IMAGE EVALUATION TEST TARGET (MT-3) 1.0 1.1 m|4i |22 ^ Ug 12.0 \\25 il.4 lit 1.6 Hiotographic Sciences Corporalion 23 WEST MAIN STREET WEBSTER, N.Y. 14SS0 (716) S72-4S03 ^^V-/-^^ >.^^^ ^ CIHM/ICMH Microfiche Series. CIHIVI/ICIVIH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques Tachnical and Bibliographic Notaa/Notas tachniquaa at bibliographiquaa Tha Instituta has anamptad to obtain tha baat original copy avaiiabia for filming. Faaturaa of thia copy which may ba bibliographieaUy uniqua, which may altar any of tha imagaa in tha raproduction. or which may significantly changa tha uaual mathod of filming, ara chackad balow. D Colourad covars/ Couvartura da coulaur I I Cova«rs damagad/ Couvartura andommagia Covars rastorad and/or laminatad/ Couvartura rastauria at/ou palliculAa Covar titia misaing/ La titra da couvartura manqua Colourad mapa/ Cairtaa giographiquas wi coulaur Colourad ink (i.a. othar than blua or black)/ Encra da coulaur (i.a. autra qua blaua ou noira) Colourad plataa and/or illuatrationa/ Planchaa at/ou illuatrationa an coulaur Bound '^th othar matarial/ Rail* avac d'autraa documanta D D D Tight binding may causa shadows or distortion along intarior margin/ La r9 liura sarria paut causar da I'ombra ou da la distorsion la long da la marga int*riauro Blank laavas addad during raatoration may appaar within tha taxt. Whanavar possibla. thasa hava baan omittad from filming/ II sa paut qua eartainas pagaa blanchaa aJout«as lors d'una rastauration apparaiaaant dana la taxta, maia. lorsqua cala Atait possibla, cas pagaa n'ont paa «t« fiimiaa. Additional commants:/ Commantairas supplAmantairas: L'Institut a microfilm* la maillaur axamplaira qu'il lui a «t« possibla da sa procurar. Las details da cat axamplaira qui sont paut-itre uniquas du point da vua bibliogrrphiqua. qui pauvant modifiar una imaga raproduita. ou qui pauvant axigar una modification dana la m«thoda normala da filmaga sont indiquAs ci-dassous. Tha toti D D D D E D D D D Colourad pagas/ Pagaa da coulaur Pagas damagad/ Pagaa andommagias Pagas rastorad and/or laminatad/ Pagas raataurias at/ou pailicuiias Pagaa discolourad. stained or foxad/ Pagan dAcoiorias. tachatias ou piquies Pagas datachad/ Pagas ditachtes Showthrough/ Transparanca Quality of print varias/ Qualit* inigala da I'imprasston Includas supplamantary matarial/ Comprand du material suppl^mantaira Only adition avaiiabia/ Saula Mition disponibia Pagas wholly or partially obscured by errata slips, tissues, etc.. have been ref limed to ensure the best possible image/ Lea pagas totalament ou partiallement obscurcies par un fauillet d'errata. una pelure. etc.. ont 6tt fiimies A nouveau da fapon A obtanir la mailleure imaga possible. Tha poai ofti filmi Orig bagi tha sion othfl first sion or ill Tha shall TIN! whi( Map diffa antir bagii right raqu matt This item is filmed at the reduction ratio chackad below/ Ce document est film* au taux da reduction indiqu* ci-deasous. lOX 14X 18X 22X ■^aa — — — ^—B — — WW ^M^^— — I III J J r ' ■ ■ '»'- '■ L I I „ima«BBBB^B^^l^M^MnaBHH^H^S J 2SX 30X 12X 18X 20X 24X 28X 32X Th« copv filmad h«r« Hm b—n r«produc«d thanks to th« (|«n«rosity of: D. B. Weidon Library University of Wetttm Ontirio (Regional Hittory Room) Tho imago* appoaring har* ara tha baat quality posaibia eonaidaring tha condition and lagibiiity of tha originai copy and in icaaping with tha Aiming contract spacificadona. Originai copioa in printad papar covara ara filmad baginning with tha front covor and anding on tha laat paga with a printad or iiluatratad impraa- tion, or tha back covar whan appropriata. Ail othar originai copioa ara filmad baginning on tha first paga with a printad or iiluatratad impraa- sion, and anding on tha laat paga with a printad or iiluatratad impraaaion. Tha laat recordad f rama on aach microfieha shall contain tha symbol — ^> (moaning "CON- TINUED"), or tha symbol ▼ (moaning "END"), whichavar appiiaa. Mapa, plataa. charta. ate., may ba filmad at diffarant raduction ratioa. Thoaa too largo to ba antlraly includad in ona axpoaur* ara filmad baginning in tha uppar laft hand comar, laft to right and top to bottom, aa many framaa aa raquirad. Tha following diagram* illuatrata tha mathod: L'axamplaira film4 fut raproduit grica i la g*n4roaiti da: D. B. Wakton Library Univanity of Wastarn Ontario (RagkNMl Hiitory Room) Laa imagaa auh/antaa ont 4t* raproduitoa avac la plua grand aoin. compta tanu da la condition at da la nattat* da I'aKamplaira film«, at an conformitA avae laa eondltionf du eontrat da fllmaga. Laa anamplairaa originaux dont la couvartura an paplar aat imprim4a sont filmAs an commonpant par la pramiar plat at an tarminant soit par la damlAra paga qui comporto una amprainta d'imprassion ou dlllustration, soit par la sacond plat, salon la oaa. Toua laa autraa axamplairaa originaux sont filmto an commandant par la pramMra paga qui comporto una amprainta dlmpraaaion ou d'illuatrcdon at an tarminant par la damlAra paga qui comporto uno talia amprainta. Un daa symbolaa suh^ants apparaftra sur la damlAra imaga da chaqua microfieha. salon la caa: la symbola «*> signifia "A SUIVRE", la aymboia V signifia "FIN". Laa cartaa. planchaa, tabiaaux. ate., pauvant Atra filmAa i daa taux da rMuetion diffArants. Lxiraqua la documant aat trop grand pour Atra raproduit an un saui ciichA. il ast filmA A partir da I'angia aupAriaur gaueha. da gauche A droito, at da haut an baa. an pranant la nombra d'Imagaa nAcaaaaira. Laa diagrammaa suivants iiluatrant la mAthoda. 1 2 3 1 2 3 4 5 6 ra .. r\rr OITSMHTI Y.ff -i i-A.\^ !.SJ KEY to fBB ELEMENTARY ARITHMETIC; IVOLUBIVO Wit SMm ttt mmlz all %:$nrWm It tm iKKiEET smm% u., JUTHBllAtlOAL WA8TBB. ATO LBCTtTBBB n CAJOitmt AOT) KATUHAL PHILOSOPHY. I3f THB KOBMAL 8C^ FOB UPPBB SiTi9^jf Exe] CONTENTS. 3 6 Exercise 1 5 .. 6 8 8 .. 9 .. 10 .. 11 .. 11 .. 14 .'. 14 .. 16 .. 19 .. 19 .. 23 .. 2» .. 31 .. 35 .. 43 .. 49 .. 62 .. 69 . 10 . 72 . 11 . 83 . 86 . 87 . 92 8 9 10 11 12 13 ]4 16 16 17, 18 . 19 . 23 , 24. 26 . 26 27 28 29 33 84 86 •• • • 4 f Exercise 36 95 37 97 38.., 100 39 108 40 106 41 110 42 113 43 117 44 120 47 123 48 1^4 49 126 51........ 127 62 129 63 130 64 132 66 137 66 144 67 146 68 147 . , 69.. 164 60 «.. 161 62 172 63 174 64 176 66 176 66 178 (i*f ten iT CONTENTS. Exercise 69 ,, isl 20 :... 188 Jl 191 ^2 192 ^3 ]96l ^84 I Exercise 77 78 79 80 Paob . 203 . 205 . 206 . 208 oX •■•••••• 21o oiTjit/jj ; • .>'.^. .V wf pi^MJE ai ::::::im 201 ^e 2021 83 84 222 235 . Jf , . .i. J^ c- ■ .•- Ci ;^K ^L. fl. / ■ 1 .r^ ^"'^•. .rn A> .„;..■ 1 - ;^?^r" » .<'f\ IP. v-,ej: j8s «■ I ■r> -■■ '^i. gJ-il'i „i;« ? f 1 :iti^ ?'%■ ■';-'(*n|ji!» ■nr9T9-B-'^: .J ; . ' •- I • KEY TO ELEMEN-tARt ARITHMETfe. a O » i f '■;•.' , BXIBOIBI 1. ^* ^' \ ^;. \\ *' ^' *» •' •' ^^» 1^' 12, 13, 14, 1«, 16, It, 18, 1», 20, 21, 22, 23, 24, 25, 26, 27 28, 2», 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 40 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 61, 52 53 64, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65 66 ^h 68, 69, 70, 71, 72, 73, 74, 75 76 77 78 79 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90 91,' 92; 93, 94, 95, 96, 97, 98, 99, 100. * * 2. 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110 111, 112, 113, 114, 116, 116, 117, 118, 11^ 120' 121, 122, 123, 124, 125, 126, 127, 128 129 130* 131, 132, 133, 134, 135, 136, 13r, 138, 139 14o' Jk!' ]ty.^' '^*' '*^'*^*^' ^*^' ^*«» 1^^> 160,' 161, 152. 153, 154, 165, 166, 167, 158, 159 160 161, 162, 163, 164, 166, 166, 167, 168, 169 17o' 171, 172, 173, 174, 175, 176, 177, 178, 179 180,' 181, 182, 183, 184, 185, 186, 187, 188, 189, 190 101, 192, 193, 194, 196, 196, 197, 198, 199, 20o! 3. Twetity^Tehj onehundred and siitj-four; nine- teen J ntnety^ne ; one hnnd;-ed and seven : seren hnndred and eighty-nine ; four hnndred and iweniy-six ; nine hundred and ninety-nine. ' KIT. [Elim. Aritb. 4. Sixteen; thirteen; twelve; aixty-one; thirty^ne; twenty-one ; four hundred and nine ; seven hun- dred and seventeen ; eight hundred. 6. 28, 517, 11, 65, 209, 40, 19. 6. 137, 906, 71, 807, 260. 'r. One handred and sixty-three ; four hundred and >J' -three; seven hundred and one; eight hnndred and eight ; nine hundred and seventeen ; eight hundred ; seven hundred and eleven. 8. '79,840,711,416,605. . . ..«, 9- Nine hundred and nine; eighty-one; seventeei ; one hundred and eleven ; six hnndred and six; fire hundped and ten ; one hundce4«li4.seventy ; nine hundred and nineteen. r ^ *' ,,, 10. 89,17,71, 19,940,61,412. EXBROISB 2. 