra 79, 80. 81. Ar.iTHMETIC. If his harrow he 00 inches wide and the farm worth J^weSl^X,'"' ^'" ^''^"« ^' '^^ ,ro^yXr. w It wouli i. >;^'* ""1^* ^^- ^•^"S. into three lengths mus't be"takPn ."^''* "' *?°-' ^- ""^^ ^Oc. per lb. V6c a lb ? "" ^ "''**^"''^ °^ ^ Iba,, worth I bought a farm for $10,000, payable one-half cash the remainder in 1 year, with interest at V/ T ii nnmed ately for «12 000 nn^iili • o '^^ ^ ^®" interest at 47 Wh'aVi mv ni '", ^ '?^''- ^'^^'^ being worth 5% ? ^ P'*'®''* «*»"' «^«ney of each payment. -^'""^ *^® *"^°"nt A has 1^ as much money as B, and B has ^ as i A Ao/''''\^ ^^' ^"'^ «*'»^«« twice as mucn ^s A. How n-.uch money has A ? " nf rT.f^"' ^2 ^''«- °f ^^e*^ and sugar for 818 89 He sells the tea at 66c. per lb., and the suLfitlc' per lb Find how much he sold of each. ^''*'^°- circle, the diameter being 20 feet ^ tf 62*"/ •''hnr.h'l "«"\g««d? to a merchant at a profit or lose ? P "^'^^ *^® manufacturer gain A merchant sells goods for «1 287 Woif i, u . nn advance of ^'ifo/T :V *^»*o'- iialf he sold at yny ^ fi, ^<° ^" the cost ; i at an advance of A« agent sold flour on a commission of 37 and with the proceeds, minus his commission on tthtrlis^ 8 mucn as GENERAL PROBLEMS. A# ^ffST' 1,1: ™ ,•,:'"■">■'»!'"■ ••' n on the »« agent f„? | rthRj'"'"Sl'''%»'''<''e thmu.). 87 A'sfarmi-l , ^"""^ *^® ^^e* "^ the circle ^^itrt^Z^ ll r,^- i of a square Ho^ many aJres are in C W^f ^ « P"<= <^etb.r. per Kai. of the superior quality '^' ^^ ^^^ ^^^^^ centric walk of the Mme tSSh . t ""'' '"'"''«'• °™- fcrence fa 12 feet frlXt'„^t;:''""SS!; «'«■»»■ .^bndge. fa 18 '^r^'fZ'ltll^.^TZ .tock did e«,nontribu?e?'°" "™' ^ ^ow muci; 94 ARITHMEtlC. 96. -u ou per cent., for 10 per cent, stock at 125 nere«nf Ho>. much was his yearly income increaaed ?^ the field ? ^*''' '"^^y *«"» »w there in 95. What sum must be inveaf * t^e and the cTrcX7e?fence of tJ^ ".^^?°»«<'"bed square 99. A man's income consists of a fixed salarv of ^PKift « annum, of dividends on «harelnavin„ kv *^^^ P®' and of rents ; if his dividends Kf o/h^i^'S""*' for managing the busintd^'hi'"^'^^ of the profits 11,600; ^d^thesh'rreaoh^^r ^"^^ ^"^ 101. Fmd the cost of a draft in Montreal for |1,000. OBNERAL PROBLEMS. 95 cent, stock 26 percent, ed? 9nts 13,824 t scale is it ^n isosceles 'ds. and the •ro there in ingof each Aie at the ' cent, per days, find e meadow sum ; and iie sum of inscribed ea of the ed square , also the imference £610 per * annum, > total in- apital he by three 313,000, ^ and B, le profits 'ofits are |1«000, n^^h ^' ^"y" ?^.'^' ^•K^'^' exchange being 4 per cent, premium, and interest 6%. 