'ilU 't 1. Soven thousand and forty; eigu'tloil^and one hundred and one ; eight thousand aiid nine ; four thousand and seventy ; ei^ht thousahd and nine- Jeen ; six thousand one hundred and eleven ; nin^ty-six thousand arid three ; eight millions six hundred and seventy-four thousand five hundred and sixty* seven. Ninety.one millions one hundred and thir ty-one thousaiid one hundred and forty ; nine hnndred and sixty-seven millions four thousand two hun- dred^ md ni^ety,|ixj sixty-one triUiouA three .bj^4red.hiUioijs%r, hundred mijUoigyi seven thousand six hundred and twenty-three. Bieroises 1, 2.] KIT. 3. OnD trillion one billion one million one thoniand and one ; six hundrad and teveBty billions and ^ixty-nine ; eighty-one trillions eight billions one hundred millions eight hundred and ten thousand and eighty-one. ^ Ninefy^»e billions two hundred and thirty-four i^^iu. mUlions t lirteen thousand four hundred and two ; "^ ninety-one billions two hundred and thirty-four millions two hundred and sixty-seven thousand one hundred and nine ; one hundred trillions two hundred millions three thousand and four. ' 6. Biity-soTen trillions one hundred and eighty-nine billions four hundred and fifty-six millions seven hundred and thirteen thousand four hund^d and twenty-seven; nine quintiUions one hundred quadrillions nine trillions one hundred and thiry- four billions six hundred and seventy-one thou- sand and one. 6. Seven hundred and thirteen sextillions ^ur hun- dred and fifty-six quintiUions seven hundred and nineteen quadrUlions one hundred and thirty-four trillions six hundred and thirteen billions forty- one thousand two hundred and thirty-four. * 7. One hundred quadrillions one trillion and one miUion; two hundred and three tcUons forty billions five hundred and six millions seventy thousand eight hundred and nino^..^^ r 8. Nine hundred and eight trillions seven billions six hu^red thousand and five ; four trillions three „ !,«i.^4t^{5 luutisuaa and One. d KIT. {firaiT; itBltfl. aiJS¥"??f ^'^-»^^ ntilHons eight thooawdand ^war f Wf^^ canons one l^andred aad eleven bam^r dde-fiimdred and ele^^n millions one hnndtedand eleven fhonsand ©fee bundred and 10. Fof^000081, 40002006. 7. 140j$D2O07, 20000011. 8. 80J702O 110, 700020000. 9. 5(H>ilS006005, 2OOOci00O0Ol. 10. 60^^^0000060.' 11. 17000007000070. 12. 6m^92l6. ^000 EXBROISB 4. 1. 9, 18, 33, 44, 99, 478, 330, 47, 74. ' 2. 777, 296, $4^^ 910, 1001, 1400. 3. 102, 611, im, 3030, 2868, 301. 4. 333, 10000,^^0000, 6000, 6977, 27027, 40444 6. 1899, 2222, m5, 9604, 8888. 6. OOII, XLYII, XOI, LXXX, XX, LXXVlI, CI, X, ISjcercJsefl d^.j KIT. 'i 1. ODxxxTii, cimn, dcwoxoix. i)ocLxm , . CDXCVII. D(JCOixiX. DOCoSvm^^ ' ; CMxoix, DCooLMav^r. : ^'*^ MMMOaiiVMDCCXm. V - 713 eo 3 796 EZBROISB 5. (8) 12100 2210 1001 421 10002 25734 (11) 60004 8000 •741 21000 39745 im (9) 1020 304 lirt 3212 ■ 6647 jk 9Sa.iB 0" (12) 23 il6 ' - ■ -■ s ^ 3499 ,<■> .0 .01 u .t^ ■ '^* . 10 KIT. [BiiBM. Abitb. Ciif 124^ 9iett 2'? 1987 1800 , 1796 98536 BXKBOISI 6. (18) 13147 9 61946 27 1416 934 1346 16137 100 76649 8 967 172686 (22) 27016 8007 60426 84611 19019 66700 9070f 346482 (19) 6 27 93 47 679 496 9999 11347 (23) 67009 49686 526016 3011 88727 16007 746456 (20) 12 21 Sid 976 .769 9198 4617 9860 26132 (24) 207609 11000016 6400720 66229087 987000617 6736 8069843784 864 (26) 63 68 79 57 63 320 * (27) $13626166 642Q224 4566376 3545608 849392 624264 $29431920 ' (28) 2248016 3646320 4647224 4276896 6496718 20213174 Exercises 6-8.] KEY. (29) (^749 >-~ 1117 ^ 890 V1279 (3a) 1497 my^ 1609 r 1164 1447 V 4035 1523 1498 tit 8688 Tiacsrajoti r»-i,; BXBRCISK 7J' 807966778 603861725 (10) 5704980 5304640 204104053 400340 i ' '. BZBBOISR 8. (13) 70460 9086 ti4) 806000 98647 u (31) 84 1877 61374 (16) 76000008 11978529 6402M:?a "^ii'^'t^o) ;^iT090 28796 18294 (14) 806000 (1«) 407080 98647 998 701353 . 406082 (11) 4070090 (18) (19) 27043006 960 680704 20700080 576 ^99^(i, 6342926 384 jn) 4260000 3000000 (22) 17+61+63+24=165 . - 276 165 1260000 HI 12 (23) CBtiM; Awtp, Take $ae28 r cu' -mrfff oxij j,; To $714 Add $417 Sum = $1131 (26) ^ $17896 $14070 $3826 :i'£5>\> .!,■*!■•( , $1072 = Remaittder. J'rom $1793 9^e $1131 Remaindv =^$662 = share of 3rd. (26) 769 861 f■,^r'^ ■ 1630 = siinL 270QpC|lt ^ake 908 922 = rem. 50000 doood 26000 46000 10000 10000 16000 236000 (28) From 600000 Talte 336000 .365000 =: rei^^iodef. ""? 1^ fc*5./.;i Uf; AUTfl. ^$1688 'i .6i/dT ter. ^^ft^^ e of 3rd. ■■ • .i = rem. idet^ Exercise 8.] KftT. Id. T#ke Any / I! ' )l i»i 646^66 2587424 ^16914 12 8602968 12 Bxaad«||i]^o: (2) 916704 6416928 12 5807538 103235616 9026046 Szercise 10.] KEY. 15 (9) 19181B 6 1151268 r 8068876 (12) 766439 11 8419829 12 $7203 (10) 891476 8 7131808 8 57054464 <13) 604679 X 72 8 4836632 9 43529688 (16) $3024 (18) 412 X 42 6 2472 7 17304 X 66 7 121128 8 969024 ••*.!.»rj' (U) 918978 9 8270802 12 ,99249624 (14) 8|»68476 X 49 62779332 T I mi I II p .; 439455324 8 10 78990 (19) nsx 121 u 3443 U 87873 ♦ 987 at 080 each come to the same as 80 at #987 each. 'JtSk 16 KXt. EX9B«I8I 11. M382972 1664a4l7€l^ •t)t 819^i& wa77?o 4ai8290 J l l. l jit I 111 ! 6^t«1070 ^•B-. <^' 3040 . ipM.'D'i'.ri'i 'iff- 2ei«8#400 5232T2$$0 5258891«400 67834328- 848179100 76426119 ' 772820916328 [Sunc. Aiuyiii 814976 89 0.C 6*^19^^ -i'C^a 72532864 ' -W 7819164 908 62053312 703724760 7099800913 ^' ' ' • ■^•f 7l9ii^.g 8046 43146202 28763468 576269360 67857716882 (8) JI8700046 ^'^^190870 2609#«d220 229600868 2583004140 2607973190020 71400000 900)^08 671^104900 49980490(11)^ 64260540000 64311091634600 i #1 ' (11) 811^46067 900004 3fr780O268 9266066008a^^ (13) 71476 9187 600332 671808 71476 648284 v^ X^iXX 91476 8190 8232840 91476 731808 749188440^ r .; ■ .ivjr.:4y-' w (16) 8I000Y0 81009 Y3900630 81000 YOOO 64800560 6561^8070630 (17) 6307918 20790 S67712620 44155426 126158360 13114l6l52iO 907 740 36280 6349 671180 KIT. (19) 671180 2821 671180 1342360 5369440 1342360 (Bhwu, AwfH. (16) 5858857 606007 41011999 3516314200 292942850 2964622653999 (18) 78486 - 20 1569720 7019 14127480 1569720 109880400 11017864680 217 13 651 217 2821 1 Bzeroises 11-13.3 Kiy. 19 (20) 149 29 1341 29t ' 4321 (23) 360 320 7200 1080 115200 (26) 12)200729711 16727475H (1) 4)714967 (21) $106 217 742 106 212 $23002 (24) 97 X 17 . 17 679 97 1649X304 304 ^.6696 49470 ■■^A*IU (22) 1149 83 ..8447 > 1^0192 $95367 (26) 183 5® 549 915 968d 307 (26) 23 47 );^.f p/«' 161 92 1081 67893 290970 501296 2977593 EXERCISB 12. (27) (26) 7)882 126 11)746 (28) 12)1932 161 3SXBR0I8S 13. . (2) ^6)100901 4) 178741 ^3)1X4=4 9)33633—2 | X 3=0 ) 44685-j^ 3737—0 ) 0-1-21=2 ) 373.7-^ I^C^4'* [BiftMt. AiMT. (3) 9)9186713 9)1020746—8)1 X 9 ss 9 113416—1 113416H (4) 12)16151712 !1 X9ss 9> •« V r^ 96 ) ==96> 12)1845976—0 ) 8 X T2 tzz 96 112164—8 ; 96 + . 112164^ (6) 6)1671932 7)378655^2 ) 6 X »^ 36 l»A 39807 3989TJf ^2)6 X «^36) — 6)36 + 23=38) fl 9)22222222 («> 12)2469135— 7 > 3 X 9 = 27 205T61— 3 205'rGlY^;V Il)617i4i»a24 } 3X9 = 27) ii., ) 27 +7=? 84) 0) •Ai^i^;>05l*Cir 11)561444^34-41 /, 7 X 11 = 77 5100407«-7 61004^1^^ ^il^ 577+0^771^^ I ■fl: Iiereis* 13.] 10)6182838485 KIT. (8) n 10^|18283848-.61 § X W =s 80 dl838384->8 81828384^V 8)667788991 0—0 1 9 X to =: 80 ^ 4—8)804. 5 2=86) "" ^^0 (8) 'i^fOfi^l 8)83473623— 7 i 7 X 8 =r 68 ws 10434202 1043420211 6)78998778998 «— 7 J 7 X 8 =r 66 1 —7)66 4. 7s5 63> "" (10) 9)13166463166— 2 > 7 X 6 = 43 4^ ^ ' 1463940361 146294035111 (U) 10)917048006 -f- 110 100— 2 i 7 X 6ss4a) W1--7 y 42 ^ 2^44 > "^^^ ' ■■ O' 11)91704800—6) X 10 sad 8336800—0) 0-h 6 =6> "" ' 8336800Tfjy (12) 7)70004019 -^ 63 'fiiidi ^f: 9)10600574^1) 8,x 7^=* 56 1111174- 1111174H H B' 22 [Buii..A|}9. (18) 411609 X 79 = 3251tlll 7)326inil-^5e 8)4646301—4 ) 6x7:=; 680662— 5 )[35 + 4 :;;; 68066231 (H) 10)71496-5-60 ? 6)7149— 6^3 X 10 = llyl—S 5 30 4» e s 1191^^. (1«) 7)918674 4-66 3J^ 39. t- 30 36 8)131239— I, Ji;^ 7 X T 16404— 7 J 49 -f 1:?; 49 16404^. (16) 6)291717 -^ 48 r f ., «^:tf t. d)4861»— 3 ^3X6 6077—3 > 18 + 8 6077H. (17) 6)1774 -h 48 8)296—4^ 7X6 $36lf. 18 21 = H = 421 If EUDI..iLil9. DllMAiaiVria, 14.J Ul^. ^ _ fk (13) 3)iaeo^2i _ ■ ■ . -1 ■ -- 7)420 ^ =11 60 (19) , 71496 X 7x 17 = 8508024 6)8508024-^66 > 11)1418004—0^ 6x6=r30J = «J ( 128909^5 )30 + a = 30 y^" 128909|g. (20) 5)71498 -^ 45 5=« 1 9)14299—3^ 7 X 5 = a5i 1588—7 ) 35 + 3 = 38 V "* ^ I $1588if. 1 . Eubcisb 14. (1) (2) 227)8916740(39390^1^ 1116)8161413(7313^0^^ 681 7812 2106 340J 2043 3343 «37 ^^ 454 me^ 18«* . 345I 1816 3848^ 189 10» u ^XXn [EUBM, A«i^. (3). 