102. A man buys stock at 90^, and^sells out at 90, there- by losmg $206 ; he then Invests in stock whidx i^ "t t^^^^l premium, and sellh again when it has Inlt^it Rf' f "'• P''^"^^"™- With the proceeds he investe m the 3 per cent, at 81. Find hiJ yearly in- come from the last investment. ^ 103. Copper is bought at |76.50 per ton payable in 6 months ; how should it be soirthe same day (giving in^ T '^ '"**"®^ ""« ^"^^^ *% per annum. A ^/ir."*'''^^^ '°' *^^^ ; if I seU both and lose other eri*n,r? T^ ^T' ^"* «*^" «^ °" ^^^^ '»»« other cost n.e, I should gam on the whole U%; what was the price of each ? ^^^'it "°^n«»l»' I'in which contains 480 cub. fL hw Its depth, length and breadth each iniiii—itl TOT What IS the capacity after this is done ? ^^'J5.f?'''u?u®'^"^¥•■8«"* in Chicago 3,000 bus. lu^ ^^ "^ "?^^ *<^ »^- » ^"»- The ^gent dt 2i^« onT""'"'"".' *^^ *^«° * *% commission in advance on tea purchased for his employer. The tK^oiir""^ amounted to ^200 ; find the rate of LTerdl'^'^^P^^^-'- iha\:t's?h"eamouni 108. A dealer shipped 200 bbls. of apples to Liverpool he^h^v^ ?r^ •J-^^.P^' ^^^' *^r what sum^i a^ainJ all^l^PP ^^ "'""''^^ ** ^^% ?'«>"• ^ guard against all loss xn case of shipwreck; his other ex- penses being 175 ? *- , "« uwior ex ^^"A^fhf «?/''? i**'*"*"v^'" °*Pi*»l »>eing f of B'8. Ual and at t^'^^T^' ^ withdraws ^of his cap- hS How .1^^^ f ri^^ nine months B withdraws i Sf the end o7 tT^Ji'^ ^"'^ * «"" «^ 14.222.31 at ii ft I 96 ARITHMETIC. of 12kV nilhfTT • ,^' **• further discount and a still f. rf., ''f ^'"'^ ^'' *^'^'*'"« '^ a"«ntity, cish F Ll . • '^"'"""*^ "^ ^0% '^ff li« bill fc,; ^^^" 8^541 iV-/ ''•"'"' "^ '^ '^ ^'^y d'-^ft in Detroit for 92,545 at ] ;/ preiii. and interest 0%^ * at RjV/Luri '' ^^;,' V ^b' «nd 4 months' credit; WKof • fl ^ n'^^nths' credit ; or at 43.01 cash What 18 the cost of 350 bbls. bought on the To^t itTnnrr ^^ '''-' ^^^-«' --^-"^ -^thl? Kit"pTrLr/^^'-^- ^« ^^' rlitVofrt^L^^^ ^^*" J/^ ??^" ^t ^"^ ''■''" "^^'S^^ 441 lb.., find the weieht thicV cannon baU. the metal' being 2 3es ^^^•c^nl""?' ^ r"^^ '^ '^^^^^ *« kalsomine the walls and 20 ft^bv25lr"'"r'^f ^^- '^«^'- >'d" the room being 116. Assunung that the 4.1b. loaf sells for 9c. when flour "/* ^"- ^"'« sell tor If flour advances 507 an/1 f h« cost of making and delivering remain as biC? 117. A merchant marks his eooda af fioy »^ cos, b^t allows two succeSd^L'u'i^tsoTand 2,280? « 1"« gam on sales which amoult to ^'^"a^d^ London "^XfZ "^ ^^^^^^ ^^^ween Boston «3-107s« fj' England, when a bill of £640 costs ,in *X'/^'^^^' the broker's commission bein- | °/ ? 119 Find the volume of the largest sphere "that can be formed from a cube whose volume is 2.744 cub Let GENERAL PROBLEMS. 97 120. On what scale is a map drawn where 240 000 square miles of temtory are represented on the map by a space of 6 inches long and 4 inches wide ? ^^^' tor\^«"lT. 1^^" """^bers is 578 ; their common fac- fnlXl ' *£?. ^^iff^'^-e^ce between the other two fac tors 18 8. What are the numbers ? J 22. Thearec of an equilateral triangle described on a side of a rectangle is equal to the area of the rectan- fi« M!"