2106)1498706miif^g 2450 2106 3446 2106 8161)82228tta,Cl007|m. 8161' * 61800r 57m •■^55 4673 1340 (5) 23)7142347(31053611 69 24 23 :--:•':: 123:.:^ 115 84:"':'-'. ' 69 157 13ft 19 (t) 28161)8891B76(3l6|Hg} 8448$ 44367 28161 (6) 17)61 7 11 12(863006 t? 61 161966 140805 21161 107 102 1 )344 61 112 1(^ ; • M-'V (8) 1003a 11913 10032 18814 16720 20944 20064 -JLV, 880 [Eiouc. Ami^» 80ff 344(3366,V4^ 3 2 14 20 )44 )64 880 Bisei^iie i4.] .ft- , C») (10) ■> 81007 19123 ri27 1673 ■ 1092^ ^ ■ 81007- iv^ii'-* I 282169 I 2(43021 [6) 2(863006 t? 1 391484 I 324028 » 1 67456 1 (11) ■ 7x17x93=11067 ■ 11067)9167492(828 A * 114477358 109995060 t 44822986 27498765 173242219 164992590 ,-v 82496295 82496295 (13) (16) 50406)405768300(8050 538362)4984155396( 403248 4845258 252030 252030 1388973 1076724 3122499 2691818 4306896 4306896 Bcm. Afirl%; 1^23 X 417 E2 301401 917)301491(328|H 2761 2T (18) 1476 X 238 = 361288 91)361288(3860|f 273 2639 782 1834 728 8051 648 7336 646 715 28 (19) (20) 1271 X 2986 5= 3796206 271 X 777 = 210667 407 X 11 = 4477 1027)210567(205TB|y 2054 4477)3795206(847fif f 35816 5167 5135 32 21360 17908 34&26 31339 ■T fi r |-i ill! («) 2l7)9l4a(42^/V 853 462 434 28 3187 793 = 35880 ghillingg. 5)35960(«S*lf 12 2B CBlcv. AsnttV (23> 40n>27004009(6722i^ff 241M 29020 28119 (?4). 40690)807000000e( 198328i§||f 40690 ^010 8034 9769 8034 1735 400100 366210 • 338900 325520 133800 122070 117300 81380 359206 325520 33686 79410)70400006l(8866fff^^ 635280 ?1^ 687260 619200 476460 42740^ 397050 30351 (26) 29)677(23^1 58 97 *nt' ■■ n^ • ^ '•.-■' . . • . ■ - • ,: :■ X tt BteriDiaes li, 15.] V19X400 = 287600 leX 20= 320 19X5-2-12= 7^ » EZSROISI 15. (2) 071X400 = 268400 12X 20 =r 240 32X5-M2= 13VV $2879'27|| (3) 167X400=66800 41X5-M2= 17iV $6ef«17yy (3) 655x400±::26a000 19 X 20= 380 36x6-M2= 14^3^ $2623 •94t^ 0) 111^^400^44400 11 X 20= 220 44X6-2-12= I8i • $446*384 67X400=22800 8X 20= 160 22X6-2-12= '3-— — -' vsrir $2686-63^ (4) 17X400=6800 I7x'20=340 30X6-2-12= 12i $71-621 (e) 777X400=310800 11 X 20= 220 12X5-M2= 5 $3110*26 367^400=220800 ^^ 8X 20= 160 37x6-f.l2= 16t«^ $22^v^75t»^ ■(10):;:;. 704X400=281600 19X 20afe 380 47X6^t23ss^ la^ $2819*99^^ ^ (Bilm. Aftttft. ExiEROISB'ie. $719*40 (1) $017*10 $719 -r 4 := £179 +43 $917 ^ 4 = £239 + $1 84,0 Mntt -f. 20 « 17». 110 cts. 4- 20 = ftf. + lo cts, £179 178 $69-70 $69 + 4 = £17 + $1 10 cents X 3 + 6 = 6d. £^29 6a. 6d. $417*95 170ctel.-5-20sft8S;4-10ct8. $417 +4 ^£104 + $1 '1 10 cents X 3 + 5 ±= ed. 195 cts. -f 20 = 98. + 15 cts £17 8IB. 6d $171-11 15c x3-5-5 = od. Jei04 9s. 9d. (2) $19009 $171 +4 =^£42 + $3. $190 + 4 = £47 + ^... 311 Cti.+20ss:l6s. + lie. 209 cts. -*- 20 = ^Os. + 9 cts $2. 11 cts. X 3-|.6=r d642HJs6|d 9C. X 3 + 5 = 5|d. ram I a il 1*11 £47 lOs. 5f d. $777*77 fif ^ t^^>^® + ^2. $777 + 4 = £194 + ^x 223 o.+2a« lU + 3 c. 177 cento H- 20 =8^.4- l7c 3X3-T-6 = 1R 17X3+5=10W. $1 ^^418 118. I|d $444*44 $444 4- 4= £111 (3) 10^. £194 8s. lOid 1111*36 $lll+4=:£i7 + $3 1^J%2? f 2«; + 4c. 326 cente + 20= 16s. + 6c 4Xo-ro = 2fd. /.-.-«.- — £111 2s. 2|d. $70*07 ■AM* 6c X 3-i-5=:^fd. £27l8B^3f4. 2o V «_?_k"_:_ f 1 J 2c. £47 19s. lid Eirtiffelires 16, 17.] KMTi m (4) $714-23 $2117 $7l4-f-4 = jei78 + $Jj $21-^4 = i:64-$i 223c -4- 20 = lis. + ae 117c -5- 20 = 68. + ITC*'^^^' 3c X 3 -^ 6 = l|d. 17 X 3 -^ 6 = 10^^'^ '^*" £178 lis. 1^. $5 58. lO^d. $1616 - £7934-98 $16 -^ 4 =: £4 $7934 -^ 4 = £1983 + $»i^ 16c -^ 20 = 08. + 16c 298c -^ 20 = 148. + 18e 16cX3^6=r9?d. I8c X 3 -f- 6 = 10|d. £4 08.9id. £1983 14d. I0|d. BXBBOISB 17. (0 , (2) (3) $749-86 $888-77 £9 88. 7id.=$37-721 -' 614-91 916-66 $617-49 , 9167-14 1147*98 74*27 918-40 91867-42 ^3-33 21-74 1919-19 37-721 614-29 981-93 29-78 444-59 ^^m..Bi, $12116*12 $98166*53 (4) $6714*98 982-49 (5) $4216-23 2437-86 $5732-49 (6) £471 16s. 10|d.=$1887-37l $1887-371 914-71 $lt78^3i 0) £29 18s. 9d.=r$119*75/ $649-32 $972*661 $629-57 ^m $32218*08 (U) $6U9»^3^67 = 614973 cents -^ 67. 67)$6149.73($91.78*^ . , 603 ^^ 119 67 469 683 636 "47 KMT. [Buw, JkMnau 467334 415408 363482 ..fmm $8903*07 $409696*14 (12) I49)$18793*67($126*13:,8^. 149 389 298 913 894 Oil-- 149 ^,^ 477 447 30 j.'ft (m >Itl4.86^$71.42 = i7t4e6cents^7U2centi :tt42)l7l486(24^|, ''^' • U4284 'is.cmm':!'-: 28646 28668 >0! 78 Siwciie 11} Klfl <^0 (U) f»I67-42 ^ $14M3 = 916742 centa + 14t83 ceifif. 14783)916742(e2TiMj 88698 8sa it ^?rji^ ?'r^ ■Ut $671-90 4-13= ; 67190 cents -i-lB 13)67190 (5;68W Cts. = «» $51-68W 21 ■ 13 89 110 1Q4 6 )305*68 — 0)3 X 3=:9| 3 $33*96 — 3 ) 9 -f = 9 ) ^ $33*96^^. :■ , (18) \ [ £11 168. 7id = $287*321 $17-80 21-63 :; 123-76 ['^. 37-26 fV Sum =r $200-45 From 287-321 Tiike 200-45? » » $86-87J = Remainder '^*"-.- --1-1 "-r ■*. m KBT. Vium^AMm (19) (20) 9i1'Hix 11 ' $728*86 IT 297-42 .. 12215 0- 1U5 .: $426-44 X 63 9 $296*65 3837-96 7 2l7)$26866-t2($m-80H? 217 ~M\StMXiifJ7h : ^^, _ i^ $22728969 516 434 825 651 1747 1736: Mi^ (22) $314823 $29078527 *ti^m 22728969 M47727 246ai6ff $6349558 *^^m^9 3^5a76 1125311; 144304^^ tUBplf^t JL7, 18.J » (23) 2954600) $29078627 ($9*84/^^0^ 36591400 (3) (4) i:97 16fl. 8id. a<}re8. roods, wt, yds. ft. in. 137 2 17 19 8 lai 4 20 1956 12 23480 4 93912 510 40 2O4T7 36i 612529 51041- 617633J yds. = 617633 Add ft. in. 2 36 8 121 617634 5u58708 144 2 13 22234845 222348321 655870R 800453965 24871270 23636800 12344700 11811400 1 B26300 « EziBoisi 18. (1) 47 X 128 =: 6016 6497 X (2) 16 = 103952 36 Ktf, k£ (6) tons 569 20 cVt. gre. 4 3 lbs. 6i. ' drs 17 4 7 11384 4 % ■ >i" 45539 25 ,. 227712 91078 1138492 « 16 6830956 .- ■, **, 1138492 Pipes 1 4 2 (6) 18215876 16 inds. brl. gal. qu 1 1 19 3 109295263 9 18215876 2 291454023 19 31} 38 57 ' .1 6171 4 ^ 2473 qtf. Ilfyt^iie 18. j . n .;•- Kl?. ai 0) 17 t 7 2 2 4 8 . 143 4(T 5727 28637 28631 316001 3 13608562111168. 6» 60 (8) ir 49" 317 ■■'-■- ........ 60 > 1S069 sec. Ch. 2 " 36 bush. pks. gal. qt 17 2 1 1 * 89 4 ■ ■'■■■'mi . 358 ' ' ■" ' ! 2 " ' "" - 717 , 4 '2869 i^^' 2 ^-5738 pt B^ i 1 i - \. 38: ^ ' t$smi^4Mm^ 1 (10) (U) Pr.el 9 55 4 223 — 56| 503 in Is. qr. na. id, Weekt^ days^lurs. m. sec. I B n 11 4 9 29 17 7 . 123 24 501 246 2961 60 177689 60 loeeiss*? J (12) . (U).- E. $ d. c. m. lbs. 29 9 ^ 2 4 7 299624 12 oz. dwt. grs. 9 16,. 11 •^ 213 20 4276 5il • ItllS 8562 102635 <»r3. (U) C^b. y^. cub. ft. cub. in. 37;' 9 nil u loog 1728 9175 2016 7056 1008 u (16) ID. oz. scr. grs, 129 4 2 11 12 1662 '"' 9 12416 3 37250 20 746011 grs. 1742935 cub. in. (16) 12r 3810 3i|' . 38411 f^ 9 34676J = 34576 ft. 1(^ in. (17) B. ell. « U4)17U961 inehet. 9)n»o8ft.«i*. '-.:i.: 30i 1323 yda. 2ft. as in. ^ ' "^i™. ' 121 ) 6292 - ^Axf • "^- P*'- ®^ V. yds. 2 ft. 65 in. = 40)43 sq. per. 22 yds. 4 ft. 101 in. 1 rood 3 per. 12 yds. 4 ft. 101 in. 4)171439 qts. ^^^^ * 31i 42859 gal. 3 qts. 2 2 63)86718 ■ '"* .-,;.■ 2)1360 bar. 38 halligal. 3 ^te|; 2)680 hhds. 19 gal. 3 qts. ~T 2)340 pi. 19 gal. 3 qts. U0tun8l9gal.3qts. (12) ■ ' -^^•^^-'^-"■' - 60 )171491642. gee. 6 0) 2868194 min. 2 sec. 24 )4r686 hrs. 34 min. 2 sec. 366i 1084 dys. 20 hrs. 34 m. 2 sec. j_^ 4 1461 )""755f :^^ , ^5yrs. 631qr^jiys.20hrB.34in.3scc. *- 6 yrs. 1671 dys. 30 hrs. 34 m. 2 sec. = 6 yrs. 168 dyB. 14 hrs. 34 m. 2 sec. m (IS) «. 4)171496894 Ikr. V^Bm^mti. (U) 10)2987149 «illf. 12)4287422814. 10)298714.,.' ,>«tf||.. 20)3572851 .Wl. ll,d. 10>3987l d. 4 c. g^mill,. ^178642 111. UJd. 10)2987$ Id. 4 crtMnflls. 144)21111496 Inohea. 0)146607 ft. B8 in. 304 16289 ydi. 6 ft. 88 in. 4 4 a98B. 7$ld.4or9inm8. n 121 ) 65156 ... JJ2 per. 14| ydi. « ft. 88 1n.-=: 40)538 j«r. l«^^.iji||.,0^^ 4) W roedg I8*i^r. i5vj»^.|^ ig 1^, 3 a. I P.4»p«r^f5^yi|.4lft, 16 in. 118 )17498 cub. ft. 12)919817 pence 136 ;>t9i 50)999 dwt. 2)1771 gm. ^ 'lJ|)^p«..|«f^. ^|*;igal. , 41%. *:ai,iaiw«, ^laTrbui..!, pk. i gai. h (20) i** , 2)91666 PI. ttisr 45833 Fr. ells. (22) 3)17110 ft. «J ) 6703 yds. 1 ft. 2 2 (21) 2g)iTUg,4ji». ' ^9ni|<^.l;^r.241bs. '8||^nowt.lqr.24lb8. (23) 60)1111^1 |eo. 9<^i*ff.ra8m.3l8ec. 11 11406 40)1036per. 6 yds. 1ft. 8)26 fur. 36 per. 5 yds. 1ft. 3 m. 1 ibr. 36 per. 5 yds. 1 ft (24) 1728)667789 cub. in. 27)386 cub. ft. 781-«ib..iii. 14 cub. yds.*.attb..ft. 781 cub, in, (26) 20)7891427 grs, 3) 394671 sor. 7 grs. 8)131623 4rs. 2 scr. 7 gw. 12) 16440 oz. 3 drs. 2 scr. 7 grg. 1370 lbs. oz. 3 drs. 2 scr. 7 grs. 48 If I [Ksuff. (26) 2,4)678846 gn, ' 20)2828« dwt. 6 grg. 12 )1414 oz. 6 dwt. 6 grg. nriba. lOoz. 6dwt. 6grs. 16)298tl4 drams. ""^^ 16)18669 02. 10 drs. - 25)1166 lbs. 13 oz. 10 dra. 4)46 qrs. 16 lbs. 13 oz. 10 drs. - *: cwt. 2 qrs. 16 lbs. 13 oz. 10 drs. (28) 144)61479867 inches. 9)426943 ft. 76 in. 30O47i38yd 1 ft. 76 in. -4 4" 121 189762 '■'- • \ I- , 40)1668 per. 6 yds. 1 ft. 7«in. 4)39 r. 8 per. 6 yds. 1 ft. 75 in. 9 a. 3 r. 8 per. ^ rds. i fk ep. Ihalfyd. 8)418 ftir. 7 per. 1 ft. 6 in. 3)52 m. 2 fur. 7 per. 1 ft. 6 in. 171ea.lm. 2 fur. 7 per. 1 ft. 6 in. (30) 12)714986 in. 6)69682 ft. 2 in. 993a4iithoms 2 ft. 2 in. EzBItCISB 23. £U 19 4i X 16 4 299 17 7 4 (2) lbs. oz. dwt. 75 4 7 X 18 3 Jeil99 10 4 ^ <3) Days hrs. min. 16 4 17 X 21 3 ns I 1 6 1366 6 6 (4) Fl. ells. qrs. na. 31 a 1 X 35 339 17 67 188 1321 2 1 511^ tmmiJmm (ft) m. fur. per. 63 4 ^X66 8 608 1 16 7 3687 1 32 Lr»* mln. sec. 43 19 36X84 ' 7 303 17 12 12 (e) gilt. qU. pts^ 71- 2 1 > 1. 7' 601' 1 1 11 77 6515 I (8) a. r. per. 16 3 17 X 108 9 151 2 33 12 3639 26 24 18^0 1 36 oz. drs. sc?,. grs. 91 6 2 19 X 121 11 (10) jeil6 llfl.'llid. X 42 6 1010 4 2 9 U 11116 4 2 19 (11> per. yds. ft. 115 4 7 X 144 12 1381 26i 3 12 « =16682 22 4 ft. 72^1; 699 11 \' 4897 1 ii (12) cwt.qr8ilbs. 93 3 17 X 89 9 845 1 3 11 9208 8 ^mfM^ujf Kwn yrs. days^ hours. 16 110 11 X 60 10 163 8): 14 815 43i 22 = 815 44 c.yds. eft. c.in. 29 17 1110x48 — ..-ewv* 118 16 984 12 1423 9 1440 .'# (16) (16) bus. pk. gi^ qt. pi. 126 1 1X54 £27 16s. OJd. X 100 6 10 756 1 1 9 278 7| 10 6806 3 (17) per. yds. ft. 74 4 2 1 in. Hi 6 < 600 X22780 6 3 (18) • hrs. min. sec< 93 17 67 X 1100 10 I^^^^^^H 449 1| 2 . \ ■ 6 10 932*.^ 59 30 . 10 1 ■ 4494 1 1 10 9329 55 a 1 44942 2 1 0^ 102629 5 . ; • -■ • ....,..■; ,; i. ■ &z KKT. (19) a. r. per. yds. (20) 6 2 7 9 X 660 £63 Us. 9Jd. X 8100 10 38 3 11 2| ■*. 8 310 2 8 20 10 637 7 11 10 6373 19 2 9 57365 12 6 9 3105 2 6 18i JE510290 12 6 3105 a. 2p. 6 per. 18 yds. 4 ft. 72 in. BtlROIBB 24. (1) 718 = 700 + 10 4- 8 bush. rk. gal. qt. bush. pk. gal. 4 10 1X8= 34 1 qti. 10 42 3 2X1= 42 3 10 428 1 0x7 = 2996 3 1 ovia o i 2 «t4.J, (2) W 867 s 8Q0 -f 60 4> Ik £ie Us. iijii.xr=: xur 10 4s. 6jd. i«5r e 4i X 6 = " 1004 16 10 1694 13 » X 8 = 13397 10 i:i4519 10 9} (3) 263=200 4-60 + 3 djs. hrs. min. 11 X 3 10 dys. hrs. min. 27 12 61 ^1 18 60X6=; 650 10 917 20 20 X 2 =r 1835 17 16 40 2 2413 22 31 yds. ft, in. (4> 83 = 80 + 3 47 7X3= 143 yds. -Hi IB. 10 478 1 10 X 8 = 3828 2 f f 3972 9 8 di tfsM'n^. '^i.j. lbs. OS. dwt 6 4 10 (5) IDTsi 1^4.904. 7 63 * 10 X 9 = 5W t 636 3 10 X 1 = 6te 8 10 1253 (6) 19 »• r. P^yd-ft 986 = 900 4- 80 + 6 ^ 4 3 X S :- 3$ a. r. p. yd. ft. 10 VO 1 3 3X8= 5ef2 10 20 1 6 2d 6 V02 2 1 2f 3 X 9 =: 6323 2 9 2tf ^^-^ « 6919 , 2 30 254 3 — 6919 a. 2 r. 30 per. 26 yds. 7 ft. 7 "" 1149 = 1000 + 100 + 40 4- 9 m. yds. qr. na, yds. qr. na. 16 3 1X9= 161 1 1 10 168 2 10 1681 1 10 16812 2 a X 4 = 672 2 X 1 = 1681 1 19317 a 1 jm^e f4.j Kif; 96 13 6i 10 956 15 5 Y 10 I. X 9 = 861 1 >< 2 = 1913 10 10^ 10 9567 14 2 X af =: 76641 13 (10) iJ79392 16 lOj 67 = 60 + 7, cwt. qr. Iba. ^3 1 1^X7 = 10 734^ a i l)ee = cwt 613 4404 qr. lbs. 3 12 2 10 4918 1 22 56 KX7. [Elbm. Abiti. m. fur. per. yd. ft. in (U) 64T = 600 + 40 + 7 7 4 16 a m. fur. per. yd. ft. in. 8 6X7= 52 6 35 2i 2 6 10 75 45^1 0X4= 302 10 75§ 1 11 1 X 6 = 4530 4885 20 3 10 7 29 • __ ^ _ 7 6 H 06 = 4885 7 5 1 3 E. ells. qr. na. in. (12) 217 = 200+10+7 17 E. ells. qr. na. 1 X 7 = 126 10 m. H 179 1X1= 179 10 1792 1X2 = 3584 2 3889 cwt. qrs. lbs. oz. drs (13) 982 = 900 +80 + 2 1 17 cwt. qrs. lbs. oz. drs. 7X2= 12 3 9 8 14 10 64 22 12 6X8= 513 10 642 1 2 11 19VQr? MfU\ 1 4)1 o in T^ f% " 6370 16 6 10 EzeteiM 24.] 6» J (14) 2346.= 2000 + 300 + 40 + 6 a. r. p. yd.it in 8 2 14 17 16 UT X 6 = 10 a, X. p. yd. ft.^'n. 42 3 32 28 2 81 85 3 26 26 2 126 X 4 = 343 2 10 23 14 4 108 869 18 21 1 108 X 3 = hl1 1 16 3 108 10 8591 26 30 4 0X2= 17182 1 13 30 6 108 20146 1 6 16 45 (15) 567 = 500 + 60+7 yrs. dys. brs. min. sec 11 217 23 47 18 X 7 = 10 115 352^ 20 63 0X6 = 10 yrs. dys. hri. min. sec. 81 64 22 31 6 696 295J 5 18 1169 248i 16 50 OX 6 = 5798 148^ 12 10 6676 143^ 17 69 6 = 6676 144 11 59 6 c. eft. cub.ft. (16) 103 = 100 + c. c. ft. cub. ft. 2 7 14 X 3 = 8 7 10 10 21 6 12 X 10 = 298 3 8 307 3 4^ .«?• m^' 4*81. 3218 :=: 3000 + 200 + 10 + 9 bush. pk.gl. qt. pt. " hunk. pk. gl. qt. ^ 1 i Jl 1x9=; 59 i 1 10 74 1 3 Q X 1 = u oTSr 3 . 10-." -'^ ■ ■ v "-- 742 Q 1 a Q )^ 2= U84 1 ,1 10 7421 3 10 Q X 3 =? 22265 2 10 23883 2 3 «76s:90Q+70 + 5 Iba. oz. dr. scr. grs. lbs. oz. dr. scr. grs. 67 4 6 1 11X5= 33^6 il -3 1 15 ' 10 ^ ' 673 10 7 10X7= 4717 4 2 a 10 10 6739 117 2 0X7 = 60651 8 5 65706 2 2 5 (19) ' 780=700 4-80 X 174 163. OJd. 10 1748 2J X 8 =£13984 1 8 I 10 " 17480 2 1^ X 7 = 122360 14 7 Jei36344 16 3 359 :;: 3Q0 + ^9 4- 9 lbs. oz. dwt. gfs. > lbs. oz. dwt. grs. 23 11 16 11X9= W 10 8 3 239 10 4 J4X6=:1199 3 2 22 10 W 2398 6 20 X 8 == 7195 6 IT 12 8610. 8 8 13 EXBJB^QISB %5t, (11) 24 :;s 2 X 18 2)jC196 7s.. 8d. li) 98 3 10 .■ "I *" " ' V. .ny/ 'i ' } ■ X8 3 m (12) 35 = 7X5 fap» per. yds. ft, in. 7)149 17 4 6)21 3 6^^0 10.. 2 rem. > 4 x 7 = 28 10 4 10 4 = 4 far. 10 12. .4 rem. > 28 + 2 = 30 per. 4 yds. 1 fi. efj u lilf. [SiLik. Atiti, (13) 81 = 0X9 hrs. min. nc. 9)14^9 41 16 9)164 25 15.. 1 rem. te?; 18 16 8.. 3 rem. 3 X 9 = 27 4- 1 = 28 = true 18 hrs. 16 min, 8ff sec. (14) 108 = 9 X 12. rem. lbs. 9)1890 02. dwt. 1 12 12)210 16 21.. 3 rem. It 6 9.. 9 rem. 9 X 9 = 81 + 3=; 84 = true rem. 17 lbs. 6 oz. 1 dwt. 9AV grs. (15) 132 = 11X12 sq*per* yds. ft. In. 11)679 7 107 12)61 22 101 . .4 rem. 6 • 4 3 35..^ 5 X 11 = 66 4* 4 = 69 true rem. 6 sq. per, 4 yds. 3 ft. 35 ■]% in. rem. ttrfl Sx^^g^k 1. . ';t*c ^%=: SIT. ex 12 qf 8. lbs. oz. drs. 6)3 19 11 t 12)15 12 9..1 rem. 0..9rem. 9 X 6 = 64 4- 1 = 65. 1 lb. 5 oz. OH dr. (It) 144SS12 X 12 t !r- r yrs. days. hrs. miii. 12)116t 119 11 sec. 12)97 101 ITM 8 - 38 - 20- SJi -35 (18) oz. drs. scrs* grs. oz. drs. scrs. grs. 9'7)98V 7 1 16 (10 1 1 8f9 91 8 "-^ 143 „ „ 97 46 3 139 97 42 scr. 20 856 776 1 42 scr. 80 m roodi. per. A. in. tooig. per. yd. ft. in. 117)1679 4 7 96 (H U 1 6 Sfff 117 m 469 ii l >' ,in« l &«iM »«<|lo 41 40 1644 117 '^ 1811 lif 641 9 S87| 685 "H 144 466 351 U-i: 105 'imn^m <20) 'A ©16)7967 4 r (84 21 ^. 4511. 7328 639 7 4477 3664 313 24 19612 1^32 1192 916 276 60 16560 916 7400 7328 72 60 4337 3664 673 ^ ttl^. [SmtAmii . . , . (21) Il1)£m49 16s njcT (iC826 18s 5d IWfkr 314 234 809 ro2 107 20 2156 117 986 936 50 12 611 585 26 4 105 'ilt,' (22) c. c. ft. cub. ft c. 0. ft. cub. ft. 89)479 7 11 ( 5 3 2ifi 445 , ^ 34 8 279 267 12 16 203 178 26 nnroise 2fi4 (2^) 14T)7171« iri9" (48« 47'3AV M8 vV 1291 1176 60 6917 688 1037 1029 8 60 (24) Pr.eUs. qr. na. in. Fr.ells. qrs. na. in. 115 267(U67 1 2 1(5 2 a 2tt^ 1335 132 6 793 534 259 j^taM^'-' 1 A.-^ i..it 499 441 58 1038 801 237 ' 2i 4^5 ^ 59i 534i 534 ;, i • -• i -5- 267 = 1 ^ 1068 = T^fei. ttf KIT. iii^.i§m ii (25) mUes. fur. per. yds. miles, fur. per. yds; ft. 67)916 6 67 45 8 366 335 31 40 1240 67 570 536 in. 4 ( 13 5 18 3 2 6^? V-^'\ .■.i~z^-ij0,^ 34 191 134 3 Tti 134 37 ft. 37 ft. 12 444 Alio 42 i^^imi kj ^6) 67 161>^1911 178. Old. X £11 i78 6id,iBfer. 161 •' 301 161 20 2817 161 1207 1127 lbs. 01. dwt. lb«. oz. dtrt gn. 140 963)9134 4 17 ( 9 5 10 lljjf 8667 467 12 5608 4816 80 12 793 20 960 805 16877 963 155 4 6247 5778 623 483 469 24 140 11266 963 1626 963 663 68 f I. I [9i4^. Arith. (28) bush. pk. gal. qt. pt. bush. pk. gal. ^t pt 417)7149 11 "( 17 417 2979 2919 1 10 1^ 240 2 480 417 63 253 607 417 90 (29) — days. hrs. min. sec. days, hm min. sec. 60 603)2716 14 17 9(4 12 7 23iSg 2412 304 24 7310 603 1280 1206 .. L 74 « 60 4457 4221 r 236 e-?^ 60 > ■,"' 14169 1206 • • 2109 i .- 1809 ( 300 V' '. J m (m cwt Iba. Oft. cwt qrs. Ibg. oi. dw. 3 3 U lliif ?Mi5r>4000 l» 11 c IZ 183 4 694 2i 96» 694 275 16 4411 347 941 694 247 H 3952 84t 482 84f V^ [BiiW. Aura. II 11 M If ; ■ I KIT. E^BBOISB 26. 739 days 4 hrs ^f. mii. ::^iMUMQ sec, 23 hrs. 14 min. 4:? sec. = 83a8b se^, 6S864950 -f- 83682 =: *i^S^fi |, (3) i;496'7 Os. Oid. = 4768321 far, £63 I'7s. = 61396 far. 47683in -^ 6129G "~ 77^f|^. (3) ■ ■ ' ' ■ "£1192 I7s. 8d. = 1145168 far. £9 17s. 4|d. = 9475 far. 1145168 -i' 9475 = 120fiff. (4) 986 cwt. 2 qrs. 17 lbs. = 1578672 oz. 6 cwt. 1 qr. 17 lbs. 9 oz. = 10281 oz. 1578672 -i- 10281 = ISaifi^"^^. (5) 426 a. 1 r. 23 per. = 74294847. qnarter-feet, 2 a. 8 per. 17 yds. 4 ft. = 357820 qtiarter-feet. 74294847 -^ 357820 = 207|HiS^. (6) 71 fur. 16 per. 3 yds. 1 ft. = 565608 inches. 27 per. 3 yds. 2 ft. 7 in. = 5485 inches. 565608 4- 5485 = 103^^^^^ 1122 cords 3 c ft. = 143664 cub. ft. 12 cords 11 c. ft. = 1547 cub. ft. 143^64 •■ ]547 = 92if^. Exercise 26. J KEY. (8) 71^ 111 lbs. 4 oz. 7 dwt. = 641448 grains. 9oz. 7 dwt. 17 gr8. = 4505 grains. 641448 -r 4506 = 142H^. (9) ''Vm T^ '''; ' °*- = '''''' quarter-inches. 7JF1. ells 1 na. 1 m. = 7897 quarter-inches. 264321 ^ 7897 = 33f|ff. (10) . 476 bush. 1 gal. 1 pt. = 30473 pints. 3 bush. 1 pk. 1 qt. = 210 pints. 30473 -5- 210 = 145^^^-. (11) 6 lbs. 4 oz. 1 dr. = 36540 grs. 1 oz. 7 drs. 1 scr. 7 grs. = 927 grs. 36540-^927 = 39^1 J. (12) ^9 4s. lid. = 8862 far. vv 3s. Hid. = 189 far. " 8862-M89 = 46if$. (13) 7 acres =r 43908480 sq. in. IT sq. yds. 6 ft. 4 in. = 22900 sq in 43908480 ^ 22900 = 1917^^9%. (14) 927 m. 4 fur. 7 per. = 58767786 inches. 