^//u ^ ''/.^''° rectangle is 16 feet ; what is the length of the other side ? ^'^^'ll'f *f """li^in* ^""^J^^ * ''^"^ «^ exchange on Man- Chester for £240, and received W,166.54 as the ne^ proceeda At what rate of exchange was the bill sold, allowing 1% for brokerage ? ' 124. The boundary lines of a field are the following : the first runs north 36 rods; the second, north east 60 rods; the third, south 72 rods; and the fourth, west to the place of beginning, 48 rods ; required the number of acres in the field. The sides of a triangle are 30, 40 and 50, respective- IL T^ the area of the triangle formed by joining the middle points of these sides. 126 I I. 99. ( (8) 4 B.— (J 6471. 892411 (10) 71 II. (5) 3V 3J. (1 III. «16700. «l7b2.6 n lirs. (U) 22( IV. (3) 549 9.98907! 114.172: 201.072^ V. I (3) 246.f (6; 246.! 28.72483 ^^ ARITHMETIC EXERCISES POR FIFTH BOOK CLASSES. I. Page », A^SW£R8. 99. (4) 315 (10) 713. (lb 297f fr (12) ^tl ^^^' (9> «8S90142. 9.989079. (7) 40.03822185. (8) 35 SS* n 114.17229528358241. (lO) 67 4105429fii^i o«k /^^ 20L07280049626.84. (12/84^37'^^ <^^> /ox • . "^* **— (1) 2600.08392. (2) 32 39787rfi^ (3)246.85164437. (4)367.33277459 (gf 70, t">?!?!' (6; 246.90943502458353. (7) 79 7899^m-;8^h^^^^^^ 28.7248373204452766. ^^^»yyt>66777488i>5. (8> (99) t i ilir- 100 AIUTIIMETIC. (3) A 4Uf> • (10) (4) (10) ^oJh..^^^ I5.-(I) 111.5524a (2) 182.161828 $?^ 73.64101}i44. (4) :J(J5. 4860570. (5) 11008.662869(5' lnLi?.o'**-2^^- <^> ^'*^^''^^''- (8) 12344.365. (9) d529.l63. (10) 150.8741. (11) 4.1581. (12) 2.3758 2^1^51- (14) -2304. (15)13.5169. (16 6689.6527: i^^lf}^^-^^' ^^^> *13*'-^- <1*-^) «122.93. (20) /..^'.tt J**"^*.v"^-^'> •^^*- ^2) 33.080. (3) 1.732. li\-5^^^-. <^^ -4^241. (6) .3183. (7) .6931. (H) JOlOa. (9) 29.956. (10) 7.9577. (11) 23.0258. (12 .03183. (13) .43429448. (14) 3.186. (16) 3.8236. ' 8.0219. (17) .1013. VIII. Page n. A,-(l)fJ. (2)U. i7' (o) ^U- («) ti. (7) ,V- W ^U (^ ?. (11) A. (12) ^^i>^. B.-(6) .714285. (7) .840163. (8) .421062631578947368. (9) .6470588235294117. IX. Page 18. A.— (1) 1.99999. (2) 1 49999. 1.33333. (4) 1.24999. (6) 1.19999. (6) 2.7183. 2.4107. (8) -.2027. (9) 2.7180'6. (10) 4.063492. (1) .0338235. (2) jSiiS^. (3) J^ (4) JU r5W \n:. (7) io.iWV-^\^d;9. ^ \lo) 12 i^'diSV" 4.605. X. Page SO. A.— (1) 18 ; 5.56 ; $14.58; 822.12 • J67.05 (2) 76; 195; 648; 3025 ; 278 (3) ^625. (4) f^^f'l^' ^^l^'^^^' (6)^500. '(7)85025. (8) 460a (9) loO. (10) 801. (11) ^4(J0. (12) 387. B -(1) ^ll^%.?:i^l"M- <3>^%- <*)2gal. (5)88. (6 l\Kk <^V^- W «160000. (9) 75%. (10) 223%. (U) $3600 (12) $3125. C.-(l) 216. (2) 66^%. (3) $439- .68 ; 6293.12 ; $183.20. (4) 65c - ~ ' • ' (7) 800. (8) $50. (9) $28UO. 58jV%. (12) 35c. ««S';« ^^^ ^^' ^—(1) «227.50. (2) $448.04. $676.60. (4) $.376.96. (5) $505.40. (6) $696.16 $855. (8) $1451.62. (9) $1692.62. (10) $596.03. l?2^-^^f{ 41S: *'.S-^,¥- B -d) «950. (2) 15%. . *16. (4) v9^ (5) l|c. (6) $6. (7) bW/. iH) '2UY (9) iii%. (^ iio%. (iVi« (4 i>f% ^ U- (3) (7) B— • (6) (12) (S)8t^%. (6) $1.76 (10) $139.10. (11) (3) (7) (11) (3) ANSWERS. 101 82.161828. «.662869(). 365. (9) 12) 2.3768. 6(J89.(>527. 1)3. (20) (3) 1.732. 93 I. (H) 258. (12) 1235. (l(i) ) ifi- (4) ) .840153. 7. 999. (3) 183. (7) )2. B.— )il (6) l (12) $22.12; 1625. (4) (8) 4008. B-(l) ) 88. (0) T/o- (11) [3) $439- 6) $1.76. \i. (11) i.04. (3) 10. (7) 03. (11) 15%. (3) . o.— (10) (l-fi) 2^/. B— (1) 125. $1716.49! (2) $140.50. (0) $17,523. (10) $8 77^. (2) $1612. (3) (7) (11) (3) w'm&, KSJb &'% ri*^^^^^^^ (6) $300. Vo) $96 . »~!''^°' ^l^£^^° ^""^ (**) «2.76. r8^fioy /m ..,n.i***'-^' <7) $1040.60; 32A5+A/ (6) (0) (3) (7) (il) (4) «43750a- (5) «^0.-(6f2Slls.^^7?f&'^'^' 3107.10. (8) $144.20. $916.60. B.-(l «i.05. (2) <^67 20 I 29 6-, %W^^ (?>«52.5a.- (lor$8125: $916:60 ""'b^^V'^^^^^^ ©e^O?! (14)18.40. $85.07. (8) (9)4%. (10) $783.36. i 102 ARITHMETIC. SoH'i„/®>,^^^^'^^- (9)81331.90. (10) $413.10 (m S32.62J. (12) 69c. B.-(l) $2.80. (2) $3398.72. (3 (8) 240 bags. (9) 80c. (10) $85. v / v w XVII. Page 38. A —(1) $5760. r2^ $12600 f^\ fWOO (4) $23856. (5) $36330 (?) $33M.' (7)^^^^ ^IV ^x^So«/i^> ^,^5- (14) ^262.75. (15) $9066- .25. (16) £3542. (17) £26031. (18) $3276 ri9^ 02^^ «.«^'%il'^fo?- (21) $ll03/.26. (22) $14^22 (23) $36. (24) $61.25. (25) $169.60. (26) $111 mi /ifL?^^- (29)«276. (36)$56ii. 31 None. 3) $992. (4) $56.25. (5) Former '6^' JI?U^nn. ^-^1> ^34.20. (2) 60 shares^ (3) $17ldo' iVr,l2Tm l?^l^f • («>yi808- (7)12^yiar8^) (^2) $5'02g ^ "^'* (^®>13A^- (11) 384 sharer. (^)''$16V7*7. ""^Mo^^--^^'-"^^''^' <^> ^^• (7) $81.91. (8)3% mos. (12) $675.89. $2475. (23) $3 $228.80, $2550. $5200. (44) (48) (2) -(1) $66.63. (6) $156.49. (9) 8%. (10) $66. (11) 2 yrs. 7 (13) Oct. 7th. (14) $11,000. (15) (6) $109.63. :il) 2 yrs. 7 $373^. B.~(l) 7^1%: '(2)~$525"'25- W^(3\!^iy ^u\ 1890. (8) Lose $108. (9; $21.. days. (7)' Dec. 26th, 58J. (10) 6 mos. ^„XIX. Page 44.— (1) $139.92. (2) $260 (^\ «ft9 56;, (4) 8115 49. (6)$178.93. (6)$2S (7) $1*" 266.36. (8) $98.68. (9) $295.94. ^ (10) $22.58. ^ ^ ' * XX. Page 45. A.— (l) $1.116 67 S^ *i2?-2Sool*> «*7»-6«- (5) $i,9&. 33. (7) $722.72. (8) $600.62. m «47ft 6« nO) •« 3 -(1) $119 30 (2) $67.'6b. (3) mT^U 472.94 (4) $8a3.116. (2) $616.64. (6) $4,194. ANSWERS. 103 MO. (11) 8.72. (3) (7) $960. !2600. (3) (7)13940. 1)128497. 5) 99066- 75. (19) \) $14022. 111. (27) W. (31) 00. (36) 39) 7H%. '60. (44) K). (48) J. 50. (2) (6) $79. ) $17100. ears. (8) 4 sharer. $63.09. $109.63. 2yr». 7 OO. (15) r/o' (4) .0% ; 265 (9> $21.- (3) $82.. (7) $1.- $616.64. $4,194. 10) $2,- 1247.46. 7) $730. XXI. Page 47. A.— (1) $400. (2) $500. (3) $1 .