6 m. 3 inches = 380163 inches. 68767786 -i- 380163 = 164§ff^. (15) 11 years 47 days 1 hour = 97555 hours • 23 weeks 2 days 7 hours = 3919 hours. 97556-^3919 = 24^. « KSY. [Blmc. ABItH. (16) 167 bush. 1 pk. =: 6352 qt8, 9 bush. 1 qt. = 289 qts. 5352 -i- 289 = 18^^. (It) lY tons = 1360 qrfl. 14 cwt. 3 qrs. = 59 qrs. 1360 -^ 59 = 23|pj. (18) 126 yards 1 qr. 2 na. = 9099 half-inches. 1*1 French ells 1 qr. 1 in. =: 1856 half-inches. 9099 -^ 1856 = 4if S^. (19) 963 m. 420 yds. = 1695300 yds. T fur. 63 yds. = 1603 yds. 1695300 -r 1603 = 1057^^^; (20) JEHU Us. Hid. = 1067133 far. X12 13s. 4id. = 12162 f^r:. 1067133 -f. 12162 = 87-i^ BZBIOISB 27. (1) 1789 X 3 = 5367 qrs. by 9 = 48303 in. ^12 - = 4025i feet. (5) 75000 X 123 = 922500 grs. = 160 lbs. 1 oz. 17 dwt. 12 gr. (7) 1120 X II s 12320 ft. s 2 miles 2 far. 26 per. 3 yds. 2 ft. Exercise 2T.3 kbt. T3 X24902J miles X 8 X 40 X 5J x 3 X 12 = 167Y822400 ' inches = 1577822400 cents = $15778224. 1677822400 4- 100 = 15778224 lbs. = 7889 tons 2 cwt. 24 lbs. There are five twenty-cent pieces in $1. $794671 X 6 = 3973355 pieces. 3973355 4- 108 = 36790-^ minutes = 3 weeks 4 days 13 hours 10 min. 19x\,^ sec. (10) $2-17 X 365 = $792-05. (11) 4 oz. 1 dwt. 6 grs. X 3 X 12 = 12 lbs. 2 oz. 6 dwt. (12) 1 lb. tea fd> 75 cents $0 • 75 3 lbs. coflfee /® 14 " -42 6 lbs. rice /® 5 " 0*30 27 lbs. sugar /S) 11 " 2-97 19 lbs. raisins at 13 " 2«47 1 brl. flour at $7*20 7*20 Sum = $14-11 (14) 271496 -2- 167 = 16251^ times. (15) 9167 X 714 == 6545238. (16) 67 acres 4 per. IT yds. -r 9 = 7 a. I r. 31 per. 18 yds. • 6 ft. 36 in. 74 KEY. [Elbm. Arith. From Take (17) £16 lis. 4 2 Rem. = £12 9 = sum to be equally divided among the three. £12 93. -~ ^ -r. €4 3s. = share of Ist and 2nd. 3rd person gets £4 bs. + £4 2s. = £8 5s. (18) $744 ~ 6 = $124 = share of first. $744 — $124 = $620 = remainder. $620 -7- 4 = $155 = share of second. $620 — $155 = $465 = remainder. $465 -^ 2 = $232-50 = share of each of the others. (19) 176 X 400 = 704 GO 4s. X 20 = '80 5| = 23 far. X 5 4- 12 = .091^2- jih&fi $104: '89^ £ has 694 . •. £176 4s. 5|d. __ $704-' hV (20) 'DiS. = f::Q'19^ Is. qrs na. yds qrs. na. 4 1 3X7= 31 1 10 177 44 1 2X4 10 4 3 X 10 = 443 4437 2 0X1 = 4437 2 Sum = 5189 3 1 Bzereis 27.] KBY. ^P (21) $7196-40 = 719640 cents -J- 100 = 7l96f Ibfl. 71 cwt. 96^ lbs.=3 tons 11 cwt. 3 qrs. 21 lbs. 6 oz. 6^ drs. (22) 1 miles 4 fur. 17 per. = 13293J yds -^ 2 r 6646J fath. (23) Dividend = Quotient X Divisor. = 749 X 47 = 35203. (24) XMMOI = 12101 16701—12101 = 4600. (25) .Subtrahend = Minuend — Remainder. = 71467 — 61794 = 9673. (26) $679 — $146 = $533 = twice tbe, share of the second. $533 ~ 2 = $266*50 = share of second. $266-50 + $146 = $412-50 z= share of first. (27) 5ri4 + 16 4- 179 -4- 42 4- 93 = 1044 *^1467 — 234 — 946 — 1 127 — 80040 + 2!? — • 67 + 83 = 91577 ~ 824' ' = 9163 1044 X 9163 = 9566172 (28) ^1490 f 60 = 1191ff = llOlf bush. (30) 1746 — 97. 772 (31) .g. Ud. X 23 — £1 193. Id. ♦6 Kir. [Slim. Abmh! ^T ^ <82> 62^ 4- 10 5= «| «a!lonfl = i cubic foot. U6 X 6i = 4676 gallons. mile = 1760 yds ; 1760 -^ 6 = 362 362 X 2 = 704 = number of feet J gains whfle B i» running a mile. r04 ft. = 234i yds. = whole number of yds. gained. But he started 17 yds. fcehind B. Therefore at end of race he will be 234J — 17 = 2171 yds. before B. (34) /s^^ia to hare as much as B and C together, hence ji is to have half. $749-60 -f. 2 =;: $374-80 =? ^^s share. Remainder = $374-80-J.2 = $187^40 = shareof JJ or C. ^ #- i^ + 5r = 14, hence as often as 14 is containeil times in 2366 the first receives 2, the second 6. and the third 7, . 2366 -^14 = 16d 169 X 2 = 338 cub. ft. = share of first. 169 X 6 = 846 cub. ft. = share of second. 169 X t = 1 1«3 cub. ft. = share of third. (36) a. r. per. a. r. ' 1 1 17 From24'r O ,' 17 23 Tdk« 39 3 »1 1 ,^.^ sa^ 3 •• r. p. yds. in. m 18 10 108 BMr«iie %% 38.] 'j'T 1120 X 11 = 19040 ft. = 6346 ydg. 2 ft. rr 1168 pen3 4ir yds. 2 ft. = 1163 per 6 yds. ft. 6 in. = 3- miles 4 fur. 33 per. 6 yds. 6 in, (38) 12000 X 313 = 3Y56000 = copies sold. i 3766000 X 6 = 18T80000d = gum realized. iSTSOOOOd = £78250 X78260 X 4 =: $318000 (39) 710—297=: 413 * 1 Weight = 219 X 3000 = 667000 grs. = lUlbs. 16dwt. 2s. 9id. X 3000 = £418 16s = $1676*00 $1676-00 X 600 =$837600 (41) vJv, £1 X 400 = 400 7s. X 20=140 4jd = 18 far. X 6 -M2 = 7^ .'. £1 7s. 4td. = $6-471 $6-47i X 297 = $1626-02^ $162602^ 4- $317 = 162603^ cents -f 317 cents ±a 325206 cents -f- 634 cents = -6121^ brls. of flour. . .-jt (1) 1024)2240(2 2048 EziBOisi 28. (2) 1902)24409(12 i 1902 192)1024(5 960 5389 3804 64)192(3 192 ti n u — CA 1586>1902(1 168S tfk4 l*\ <• HAW !C«, « im on) 1585 Q. 0. M. = 317 IB KEY. [Elim. Aritm. fi (3) 1624)14500(8 12992 1508)1624(1 1508 116)1508(13 116 348 348 348 <3t. 0. M. = 116 '(4) 4609)8393(1 4609 (5) 714)1176(1 714 3784)46C9(1 3784 462)714(1 462 825)3784(4 3300 (6) 219)114t6(52 1095 526 433 88)21P(2 176 484)825(1 484 252)462(1 252 210)252(1 210 341)484(1 321 143)341(2 286 42)210(6 210 Gt! 0. M. = 42 65)143(2- 110 43)88(2 86 2)43(21 42 1)2(1 a 0. M. = 1 33)55(1 33 22)33(1 22 11)22(2 22 G. 0- M. = 11 Exercise 28.J KIT. 79 0) 194706)289913(1 194706 (8) 2925)29484(10 2925 95207)194706(2 190414 4292)95207(22 8584 9367 8584 234)2925(12 234 685 468 783)4292(5 3915 117)234(2 234 Ot. 0. M. = 117 377)783(2 754 29)377(13 29 (9) 1725)27525(15 1725 10275 8625 1650)1725(1 1650 75)1650(22 150 87 87 G. 0. M. = 29 (10) 2254)71001(31 6762 3381 2254 1127)2254(2 2254 G. 0. M. = 1127 160 150 G. 0. M. = 76 89 KKt. [B»M. Aftim. (11) 11266)19899(1 11266 8643)11256(1 8643 2612)8643(3 7839 204)2613(3 2412 G. 0. M. = 201 201)804(4 804 (12) 6161)7175(1 5161 2694)51€!(1 2594 2567)2594(1 2567 27)2667(96 243 137 136 G. 0. 3f, = 1 2)27(13 26 1)2(2 t Bbceteise 28 J KlT^t m 8^14^178871(2 174294 (13) 4577)87147(19 4577 41377 • 41193 184)4677(24 368 897 736 1W)184(1 161 O. 0. M. = 23 (14) 663)1261(1 663 598)663(1 , 6f)8 65)598(9 585 r. r. .. 13)65(5 G. O.M.=:13 6& 23)161(7 161 918)1347(1 918 (1«) 429)918(2 858 60)429(7 420 9)60(6 54 6)9(1 6 G. 0. If. i= 3 6 8^ KKT. [Elvm. AsiTtf. (16) 187)255(1 187 68)187(2 136 61)68(1 51 17)51(3 61 G. CM. = 17 (17) 1914)35786(18 1914 16646 15312 1334)1914(1 1334 680)1334(2 1160 174)580(3 522 ^ ^ 68)174(3 G. 0. M. = 68 174 (18) 21671)22111(1 21671 440)21671(49 1760 4071 3960 111)440(3 333 107)111(1 107 4)107(26 104 3)4(1 3 G. 0. M. = 1 1)3(3 3 Exerdiea 28, 29.] (19) 682)82 16»(141 682 2396 2328 679 682 97)682(6 ' 682 O. 0. M. = 97 KJBY, sa (20) 212(452(2 424 28)212(7 196 16)28(1 16 12)16(1 12 G. C. M. = 4 4)12(3 12 EXBROISI 29. (1) . (2) 15) 8.. ^ 1. c. m. == 6 X 15 = 90 11 Lc.m. = 30x 11=330* 21)t^l..36..)<..20 I6)S..!(..16..36..66..63 , J? 20 35) 35 '7~^ 1. c. m. = 21 X 20 = 420 l.c.m. = 16 X 35 x 9 = 504a (5) 12) !^.. ^..^..^ ..1^.. 12, .16. .18.. 20 ,- 4 3 !. c. m. = 12 X 4 X 3 X 5 ■= 720 6 m KBT. :«) 99)H.. SI- U.. 22 .. 72 PSlMLioiM. 32 .. 9^ tt. %" {(..32 m. 5c 99 X 32 = 3168. 32)6.. 10. .11^.. 18.. 22.. 28.. 32^ 8 9 .. 11 30)l| 40 •«o^AoxyxnX7 = 110880 (8) ^^ «» ^1 •• J|^ .. 25 .. 30 .. 35 .. 4 6.. .. 7.. B. m. = 30 X 5 X 7 X 4 = 4200. i|-» :?». H.. 5.. 6 .. 7., 8.. 9 6 .. ». 7 ►. 4.. 3 Ire. m. = 6 X 7 X 4 X 3 X 6 = 2520. (10) 48)1? .. ^ .. 9 .. 1% .. 48 .. 21 .. i^ .. Uj ••3 7.. 1. C m. =; 48 X 3 X 7 = 1008. (11) 160) 1^ .. XI.. 63.. ^.. 160 . . 240 , . 300 •3 > .. ..68 .. .. ~, 1^.. 10 5 1. e. m. 3& 160 X 63^ X 5 s 6O40O. r ..L. Tixercise 29. j Kiir. (12) SS 16)16 .. 41 .. 38 .. 41 .. 19 I. c» m. = 16 X 41 X 19 = 12464, (13) 1. 0. m. = & X 16 = 144. (14) 72)112 .. 20a.. Y2 ..i r. 14 25 1. c. m. = 72 X 14 X 26 == 25200. (16) 90)90 .. 36 .. 63 .. 1^ .. t 2 • • • • 1. c. m. = 90 X 2 X 7 = 1260. (16) ? .. 6 .. 7 .. 9 .. 11 1. c. m. = 5 X 7 X 9 X 11 = 3465. (17) 18)^.^..^,.^..n.t'?..lH..1^..18..20..22..24..26..28..30..32 ^^> HS)..U.. >t..l3..14.. ^..16 5..11.. ..IsTT. .. 1. c. m. = 18 X 16 X 5 X 11 X 13 X 7 = 1441440 (18) 26)25.. v.. 44.. 60.. 63.. 56.. 5(.. 11.. 28.. 70..^ 44) .. ..44.. 12.. 63.. 11 28.. 1^, ?--63 t.. . f 98 & i KEY. (19) 120)120 .. 396.. 262.. 640 LBM. Abits. 1. c. m. == 72Q X 11 X 7 X 3 = 166320. (20) 30)ll^^l j^..l28..30.,HS{..)^..3 20 .. 96 1. c. m. = 30 X 64 = 1920. EXBBOISB 33. (1) ^J* - in = f«V = -/r (dividing in succession by 10 2, and 11, or at once by 220). . _ (2) ' UH — UH = foVf (dividing in succession by 2 and 3 or at once by their G. C. M. 6). (3) ^H, the terms have no common measure, therefore the fraction cannot be reduced. _ (4) HH — Uf = 14 (dividing in succession by 9 and 23 or at once by 207 the Q. C, M. of the terms). (5) Ws' = m' (dividing by 2). _ (6) TsUlij — slh (dividing each term by 119), (7) ?