- 660. (4) $3,375. (5) $9,450. (6) 16. (7) 18. (8) 30. (9) 42. (10) 24. (11) 6. (12; 4. (13) $650. (14) $625. (15)10mo3. B.-(l) 4 mos. (2)20. (3)41 mos. (4) 70 days, nearly. (5) Feb. 14th. (G) Dec. 30th, 1897. (7) Pec. J 7th. (8) March 20th. (9) Sept. 2nd ; $917.90. (10) Aug. 23rd. (11) $737.56. XXII. Page 50. A.— (1) $126.10. (2) $247.20. |f3) $44.93. (4) $28.81. (5) $248.77. (6) $31 "S. (7) $a8.81. (8) $153.22. (9) $94 62. (10) $268 (11 $16 33. (12> $172.21. (13) $73.76. (14) $52.56. (15) $689^84. B.-(l) $791.57. (2) $1.91. (3) $70.45. (4 $1,979.97. (5) $4,955.08. (6) $897.86. (7) 5, nearly, (8) $1,895.71. (9) $951.93. (10) $1,801.74; (11) $3,- 997.2<7+. XXIII. Page 5a.-(l) $750. (2) $2,500. (3)$1,. 250. (4) $765. (5) $1,050. (6) $72.50. (7) $160.10. (8) $420. (9) $48.30. (10) $36. (11) $925. (12) $964.90. (13) $161.92. (14).$6.72. (15) $820. (16) $826.83. (17) $2,222.60 ; $2,311 39. XXIV. Page 53. A.— (1) $750; $1,125. (2) $44.- 25; $88.50 (3) $4,752. (4) $280. (5) $5,250. (6) g,375. (7) $480 ; $420. (8) $70 ; $100 ; $150. (9) $200; $80; $80. (10) $405 ; $36t> ; $315. (11) $2,000; $3.00a. (12) $7£2^. B.-(l) ^f, ^% ^. (2) $10M !?^.t;^*^- («)«22i,$37i. (4)$1,4(S (6) $2,000 $1,500, $1,200. (6) $260. (7) $1,728. (8) A. $2,500.50 ; B. $3,549.50; C. $2,975.00. (9) $2,000. (10) $1,767.50 $1,616. .. ^?^* ***«« **• ^ -(1) ^7,218. (2) $4,688.25. (3) $3,613.50. (4) $1,503.76. (6) $1,616.87* (6) $1,- 541.60. (7) $2,048.88t. (8) $2,435.62*. (9) $3,268.- 36. (10) £96 10s. (11) $334,^02. (12) £89 10s. (13) $1,1.1.50. (14) $2,098.15. (15) $298.89. B.-(l) 9*. %. (2) $4,672. (3) $3,496. (4) $4,011.15. (5) £450. (6) £990. (7) $4,952.35. (8) $2,712,704. (9) $7.191.. 70^. (10) $5,:JS0.92, n^ary. C. -(1) |ll2.09U: (2) $3,976.70. (3) $4,010 ; $4,009.85. (4) $45. (5) $4.- 86f. (6) 7,258 francs, 64^* centimes I- t 104 ARITHMETIC. (3) (7) (3) ri^I:7h ^.^t **•-(!) J<^14 lbs. (2) $300,000. 8 3^11; ^t^^^I4^f^ ^U^^' (6)24 (7)'l80 >.;x ?I ^^- (^) *7 *<^"s, 17 cwt., 66 Jbs. (10) Mfii? ilfl^J*^'?.?:*.?**^^?*^^^) ^I'^^SJ ^2.475; ^,150; ^^?^J?j' ****? «a.-(l) 9 days. (2) $3.20. 37*; 25 days. 4) 13Mays. (5) 2f days. (6) 16 20 days. (8) 8| days. (^U^d^yl (lo) 2Fd;ys. ^«:**?E' •^*«*' 63.-(l) 20 lbs. (2) 40c. ; 31c /S7.'W*-1^^^^^^ T5) W^''- (6fl8%n^i f 4.309.43 ; $4,436.92. (8) 11. (9) 100 ac^ Viofius^ 50 ; $108.50. (11) 251^ { 2159.^ ^ (12) Sf* x„ es ^m (ife^'a- (?8?iJr- <^^>2-"-- W36;W XXXII, Page 66.— (4) 9 «.in.: 8 ».m • ? a m • r ::™-: ?„^^• « "•- , <«) ll-l? »:»•! 1 S'. mT8.']6 P- 2. /ox o ^'o?'' ""•' ^^' *^' *^J S®' ^O' E.; 0°, (8) ffi 2.o8| p.m. (10) 26 min. 40 sec. (11) Sat. June 60 W. (14) 2.15 p.m. (15) 5' 36" to 8. (16) 9.45 a.m. fi .*f^5"'' . f^t ?l--<^> ^^U P««^ 3 ; 32,^ past 64A pi't 7^''(3^V 4.^?^ ^ i"^ jy^ P««*^ * 5 2lS and 04„ past 7. (3) 43/x past 2 ; 54^j- past 4. (4) 8^ and 34}? pe 6, respe *?and (11) ^t^ XXX (3) 200€ and 909! (9)4. ( 5^5- ( (18) If , XXX (4) .20. 106. ( 3.6.33 1 8. (16) 452 72 rods. XXX (4) 1025. .887. (1 XXX^ lbs. (3 (7) 1^2 $150.40^ (4) 30 ail (8) 2341 (12) $98. XXX1 (3) 164 f1 (6) 1848 (9) 66990 113 ft. 420 ft. and 54. 11.842 ft. 40 sq. in. XXXi ft. 64 in. ft. 810 in ANSWERS. 106 Sm past 4 ; 19/,- and 45A- past 6. (5) 20?9 nagt 4 6 6 respectively («) 4.21,^74^9/, any4. 2^^ (?" 3 50- flTLV^^'-^'^^^' C«) 7.54." (9) 6.20. (10)12A. ^I'Jo^rcirSoS-'** ^'"- *'«)2«6--d833. (>«, .887. (10)3.198. (11) .4721. (12) .0416. lhs^^?^y?5a **??* 1h .^-(^> ^^21 sq. ft. (2) 297 &H F'^- <«^^«-- '^^^^^^^^^ (8) 234^ yds (9) $186.0705 (10) 8 yds. Cll^lQff (12)198. (13)¥l9.79J. (14) S^iiVd 2ft.,S"i in ' 5f^ iQ.? ^f^ ^^i^- y*^"' 6 f*^« 9 in- (5) 2310 sq. in $?S^ niN^^Jl i^-^/?A ^}^l ^^ ^^- <12) 41 a (13) ll.ift. (14) «4ft. (15) 8 yds. (16) 4 520 ff n7 420 ft. (18)1885 05. B -a) 240 yds (2) 12 ft SO ?f«LS. ^'^!V^, (4) HO 4i.*^f5t 515.^91 yds '(G) losTiS:- (lV)S5ft.^^^^^^- <^>^^-^^'^^- ^'' ft. 810 in. (6) 68 ft. (7) 32 ft. 752 in! (8) fs ft. (9) 106 ARlxaMETlC. rm fi ff^^S'. ^^^)J?f-^^- ?12 i«. 11) 1 ft. 162 in. ffiLx'^S'^'^Ax^Pn^*'"- 14)^9.713^5. (16)3144. (^^)M-B.-(l) 490 sq. ft. ; 500 c. ft (2) 253 876 mV ^m^'.^"••^'• i#.¥- <^> W22 55.^ (5) 12. T«i; if^^?n?•,JP^^^,^^g^L (8) «3,670.92. (9) (l4^072o!* ^^^^^^^^- (10 9.2727%. (12) 37^^ in. XL. Page 7S, A.~(l) I8f ft. (2) 20* vds ^3^ lift i/^i?* ^•- ^^^ (?> 1^ «q- y^ 8? sq-ft. (9) 240 sq. ft. 90 sq m. (10) 60^ sq. in. (11) 32 sq. ft. ??A^^;A"o ^^P ^.^' y^- 7 ft. H in. (13) 9f sq. ft. ?2m S^ V • M SV rT^*"^/- <>®> «72. (19) 15^ in. ;:?\#in«^~(0 174.78q. ft. (2) 8.48ft. (3) 8 05in. IJViPi.^^'^^-^ «^- **• (5) 7543.36 sq.^ yds. (^ }mt^\ ^^> ^^]\^.hJ^) l^^-^ f^ (9) 6.129 sq. ft 5!?^ J^Pk"^ "*;. (^0 ^^20 ft. (12) 20 ill. (13) 10 in. (17) 12252"24. ^^^^ *^^* ^- ''^- ^^^^ «2:534.37. }t\ Iflfj" ^\^^\.P ^' ^-^^2 sq. ft (8) 87.9643 c. iVJL^^^ °- ^^ <^^> 569.6768 cfft. (11) 212 06 c 1885f gal (J) U cords. (4) 14.306 min. (5)490.29 gal. (6) 9^ ft. (7) side 2 ft. (8) $6147.315. XLII. Page 81. A.-(l) 71^ nq. in. (2) 1273 so ""• fS^Ki^.^l:^L^' ^^- <*> 3418^ ?q. in. (5) 37 69^9 sq ft. (6) 84.948 sq. ft. (7) 29 093sq. ft. (8) 16 756 eft. (9) 64.141 c. ft. (10) 97.906 eft. (11) 19 098 ni^'J'V^''-^': (13)150i.ft. (14)18c.f 576c.i; (16) 14 eft. (16) 41.892 c. ft. (17) 31 176 c ft h8\ lff'J''J'~^'^ 'f^h'i'' ''' <4 18«4 '6".t. ^(3 15 c. ft. 540 c. in. (4) 3392.928 c. ft. (5) 29 1 vards 9 S'44 "i"- .M-^^'^"- w 17182k reft! (9) 5039.44 c. ft. (10) 9«)0 c. ft. Yiwww pugij §3^ A.— (1) 154 1 ft. ft. ft. ft. (2) .B.aim£ji* in. (3) 209 ft. 88 in. (4) 3«^ '4" fc"*" (6) ^.il1u°g: ANSWERS. 107 ft. 162 in. (15)314J. 2) 253.876 ). (5) 12,- 70.92. (9) mi in. ^yds. (3) (6) 16 yds. iq. ft. (9) 32 sq. ft. 9f sq. ft. (16) $3.. 9) 16f in. 3) 8.05 in. yds. (6) 129 sq. ft. 13) 10 in. $2,634.37. 