*5f = iWjt (j^mding eacji term by 7). Exercises 29, 33, 34.] kbY. (8) 87 l^ — llifl = f ^ (diriding in succession by 3 and 137, or at once by 411, the G. 0. M.of the terms). (9) ??i5 = U- (dividing each term by 211). (10) Vo¥^ ; the terms have no common measure, and there- fore the fraction cannot be reduced. (11) i/*iW8% = ih (dividing both terms by 991, their G.C.M.) (12) mU = ItU (dividing both terms by 101, their G.C.M.) Exercise 34. (1) 1. c. m. of 2, 4, 5, and 10 = 20. 20 i Then multiplier for 1st fraction = — = lo ; for 2nd 2 20 20 20 = 5; for 3rd =— =4; and for 4th = -. = 2. 1 X 10 10 3 X 5 15 4 X 4 16 7 X 14 O vx 1 r\ n/\ ^ . . .. « ,% Au iu 4 PS o 2U 5X4 20 10 X 2 20 «8 h e. 6^ ! 5 II f KSY. ^•ofS, 7, 9, 3, and 2^ [F?;iii. AmTB, 30. 630 630 = 126 J =: 90 ; ^ 70 630 i = 210: and 630 = 316. 2X126 262 3 6X 126 "" ^' Y X 90 4 X 70 280 X i^O 630 ' 9 X 70 2X210 420 1 <3i 3 X 210 630 ' 2 X 315 630 316 1. 0. m. of 18, 7, 9, 6, 14 = 126 18 (3) 126 126. 126 126 126 7x 7 49 8 6 X 18 14; = 21: = 6 9. 14 18 X 7 126 ' 7 108 6 X 14 X 18 126 9 X 14 70 fix 21 106 3X9 27 6X21 126' 14X9 ""ill 126 1. c. m. of 24, (4) 360 24 ■■r 12, 6, 3, 10, 18 = = 15 360 12 = 30 360 360. = 72 360 = 120 360 — = 36; =:20. 360 10 18 (uontmued on next page.) Bxendse 34.] 1 XIS 24 X 16 106 KIT. g9 (4 continued.) • 11 X 30 330 3 X 72 216 3flO 12 X 30 2 X 120 240 7 360 6 X 72 360 X 36 252 13 X 20 260 3X 12u 3,0 10X36 360 ' 18 X 1. c. m. of 180 (5) '5, 36, 9, and 5 = 180. 1 20 = 9 10 — 18 180 16 180 180 20 360 180 — 12 ; = 5 ; = 20 36 = 36. 17X9 153 20 X 9 18< 23 X 6 36 X 6 120 1 X 40 3X 40 flfl 1 V lis «. *^ a.ir I X ia u 120 8 X 16 120 10 X 12 120 ^ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I 1.25 lti|2£ |2.5 ■^ 1^ 12.2 u US 2.0 us us u I Photograplric Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 A«11 3 3 X 11 33 (11) . STATEMENT. * 9 X T X 13 X 21 X 31 4X2X 3X 4X 5 OANOBLLED. 3 5^ X t X 13 X 21 X 31 lTn23 4X2X )?X 4X 5 (12) STATEMENT. ^ V^ 4 !^1? X )?^ X 1^1^ X 11 X IISI X 1 1 X ^ X ^ X 1? X 5^1? X 5i^ 160 = luoiii. OANCBLLED. 11 X 4 44 7~ '~1 Exercise 36. (1) 1 2X6 ^ I 1X3 = ^3^ = 3i M [Buii.AHinL 11 J _ »x 1 i ¥ 9 X 11 99 (3) 4 X 11 44 \\ 1X9 63 2J (4) 11 X 1 11 9 i 4 X ^ 28 ! 5i X 11 11 3t^ if i?$X 1 4 = - = 2j. ^2 (6) 2* V- 11 X » 19f 6^ s± 9i ^ ^ «i V 13 X 1 9 = f = 2X9 = H n ^ 6X 136 0) 84 X 9 306 • 6X65 325 (8) 31 X 2 62 7 X 19 133 13 X 1 X % S n u t7 680 13 13 ¥ Xi5 135 toweJwM, »?.] K»T. H = ¥ = Si *l ¥ ' v = 16 X 4 247 2 X = 1H!. 13 19 (10) ?H X 5^ X 13 19 X 13 9 X 16 X ^ 9 X 16 135 Gi) 21 f ! 29 X 3 87 6| 4i V 11 X 13 U3 (12) ^^ 32 X 2 3ir — ^'i X 2 X 2 ♦ fi X T — -. . n = =. H - "V - "^'^^' '' H 17 — — 37 X I ¥ ?7 X 1 1 1 "":: — : 4x7. t 4X7 32 X 2 X 2 X 4 X t 612 6 X Y X 15 X 37 X 1 2775 Exbroisb37. (1) 7 11X7 (2) 4X4 jV CWt. S= 29 = Mqr. 98 KEY. (3) [Elrm. Arith. f of ^ of f of a yard = ^ yard Then | yard = 1 X 4 = Hr. And ^ of a qr. = = tV of a Fl. ell. 5X3 (4) I of -j^ of \^ of a mile = i| of a mile. mt. ,. 16X8X40 Then if mile = — = s^o. per. 38 (5) f of I of 3 J inches = | J inches. 49 ~ .??hen ft in. z= = ^^ y^a. 61 20 X 12 X 3 (6) f of f of -— of 6 oz. = ^5- oz. 4J i of f of j of a scr. = ^/V of a scr. mu ,,, IITX 8X3X28 Then IH oz. -f. ^ = . ^ =:; h^^a 21 133 + 3 iV of ^V of i of— of a pt. = ^1 of a pt. 4J f of ^ of — of a bush. = ^i^^ of a bush. 49 pt. = — 66 X 2 X 4 X 2 X 4 X tS% of a bush. = 49 49 X 25 9Qil6i. 20064 — rffn' 1^ Exercise 37.] KBT. 99 (8) MfAof6Js. = ^f ofas. Then f^ of a 8.= 64 11 X 20 = 7*1^ of a X. (9) T«r of 4 J hrs. :^ f f hps. 95 Then H hrs. = . AA V. o. " = Tfl70faweek. 44 X 24 X t (1.0) i of alb. = } of a lb., and | of i of —of !! of a dwt. = Mofadwt. ThenJofalb.-Ml^dwt.=: 6* iV 1X12X20X280 91 * 2 X 323 / (11) = ^|fF f of 4 J of — of f ? of an acre = f^ acres. m. Ky . , 57X4X40X301 7 Then f I a. -f f sq. yds. = 1 -.-=: 28 X 3 7 °^;7 **^T ^"^ ^ °^* ^*^- = t^ of a for. ThenSJofafar. = — 2.9 l&A 36 35 V 4. V IQ \/ on " = yB%Tir ofa £. r-» -"?.'% «v 100 [KtiiM. Anvfer* BxiBoira 38. (1) 2 hrs. ITmin. = 137 min. 1 wk. 17 hrfl. = 11100 « Therefore the answop is yi?^. (2) 19 lbs. 1 oz. 21 grs. = 112821 gps. 11 lbs. 7 oz. 9 dwt. = 66936 " • Therefore the answer is ^%^^ = iJf^J = ^^^. (3) 6 per. 16 yds. 2 ft. 11 in. = 266259 in. 7 r, 14 per. = li526976 in. Therefore the answer is ttI 5lfff • (4) 3 qrs. 1 na. 1 in. = 30^ in. 3 Bng. e. 1 qr. 2 na. = 146i in. 30i 11 Therefore the answer is = 146i 64 (6) ■ 27 wks. 2 dys. 4 hrs. 7 min. = 275287 min. 1 year = 525960 " Therefore the answer is Hf fH- (6) 2 qts. 1 pt. = 5 pts. 7 bus. 1 pk. = 464 pts. Therefore the answer is j^. O) 1 U^. I oz. = 17 oz. 3 cwt. 3 qra. 17 lbs. = 6272 oz. Therefore the answer is jy^Jj. Sxeroiso dS.J KEY. (8) 101 -ei76 18s. 7id. = 84927 half-pence. ^217 19s. lid. = 104638 Therefore the answer Is iW^aV- It 6s. UJd. = 335 farthings. Therefore 17 far. is ^V of 6s. lljd. (10) 1 a. = 4840 yds. Therefore 27 yds. = ^15^ of 1 acre. (11) ''"l";26eo'^^^^ Thereforej^drs. 1 scr. 17 grs. is ^U. of 7 lbs. 4 oz. (12) 17^ * off of— of £6 7s. 8id. = i of 6130 far. = 3066 far. 7117: Therefore the answer is = ^uaj Q(\OK VVUU G m KXY. [PliPX, ABIVtt. (13) f off off ofH 0^1 V' l'71bs.=-Ar of 42 lb8. = V^lbs. J of f of \^ of 6 cwt. 1 qr. = i^^^ of 625 lbs. = ^^^ lbs. V 21B Therefore the answer is = ^^ ' 6260 (14) lei iV of|of — -of 6 roods 17 per. = -jV of 111^ jda, 20 , — 31A^ yds. ^ off of ft of ^ of 9 acres 11 yds. = f of 43571 yds. — Jl|iaydS. Therefore the answer is 31^i 40 7J22. 73^ — TT6^8ff» (16) I Of 71 of 8J of i of if on7 cord feet = ^ 0^272 cub. ft. = * V^ cub. ft. fi of 5} of i of 3 cords 66 Cub. ft. = g of 440 cub. ft. = 660 cub. ft. , . Therefore the answer is = |^ = if^. ^6Q , AUTS. Sxer«isM 98, 39.] Kir. 108 [^^ lbs. ^50 r4i jdB. 571 yds. ExflBOISB 33. 272 cub. ► cub. ft. (1) wk. dys. 7) 1 (2) 1 day. i of S of a bush. = f bush. 8 bush. ^ 8 = 1 pk. 1 gal. (3) 9j ofMf--ofahhd. = fS^hhd. hhd. 466)304 bar. gal. qtg. 2( 1 10 2 608 456 163 31i 4819J^ 4550 269i* 4 1078 910 168 2 pts. m 336 104 KEY. (4) [Elbm. Arith. T^r of 8^ lbs. = J lb. and 3 lbs. -5- 4 = 9 oz. (5) f of i^f of — of an acre = -^ acres. 11 a. 7T)3 per. yds. ft. in. 4( 6 1 92f 12 40 480 462 18 30i 644^ x 639 "i 9 49i tf 144 •712? 693 198 154 n Exercise 39.J KEl' (6) 105 i of A of 6^ of ,V of a French eir= ,i^ of a Pr. ell. X' J. . O. Q a. m. 86)9( 2 l^7a 6 64 4 216 170 46 2i 103^ , 85 "l8i__ 37 85 "~ 170 loff ofaje = ^3^ofa£ i;3 -MO = 6s, 91 (8) n of 3| of- of an acre = ^^ acres. a. 8)285 r. per. - 36 20 106 KEY, [Blsic. Awm. 7f of 9^ of gV of a mile = ^ mile, miles, fur. ' 4)53 13 2 (10) of f of I of 35 cwt. = f cwt. cwt. qrs. lbs. oz. drs. 3)8 2 2 16 (11) 10 lOf i\off ofalb. = ff ofalb. lbs. oz. drs. Bcr. grs. •77)16 H — • 01 H 2 8 2 (12) of t*r of J of a £ = ^ of a £ £ t7)4 8. d. o^ EXBBOISB 40. (1) 1 + f + -^ + I + 5 . These fractions reduced to a common denominator be- Goms Bjcerdses 39, 40.> KBT, t07 + ^' (2) l-ff + f + f+iV + A. These fractions reduced to a common denominator be- come = nn == nm- (3) 4 4-f + ^ + f + iV Tliese fractions reduced to a common denominator be- come H + t§ + f.8 + ^e + ^^ = W = f* = 55^. (6) 6i 4- 11§ + im + 29^ = 6 + 11 + 196 + 29 + i + 105 4- 280 + 84 + 360 f 4- 1 4- f = 242+ = 420 242 + iU = 242 4- im = 2431^. (6) 8i+iiH + 9 + f 4-i6f = 8+ll + i64-4 + ii + f+f + « 316 4- 1155 4- 1080 4- 1008 4- 700 = S5 H , 1260 == 35 4- 4 TO = 35 4. ly^a^a _ 35 ^ 3^^ _ g^^^^^ O) 196? 4- 16H 4- 20 A = 196 4. 16 + 20 4- f 4- ii 4- A 62t + 1309 4- 532 == 232 4* . ' ■ 1463 = 232 4- I|i*« = 233HM. = 2i*2 4. U%% 108 KEY. [Elbm. Abith. (8) 200^ + 163^ + 916f r= 200 + 763 + 916 + i + ^-f- ^ = 1879 4- 35 4- 14 4- 30 70 = 1879+ ?g = 18794- 1t^ = 1880t^. (9) 17H4- 19if 4- 20i^ +211^ = 17 4- 19 4-20 + 21 + mm + mm = n + umi = n + (10) 6i + 8i + Hi + 9i + 16? =6 + 8+11 + 9+16 -!'^ + i + f + i + f 140 + 106 + 315 + 84 + 120 = 50 + 420 =. 50 + J[M = 60 + l^V/r = 51^^. (11) 1 of f + ^ of ^ + ^ of 6f =^3^ + ;^ + 5i| = 5 + 945 + 392 + 1710 4410 = mn^ (12) % of i of! + 9i + 6^^- + f of I of t^ = 9 + 6 + -,V + i +1^-+,^= 15 + 77 + 220 + 120 + 44 = 16-4^^. 440 (13) 71 + 9^ + 16? + 20i + ioff off ofi9r= T + 9 + =r 62 + 16 + 20 + i + i+f+i +11 231 + 164 + 132 + 164 + 72 308 = 52 + Ui = 62 + 2H5 = 54il^§-. . Arith. * + 21 + um + = Y7 + 9+16 f 120 m + -4V + f-44 + 9 + Exercise 40.J KEY. (14) 109 6? + i of I of 10 + ^8f of ^fif of 242 + 16iV 33 4- 21 = 6? + 4 + 24 + lefr = 50 H = 50 ^. 11 (15) lllii+ 22f +3t + i of§ of|of^=lll + 22+3 55 -f 40 + 45 + 12 + ii+§ + 3 + i=136 + 60 = 136 4--^ = 136 + 2^^ = 138^8^. (16) 671 + 89^ay + SO^ + 101i§f = 67 + 89 + 90 + 101 + l + i^(r + i^+W 41195 + 42372 + 42800 + 44440 = 347 H . 