16 sq. J98 sq. 9643 c. J.06 c. 3. ft. (5) 490.29 ) 1273 sq. [5) 37.699 8) 16.755 1) 19.098 576 c. in. . ft. (18) c. in. (3) >.l yards. 125.3 eft. 1 1386 sq. J.19 cub. ^.K -^ ^ /o.'t«o-J; '"• <^) I'^'^^J cab. in. (8) 697.2 nh'^-^a ff^ ^^^'2^ «"^- ^*- (10> 2 c. ft. 856 iA. B.~ 1) o 986 ll« (2) 732.647 oz. (3) .962 c. ft (4) 202.- }l%'^' ?1 !?^-^^ ^- ^ <«) ^11 12 lbs. (7) 2i in. (8) 7 in. (9) 8 m. (10) 17 hrs. 46§ min. ^ IK ^''/'.y oo,^¥®« ?.*•-(!> 20 ; 32. (3) tin = 128.398+ nm i*^ ®^-*i^> ?^^ ^*- (7) 60 miles. (9) 709, nearlX ISl^Jf/x'l*- S^^^^k (12) ^5 less. (13) $46. (14 i\l\- ^^^11^- W63;47. (l7)Wsoz. ?18) ^A^^ Ji?Ll^^^ '^^' (20)3465ii.^aquar^ 21 /ifi^f H ^^^ S??il™i« ^^t> 2^** ^«'«- (26) 10260271849 ^ ^ ?o^^- ^i??> *^ ^^' (28) a60. (29) 24003 oz. ; 2997 oz. (30) $2480. (31) 15 loss. (32) 16800. (33) 22I days. (34) «332.03i. (35) $231.48X. (36) tl^l-iC (37) 60 to 79. (38) 24 miles. % 2m m&Oy M $18 (42)67. (43) 8J%. (44)^0; fW (&) 55^? itoV^ft^ifo- iS^i™°.'- (48) 3 days. (49)37.(60) £?f i-rf ^^fp;^*??*.- ^^P^^- (52)60480(53)42. 54) m1?; ^- /rS^2 ^- (^7) $400'; $300. (58> 28^/. (59) $8. (60) 80: 60. (61) «81 934i (aQS fr"^' ^f^L^'^'^ (63)5#,%.%$99^%SS JJjri'-QS^JS^ *?^nx'^^!:. ^?^>^»- (68) 26 days ll^f hrs. (69)$>98.50. (70) 660 yds. (71) $1250. (72) M 07A i?«VS?' J?-^'???- (74) $1922.75.* (7^) $918 02+ (7?) $187.50 (7<) 27A ; 14^. (78) 16358.9 cub. yds. (79) gSf^M-Jo^^>^^^^^- (81)$3880. (82)lJmos. 83) SnlS^^i'oo (^?^ **• (89)«271.434. (90) 36 yds. (91) ^^^^?o'«P2S«. 1^2^*72. (93)iinchtoaiule. (94 30 80.84 ; 114.16 sq. in. (99) $2400. (100) $500 noiS ffi'?;« »J'^- a03)*$96.25.^ a04)$i);W ^S9U^^^?•/^1/A^lt^^• (107) $42750. '(108) !S?^|: (^^>^1*'1^-13J*2708.20. (110)38f%. (Ill) Mo^ J^^Si^'^i <"6> 12c. (117) $280. (118) $4.86. (119) 1.4367 c. ft. (120) 1 inch to 100 mUes. (121) 357 : JfL 1^^^^ 4 V 3 ft. or ^ ft. (123) 9i. (124) 16} acres.' (i..s6) 150. 1 til n 108 ARITHMETIC. r?^\ AioAAa/^^ it*^\fy, (Ji) 4348100. (22) 4383620 7648241464. (12) 2S8922QSf^??oC J}}> ^'^^^^^ I ' ! ANSWERS. 109 (2)729375. 16934. (7) Q86. (11) 923. (16) 5570. (19) 4383620. 70. (26) > 5249166. ) 5108710. Do. (37) 6445805. 1890. (2) 2900. (6) J95. (10) 290. (14) 3805985. 5. (21) 5097630. >5. (28) 2198370. 0. (36) 4411445. 9559^36- 928. (4) 4683401- )88. (9) ) 17514- 2147236- 5896726. '. (18) 817355- 1860348- .337962. f. (27) }9) 391- 700966- 434969- 920940- U1072. ®J?i?®^2®^^^^S706. (39) 14803826584188096 ^40^ 16664304907211608. (41)6492906. (42) TsS? S?^ 9739359. (44) 12985812 (45) 1^50114 40) 19478^ 718 (47) 22725171. (48) 30W28 aoj SsS" (50) 45450342. (51) 4852224. (62) 5458752 /S^^; 6469632. (54) 7278336. (55) 9704448. (56) 1091750^' (67) 12939264. (58) 14556672. (59) 19%8896 r^'^ 21835008. (61) 10077096. (62) 143^907 S' 2388?^ ?!?; oiS*> ^<^12224. (66) 80621568 (06) 11479125o" fliimr^^' (''>2«7*20489. (69)644l/:23i.'''7Si Division Tests. Pase 8.