47080 = 347 + ^m,o^ = 347 + Sinn = 3501HI?;. (17) n 9? 16] = 3 + 315315 + 111540 + 654199 910910 = 3 + imw = mun- ' (18) i off of 4 + 6i of9f + ISi + i? 48 + 24 + 21 + 80 ^ 1 _L ft! 3 j_ 1 Ql J.. a^Q tTA I I * T 21 i7 + = 79 + 2irV = 81>Af 84 116 [BiMv. AUttttt. m n (19) 2J + — + 13 + A of T?i of} f I = 23 + 1 i + i? f + i = 4-f 625 + llg 690 = 4flB = W6 H H (20) 6? — 0^ + 9f + m + 16? + — 11 4i = 1% + 9^ 4- 111 4- 16? + 1 ii 1071 + 1640 + 924 + Y92 + 968 = 54-1 ■ .^ . 184G = 64 + ^Hf = 64+2ffg = EZBROISB 41. (1) (2) toff-.|off=i^-^V = ^-:^=|f. (3) t»r of 63-i of 2f =1^-1^=15^1^1^^= (4)- 169^ — 23H = 168 4- If — 23{} = 168ii| - 23i^ = 145^^^. (5) 229iV — 67f i = 228 + 1,^ — 6lU = 228|t — 6711 = 161/ff. SMfoise 41.} Ill (6) 4-i 1116i — 229|f^ = imm — 229ff^ = 886|Ii. = 1115+ li^229tff iiH — iH = io + iii — 111 = loHf - lie = 9iti. (8) 14} in 196i -^ — of — =: 196}.- 1,^ 16| 9} = 196|JiS - W^ = 195ifSi. (9) ? of ^f 18^3^. of 2^^ — f of i of ^ of V = 16 — 10} = 6§. (10) J + l + iV-^ + f-^-A - } + § +/(f + ^- (^r + iV+ -1%) 420 18T0 = W(i^ - fl4g = 2,4^ - 1 WB = 1 + ii^(^ - liff ^ = mm - lime = nm- (11) 16} + 4g + 16f + 20}^— lYiV = 1 6 + 4 4- 1 6 + 20 - 1 7 + } + } + I + ^ - iV 660 + 440 + 495 + 264 — 480 = 39 + 112 KEY. [Elbm. Abith. m (12) m 4J of — — ^ of _ j^ j^f ^fl^ _ m 17 J. of^ = ^mn - mn = s^g^. (13) i of i off of 16? - Hi + 7f + 11^ — g = 19 + 50 + 1260+ 147 1470 -(ll + ) > 20 / = mm - iiM = i9iu^ - im-u = 8Hf^ (14) S6f- i of ^ of t of 63 + ^3^+ 181 - 17^^ = 96g+T3f+i8i -12 — 1711 = 114 + 33 + 24 + 44 88 — 29if=ll4^JV^-29|f = n4|||t - 29 Wf = 85VW5r. 83 (15) Hof---Aof-. = ^||_^^^. 249865 — 140049 221958 (16) H of 6i of 7f — f of 8? of 11 =: 222H - 64^ = 222iSl aA±&o Exercises 41, 42.] KSl. 113 EXBROISB 42. (1) 3 S) 151 % 1 11 1(1 1 3X2 t X U = ■^1 X A = H (2) 2X4 TX 11 — ■^. (3) 3 «i 9 ^ t A X 2i X I X 3i =— X — X — X — 11 3X9 11 = ¥^ = 2^t (4) 11 7 ^M 47 n 17 6^ X 4A X 77 X 4i = — X — X 11 11X47X 17 = 8789. (5) 1^ 11 41 3X n XHX 3A = — X — X — X — 1 2 18| . 11 3X41 = i|a=:61i. 114 [BL] (6) ^ »8X^X2x^X|J = !!ylxI^l 24 «< 11 1 11 ^ 8 X 8 < 24 11 X17 = w=w (T) 8«X9Jxi(4x~ = !!xi\!!vi 35X31 4X3 iSi = -W = 90^. (8) ^ «l ""r^TXTX-x^ = 2X7 3 t^ 5^ 3 \H V ^3 V „„_ vy vy vy i— X i X If 2X3X9X3 • _ 162 — 8^7 X 11 A 11 1^ ^ ^ T X 11 X 11 f X (18) 1 1 i^r X ^^ X -h X 6i X — X — 4i A 2 1? 4 5( 11? !^ m = -X — X-X — X — X — X — 5 11 t 11? S( S^ ^ 2X4X2 ^ ————— ^ el. 5 X 11 m . Arith. ? 1 5^ %\ X X — 2 4 *""«iM« 4a, 43.] 117 (19) m + 41 + 91) X (6^, + 3)) X (3^ w 2J) 139 369 t = 20Hx9f^xi,v = — x'i?x^ ^i^ w 139 x 36a X t 10 X 11 X 15 10 ^51 11 15 (20) Wf-2^-h3^^it)x(eA-^ Wr — 2j+a>ij [(61^ X (i rf 111 + I) = J(8l^+3^)«,(2f+7|)| 'r+2+i) - 3D } X (H + f ) - (lliVir - 9if ) X (8H - 2D X 6H = IW X 6itJ X 6if =:i^ X W^ X W EXBBOISB 43. (1) (3) ^11 7 ^ a ? X « X TV=,^eV. (3) Vi-iofiof61=!!x?xlxI = W^3^ . 5 1 s^'is^^-'^- H 118 KEY, (4) XExiiii. Abith, <| 4 Hi 9 ^ n ^ "^ *! (6) 9 1$ IT ^ 1 3i of 8i -^ 61 of 5^ = — X — X — X — = WS 32 38 (6) 6^ 4of3|of9i-r — =t X V X V-r 9^ 13 ^^ 31 19 !i(Hi) = -X-X-X = W^=40^' ^. SI !i( 189 2 1?^ i^^ ^ t gof8iof6?-5-4i|of2| = - X— X — X— X — * '^ ^ ^ K 19 r^ (8) + l + ^-f)-Mofi = (2,V-f)-^§ofi let 15 !^ M«l 5^ 1 28 41 8^ (9) 8| 17^ ,iic. Abitb, = lff. - = ws. h%. X — X — 19 1^ -riofi f = li«. Exercise 43. j KEY. lid (10) 6| a*of4fof6i^3Mf:! = Vof^of^^ 6i >f¥-f^offi = VxVx^x/, (11) 62Hf It 4i-f6JofT8fof4i = l XAxV^xJlrr 8* of— ^ (12) 4f 6|of— r^s^of^^^ 8i It ¥of|f =:^^ '*^X¥XTfirXH=:W = y^ = 26/^. (13) 0fUf8|)^(^0f4f- i^) = fili = 4V», 3 35 = (|0f|0f^/)^(||_,o.^f X*v^^ ^^'^ X i X — . X — . ^ 143 (14) 83of6iof4x|of|of^Xf^eiof!!« ^^ 1? >t J^ 4 ^^ 8 T"T^T\;xrx~x-\lx!?=i!! 1 3 ^ 11^ ^ ^^ 86 766. IW K&T4 [lIsiH. A9nm> (16) 9i of 81 of 6? -f — of — = ¥ X '^ X V-T- Iff of 6f 4tV 11 19 9S M 119 6t _X-X-X — X - = -^J^ = 27nH. 2 1^ t 1>^^ a«l 29 8 EXBBOISB 44. (1) I of f of £1 16s. 8id. = ii of £1 16s. 8id. £1 168. 8Jd. X 56 45 = £2 5s. 8^d. (2) 3i of 8 J of i»5r of H of 4 bush. 1 pk. 1 pt. as V of 4 bush. 1 pk. 1 pt. = 4bush. Ipk. Ipt. X33 8 s= It bu^. 2 pks. 3 qts. Oi pt. (3) i of f of 6i of 5f of H of 6 lbs. 4 oz. = fl of 6 lbs. 4 oz* 6 lbs. 4 oz. X 33 = 5 lbs. 14 oz. 4f drs. 35 (4) ii of ^ of ^ of 6i a. = ^ of 6 a. 1 r. 6 a. 1 r. X 1 14 = 1 r. 31 per. 12 yds. 8 ft. Ql^ in. •in. ABI«9b rlHofH 2iim' . 8id. ,d. Ipt. . 1 pt. X 33 f 6 lbs. 4 oz* f drs. Ir. I ft. 9"?^ in. Bzerdi8e44.j KIT. (8) i of f of 11 cwt. 1 qr. 11 lbs. =^ of ll _ 11 cwt. 1 qr. 11 lbs. X 2 mi cwt. Iqr.lllbs, — 3 cwt. 24 lbs. 9 02. 2f drs. (6) f of^ofiiof.3a. lr.27per.= 3 a. 1 r. 27 per. X 22 per.=|^of3a. Ir. 27per, 2 a. 23 per. 26 yds. 83^1 in. 6i of H of A of ^6 lis. 4Jd. = ^ of £6 lis. 4|d. 35 £6 lis. 4|d. X 9 16 - = £3 13s. 10|d. a far. , %t (8) 6J of 11 J of 2i of ^^ of 7 m. 4 fur. 17 per. (9) i of ^V of 3 lbs. 6 oz. + 61 of if of 6 lbs. = ^ of 3 lbs. S oz. 4- V of 6 lbs. 1 11 oz. 3 lbs. 5 oz. X 7 6 22 — + 1 oz. lbs. 11 oz. X 11 — 1 lb. 13T9r drs. + 18 lbs. 6 oz. 4 - = 19 lbs. 7 oz. l^ dre. drs, Si\ i 122 KEY. [Elim. Abitb. (10) 21 of J^ of 6 lbs. 11 oz. 4 drs. 1 scr. 16 grs. 6 lbs. 11 oz. 4 drs. 1 scr. 16 grs. X *I*J 20 = 26 lbs. 9 oz. 6 drs. Qj grs. (11) 4J of 5i of ^- of T^f of 4 yds. 3 qrs. 2 na. 4 yds. 3 qrs. 2 na. X 21 — = 25 yds. 2 qrs. 1 na. H in* 4 (12) 1 7i of of e^ of 2 qrs. IT lbs. 4 oz. 14i 2qrs. iTlbs. 4oz. X 69 22 - = 2cwt. 101bs.l4oz. 11-ffdrs. (13) -^ of 6i of if of 21 bush. 3 pks. 21 bush. 3 pks: X 14 9 = 33 bush. 3 pks. 2 qts. 1^ pts. (14) 6i i^r of 3i of -J^ of ii of — of Y wks. 4 d. 5 h. n Twks. 4d. 5h. X 1T5 228 = 5wks. 5d. 20hrs. Oxnin. I2||sec. (16) 21 lbs. 11 oz. 1 dwt. -I- * of 4 of iTi = 21 lbs. 11 oz. 7 dwt. -M2 = 1 lb. 9 oz. 18 dwt. 22 grs. iiM. Arith. Bxerciseg 44, 47.] KEY. (16) 123 4a.6per.6yds.^6ix?XM = 4a.eper.6yd8.^f _ 4a. 6p6r. 5yds. X 7 28a. Ir. 3per. 4yds . eft. 108in. " s""* 8 = 3 a. 2 p. 5 per. 11 yds. 8 ft. 63 in. (H) ^169 48. lljd.-f.3i of 6J of H8 =jei69 4s. lljd.^-^ _ ^169 4s. Hid. X 4 = X12 6s. 2^d. 66 (18) 11 cwt. 2 qrs. 17 lbs. x 6J of 4| of ^iy 11 cwt. 2 qrs. 17 lbs. x 783 drs. ^ i 3556 = 2 cwt. 2 qrs. 6 lbs. 15 oz. 6| Eajuboisb 47. (1) (2) 18-716 278-714 967 61-9134 34-71 217-8167 •271 23-7146 698-7149 ' 678-906 23-0067 12-98678 1 >i Art - J « <«>> 1274-05148 (3) 216*714763 2-9 9867- 91-0986 7-81645 -09868 10185-628493 u ssat. [ISLm. ARim. w («>) (6) 26*1111 •9167 9-64 11-22222 9-9 6111-77 34-646 8*98 967-769 1*1*191B6 7*614 463* 11-12'? •0986 7-0009 816 •'7142 17* 8-61 19'11 dR3*7l4 911-1267 916-91238 vilv 1 Xrm 11478 -»15e 1027-3333 CO (8) W 16T-914 9161-0098 71-0916714 6-814'7 7149-16716 27-1471 161*0998 2011-84264 43*9445714 (10) (11) (12) 111-1116 279-00906 627-4 22-22222 117-916 91-7469 88*88938 161-09306 636-6631 EziBOiSB 48. O) 78417 X 9 = 706753, and, since there are three deci- mal places in the multiplicand and none in the multi- plier, the answer is 705 • 758. (2) 271 X 34 r= 9214, and, as the decimal places in the mulUplier and multiplicand number 2, we point off two Bvoroise 48.] KIT. ISI (8) 21716 X 206 = 44t3496, and, since the deohnal places m multiplier and multiplicand number 6. the answer is 44*73496. (4) places m the multiplier and multipHoand nuiJber 8. there must be the same number in the product ; the number therefore is -07462746. 116791 X 8100004 = 946007667164, and, since the decimal places in the multiplier, together with those of the multiplicand, number 8, the answer i« 9460-07567164. ^ («) 11111 X 97116 = 1079056876, and, since the deci- ^ll^T" Vl r'*'^"''' together with the multi. plicand; number 7, the answer is 107-9066876. 27 X 14 X 119 = 44982, and, as in the three fac tors together, there are four dechnal places, the an- swer IS 4-4982. > «c »u (8) decimal places m the three factors together, the an- swer IS -001648098. » <'"« »u (9) Jl-""? ."^ ?' "" 27 =677686149, and, since there !!L?JrrJ P!^.«««> the three factors together, the *f. 126 KBT. [Elbii. Abitb. (10) 8008 X 66 X 2002 = 1058113056, and, since there are fire decimal places in the three factors together, the product is 10581 '13056. (11) 1012 X 719 = •r2'7628, and, since the decimal ] laces in the' multiplier, together with the multiplicand| number 8, the answer is '0072*7628. (12) 2 X 7 X 6 X '^1 = 3444, and, since there are seven decimal places in the four factors together, the answer is -0003444. EZBBOISB 49. Y8-1 -^ 1-OYl = T8100 -f. ion = 72-922, &c. (2) 91-142 -5- 7'8 = 911-42 4- 78 = 11-684, &c, (3) 61 -123 -J- -0146 = 611230^-146 = 4186-506, &c. (4) 9 • 1234 -i- -000716 = 9123400 -i- 1 16 = 12742 -178, &c. (S) •0467 -r •01471 = 4670 -f- 1471 = 3-174, &c. (6) 918 -f 914-71 = 91800 ^ 91471 = 1-003, &c. 967 • 104 -^ 12*046 = 967104 -r 12046 = 80-284, &c. Bxercisee 49, 61.] * key. 127 (8) 91.671 -f-.000916 = 9167l000 = 916 = 10007t.6109,&c. (») 8-8 ~ .0641 = 88000 ^ 641 = 137.286, &c. (10) 7147-12 -M127 = 6-341, Ac. (11) •817 -f -9147 = 8170 ^ 9147 = -893, Ac. (12) 213 ^ 91 -614 = 213000 -J- 91614= 2-324, &c. EXEBOISB 61. (4) .. 