— n^ 43128 /'9^ sTRnj l?Jo^*74. (4) 76672. (5) 86261 I) 21^54 ' ^) 28872. (8) 43308. (9) 64902. (10) 97443 /ll) 23004 (12) 34500 (13) 51769. (14) ^kU (it) Q^A (17) 36288. (18) 544S2. (19) 72676 (21)118953 (22)185038. (23) 237^. (25)356859. (26)370076. (27)475812 (29) 832671. (30) 951624. (31) 12348 (33)134456. (34)86436. (^5) 74^8 (37)317196. (38)475794. (39)56^93. (41 214632. (42)286176. (43)190784 >lStJ^o^2- (f) 119240. (47 953920: (49) 57;i362. (60) 858528. 24192 84672. 277557. 713718. 28812. 211464. 370062. 763136. 381568. 06) (20) (24) (28) (32) (36) (40) (44) (48) :l^" ■*»>, •^SCHOOL HELPS- SERIES CANADIAN HISTORY NOTES, for 3rd. 4th and 6th CIm.... .tone Ave. Schoo,'. Toron';. ^I'^' .^r' ''"'"•" '''^^ BRITISH HISTORY NOTES, for 3rd. 4th and 5th Classes By G. E. Henderson and C. G. Fraser. Price, ,5 cents. GEOGRAPHY NOTES, for 3rd. 4th. and 6th Classes. ^m "'"'"""• ""^ ""■ "^ ^~''' Hawkesville. Ont. Prfc,. EXERCISES IN ARITHMETIC FOR FIFTH CLASSES. By G. E. Hendeison and E. W. Bruce M A P.^v- Teachers' edition, containing answers. Le^t^ '^"' '' **°*" WERCISES IN ARITHMETIC FOR FOURTH CLASSES. S^od^i SchS"'T'""' """o"^- ^' ''■•°^"- ^"""P*" Church Street WERCISES IN ARITHMETIC FOR THIRD CLASSES Udi^nlAt • °' ^"~'»S cents. Te«:hers' Edition. CO.. taining Answers, ao cents. EXERCISES IN ARITHMETIC FOR SECOND CLASSES. By G. E. Henderson and E. W. Bruce M A P«V- Teachers' Edition, containing AnsweL. "; c^nt ^ " "^"^ EXERCISES IN ARITHMETIC FOR FIRST BOOK TEACHERS. By G. E. Henderson, and Miss R. Church. Miss A H«r^:— NOTES ON PHYSIOLOGY AND TEMPERANCE. By G. E. Henderson and C G. Eraser. Price, la cents. i*:. HARD PLACES IN GRAMMAR MADE EASY. By A. B. Cu.hing, B.A.. English Master in Es«x High School • . wck for Teacher., Public School Leaving, and Primary Studen.- rrice, ao cents. EXERCISES IN GRAMMAR FOR THIRD AND FOURTH CLASSES By G. E. Henderson and Geo. A. Frasei. Price, 15 cents, ^* C°LAS??S ^^"°^^ ^^^ '"*"• ^^^^^^ ^'•^ THIRD By G. E. Henderson and C G. Eraser. Price, .5 cents. ™ClS '" ^""'''OSITION FOR FOURTH AND FIFTH ByG.E. Henderson and CG.Fraser. Price, 15 cents. PHONICS. VOCAL EXPRESSION AND SPELUNG MANUAL OF PUNCTUATION. By Taylor. Price, la cents. SUMMARY OF CANADIAN HISTORY IN VERSE. By G. W. Johnson. Upper Canada College. Price, 10 cents. ENTRANCE EXAMINATION PAPERS FOR THE PAST SIX YEARS Pamphlet form with subjects grouped for class use. By G E Hender«,n. P„ce. locen.s; or. in clubsof two or mo«.7«n^' PUBLIC SCHOOL LEAVING PAPERS. Arranged same as Entrance, at same price. Stnt Postpaid OH receipt of price. Address- THE EDUCATIONAL PUBLISHING CO. XX Richmond St. W. TORONTO, ONT X Hlnh School : imary Student* [TH CLASSES !5 cent*. AND THIRD ents. AND FIFTH BlltS. iroato. Price, o cents. IX TEARS ■ By G. E. nore, 7 cents. urn CO. w. TTO, ONT /