126-1 .. 214-.a .126 = = m = -^f] -214 = 990 990 — 9^ ^ 4&f « (6) .. 2132-21 . 216-21 .2134 = . = ^^ J .216 = . 9900 "~ 9W — 60- 2114 — 21 900 -2114 = 9900 (6) •12346 = 12345 — 123 99000 = *^*»«* = JL7X . .1678 — 44^4 188 KIT.' ^ [Bmii. Amt^^ . 6714 — en . . 12T16 — 12 .6Y14 = = UU ; -12716 = 9000 99900 = um = ^N-h- (8) 9186 — 91 •, 142 — 1 .9186 = = UU = \U%', 142 = 9900 990 (9) 1234T — 1234 .. 1278 — 12 •1234'7 = = UM ; -1278 = , 90000 9900 (10) 16714—16 •16714 = = mn = ^ii?6> 99900 •9 = 1=1; -86 = 11. (11) 27-43 = 27|i ; 17-816 = H^^o* = I7f§t = l7t^J (12) 467-12345 = 467^Mro^ = ^^HUU = 467^WoV 16-16161 = 1B^4^-^J^= mUU = le^Wr. SWMUe* 61, 62.] ismr. EXBROISB 52. (I) •» = ! = 66--6 - 1, DO gg, 80 • Henoe '9 + -65 = 1 + f j^ = m (2) 189 • • • •12 = 9|^; •'r26=:|§f; hence9-12+-'r25 = 9A + m = 9-» + m = 9i^. (3) 6-14 = 6^, 2-'ru = 2HJ; henoe 6-14 — 2-n4 • = 6W* - 2^8 = smi- (4) • • t-9186 = 7§S|B, 2 -347=2^1; hence T •9186 — 2 -347 = "^iw - mi = 7iMs* - 2^108 = B%mh (5) 7-6 =7f, 1-23= l^T^, 7-191=: Hence 7-5 + 1.23+ 7-191 = 7^+ 1^V + H9 = »+l+7 + tx^ + M = 15 + ^+|t^ + ig*=15W. (6) • • • • •7 = J, -12 = ^%, -67 = fJ; henoe -7 X -12 X -67 __ 7. v> 4 v> A7 1R7A 130 KEY. [Elbv. Abith. •67 = U ; -914 = W = ill; hence -61 X -914 = (8) 6-71 = 6f^, 6-713 = 6|ff; hence 6-71 x 6-713 = m - - • • « • 614 = 1^1, 2-766 = 2f|g; hence -614-^2-766 = ■^2y = f^.M2=fltxft=|ilxit = ^W^. (10) 1-647= It^^oV; 3-621 = 3^^; hence 1-647^ 3-621 XA'r = lV^^. (1) 2 days 7 hrs. 24)7 hrs. EXBBOISB 63. 7)2-2916 days •327380962 wk. (3) 16 lbs. 7 oz. 3 drs. 16)3 drs. (2) 7 oz. 4 dwt. 9 grs. 24)9 grs. 20)4-375 dwt. 12)7-21876 oz. -6016626 lb. (4) 116 days 14 hrs. 24)14 hrs. 16)7-1876 oz. 100)16-44921875 lbs. •16449218 cwt. 366i)116-683days Exercises 62, 63.J (5) 1 rood 17 yds. 1210)17 yds. 4)1-01404959 roods •25361239 acre. KEY. 131 (6) 3 qrs. 1 na. 1 in. 2i)l inch 4)1-444 nails 6)3-3611 qrs. O) 16s. Hid. 4)2 far. 12)11-5 d, 20)16-9583 s. '8479166 •56018 F. E. (8) ^9 14s. 8id. = 4673 half-pence ^77 Os. 9d. = 36978 half-pence 4673-5-36978=3 -12637 (9) 2daysl7min. = 2897min. ^wks. 4days = 76320 min. 2897 ^76320 =.0379686. (10) 3 fur. 17 per. = 4521 half-feet. 2 miles 4 yds. 1 ft. = 21146 half-feet. 4621-^21146= -2137993. (11) l7lbB. 4<>z. = 4992 scr. 19 lbs. 7 0^. 5 drs. 1 scr. = 6666 scr. 4992 or- 6R6A — .fiQoz}AA*r ■-••■JaMVaiJ, 132 KBT. [lElilll. AUTB. (12) 2 Toods 27 yds. = 9788 quarter-yards. 29 per. 29 yds. = 3626 quarter-yards. 9788-^3626 = 2*7001379 (1) £•146785 20 a I •936700 s. 12 ExHBOisi 64. (2) '71463 week 7 6 I •00241 days 24 11 I •228400 d. 4 I -06784 hrs. 60 0| -913600 f. 2s. lid. -9136 f. (3) 2 1 •1471b. 3 I -47040 min. 60 28 I -22400 sec. 6 days o min. 28-224 sec* (4) •6143 miles 8 1 I *764oz. 8 6 I •112 drs. 3 I -336 scr. •20 4 I -9144 far. 40 36 I '6760 per. 6i 3 I, •1680 yds. 3 6 I '720 grs. 2 lbs. 1 oz. 6 drs. 6-72 grs. I -6040 ft. 12 6 |, -0480 in. 4 lur. 36 per. 3 ya^. 6-048 in. BJxercise 54.J KEY. 133 (5) - -916147 acre 4 3 I -664588 rood. 40 26 I -583520 per. 30J IT) -651480yd. 9 5 I -863320 ft. 144 124 I -318080 inches. 3 roods 26 per. U yds. 5 feet 124-31808 in. (6) 2 J -14617 Fr. ells. 6 I "87702 qrs. 4 3 I -50808 na. H 1 I -14318 in. 2Fr. ells3na. 1-14318 in. 0) 9 I -2645 hrs. 60 16 I -8700 min. 60 62 I -2000 sec. 9 hrs. 15 min. 62-2 sec. 134 KEY. [Klsm. Abith. (8> 4 I -TlTYhbd. 2 1 I -4354 brl. 311 13 I '7151 gal. 4 2 I •8604 qts. 2 1 I -7208 pta. 4 hhd. 1 brl. 13 gal. 2 qts. 1«7208 pts. (9) 11 1! 13 13 5 13 •33625 roods. 40 •45000 per. 30i '61250 yds. 9 51250 ft. 144 >80000 in. rooas i^ per. lo yus. o lu lo-o iu« Exercise 54.J KEY. (10) 9 I -914 pound 20 18 I 280 g. 12 3 I -360 d. 4 1 I -440 far. £9 18s 3id -44 far. (U) ^3 4s Vid = £3.23125 £3-23125 X6.7l4 = i:21.694'6125. ^21) •6946126 20 13 I -8922500 s. 12 ; 10| '7070000 d. 4 2 I -8280000 far. ^21 13s lOid -828 far. (12) 9 I -1467 jruars 865i 63 I -682176 days 24 13 f- 972200 hrs, , 60 68 I -332000 min. ^ 60 19 I -92000 sec. 9 years 63 days 13 hrs. 58 min. 19-92 sec. 13& I 136 EXT. [i}LBK. Ab^TH. (13) $2-78 X '12346 =$0'343191. (14) 2'7 sq. yds. 2 ft. = 245 ft. 245 sq. ft. X -65265 = 159*89925 sq. ft. 159-89925 sq. ft. = 11 sq. yds. 6-89925 sq. ft. 144 129-492 sq. in. ^7sq. yds. eft. 129*492 in. (16) 7 cwt. 2 qr. IV lbs. = I6l lbs. 767 X 7*46725 = 5727-38075 Ibg. 5727*38075 lbs. = 2 tons 17 cwt. 1 qr. 2-38075 lbs. ,(16) £7 7s 7id = £7*38125. £7*38125 X 6*4715 = £47*767759375. £47 I * 767769375 20 15 I *355187500 12 4 I *262250000 4 1 I * 049000000 £49 15s 4id '049 far. Exorcises 64, 65.J KJBT. 137 EXEROISB 55. (1) X297 X 400 = 118800 4s X 20 = 80 8id = 34far, X 5-M2= 14^ £291 4s 8id = 11188-94^ $1188-94J = $1188-9416 $1188-9416 4- -0005 = $11889416-6 ^6 = $2377883-333 1::::: fi^-^^L^:^i^_^e^eo . ~ 21. .18. . 30 l.c.m. = 22x 30X7X3 = 13860 (3) ^183 15s Hid = $735 -183 $813-83 ^$735-183 =$78,641. (4) ^•c-»iof2, 7, ll,5,andl0 = 770 no^3 = 385.m^r„o,. no "?; = ,„, 770 ~ 6 = 154 ; 770 -MO = 77 1X385 4^11^ A = 2 X 385 7 X ijQ 7 X 77 10 X 77 m. KEY. (6> [Elim. Abith. £2 4s lOid X 6 = £13 9s lid I'j i;22 8 Qi X 2 = 44 It 10 Je224 5 5 XT =1669 It .11 Sam = £1628 4 1} • (6) 44 miles -^ 13 ft. t in. 44 miles = 2t8t840 inches, and 13 ft. t in. = 163 in. 2t8t840 -s- 163 = ltl03iVy times. O) From $t498*t0 take away $t49'83 and the remainder $6t48 'St = three times the share of B or 0. Hence share of B or C = $6748 -St -r 3 = $2249 '62^, and share of A = $2249*62} + $749*83 = $2999-45}. (8) (9) $6880 $2702 9tt5 3537 6750 3830 68877 2156 9105 315^ 8750 10688 9880 26561 58712 - %^0 t X4Ef $49630 .168729 From $168729 Take 51630 ;^em. 11T099 f. Abith. = 163 in. Exercise 66, J KEr. 139 32 X 23 X 31 = 22816. X (14) ^ 3 t 75 2^5 x-x-x ^ 11 = 5;^^. ^ *^o + w + its + m = 15 + -m 1 «5 3 __ T. , _ ! r. : + ^^ + t« = ^ii to be subtr. 140 KEY. (15) [Slim. Abitb. 2 days 4 hrs. = 52 hrs. ; 3 wks. 3 days = 5t6 hrs. 62-J-5Y6= •0902^7. 17810)63294(3 53430 (16) 9864)lt810(l 9864 7946)9864(1 7946 1918)7946(4 7672 (17) ■7 = 1; •93 = |g = e; -00045 = 99999 . . 27146—27 27119 •27146 = = 99900 99900 ., (18) rood. per. yds. 274)1918(7 1918 G. 0. M. = 274. 45 5 11111 acre. 2 4 17 9 roods. 40 ' 377 per. 30i 11319 94i 114131- yds. 11413iyds. 9 102719i ft. 144 14791572 inches. JBxercise 65.J KEY. (19) » •7149625 miles. 8 5)- T 19 7000 fur, 40 28)- 7880000 per. 5i 4)-3340000 yds. 3 l)-0020000 ft. 12 9)-0240000 m. 5 fur. 28 per. 4 yds. 1 ft. 0-024 in. (20) 2i:: "^ '^ = '-'' y^''. + -625 yds. = 4.475 yds 4 475 y^s^= 4 yds. 1-425 ft ; 4 yds. 1-425 ft + ^ ft = 4 yds. 2-138 ft. "* 4 yds. 2-138 ft. = 4 yds. 2 ft. 1-646 in. 4 yds. 2 ft. 1-646 in 4- -Qi ;„ — a ^ or-7per. x5iX3X 12 "T38V .''"'•''' X 3 X 12 - 29.K " I ''''^^'' ' '^25 yds. X d X 12 -. 22-5 m.j -713 ft. x 12 = 8556 in inches. 138-6 22-5 8-556 •91 141 170-566 = 4 yds. 2 ft. 2 556 ms. 142 KEY. [Elsm. Abith. ' (21) iV = 4 -rl6 = 0-2666 + ; -^ = 9 ^ 47 -- 0.1915 ^ . l/Jf = 6 -f- 21 = 0-2380 + Therefore ^V is greatest ; and i^ least. (22) n Flem. E. = 39 na. and 1 yd. = 16 na. .-. Z\ Flem. E. is If of a yd. (23) $3-73 X 229 = $854-17 = price of sheep £11 lis. Yd. X 13 = jelSO 10s. 7d. = $602-llf = cos't of cows. $854'17 - $602.11f = $252-05] = money taken home. (24) 623525 — 20735 = 602790 doz. $2487 ^ 20735 = $0-119 + ; $66860 -f- 623525 = $0-107 4- (25) Assume 24) l^..iq..l^..5(Q..24..28..32..36..40..44 7.. 4.. 3.. 1. c. m. = 24 X 7 X 4 X 3 X 5 X 11 = 110880 11 (26) 746 times 193 = 746 X 193 x 143978 and 143978 -i- 123 = n70Tfi2«3- . , * Therefore 1170^^ times 123 is 746 times 193. (27) Dividend = quotient x divisor = 794 X 83 = 65902 <^ __ 2048 ^ ^ "^ 9 23 6X7X9X2X23 ~ 7245 = 2048 : 7245. LO-731 ; : 10324; ••89. Exercise 67. (1) (2) 21 X 40 7 X 46 46 16 7 (3) 3 X 17 51 ■— — = — = 4-,V 11 11 (5) 23 X42 91 13 '"'■ (4) 47 X 29 1363 27 X — 11 1 9 9 (6) 21X18i 7X18^ 7 i ■ -**- r\ i !— iux 111 37 2 = 3i, if 146 SET. [Slbu. Arith. III! (7) 10 X 11 110 (8) 9 = =12i. 14 X 65 9 13 = 14 X5 = 70 (9) (10) 109 X 72 109 1728 = — = 4H. 24 16 X 11 253 16 23 (11) 891 X 100 9 $61-50 X 21 9 = 99 X 100 = 9900 (12) = $20-50 X 7 = $143-50 (13) £l6 4s.llild. X147 11 = jei9s.6id.Xl47 = £217 2s.7id. $66-87 X 20 3 (14) = $22-29 X 20 = $445*80 (15) 16 X 17 272 9 :±: — = 30| days* 9 (16) 11 X 47 517 zi = — = 24jf weeks. 21 BM. AbITH. t X5 = 70 6 3 L7 2s.7id. 30 Exercises 57, 68.J KEY. 147 S !lf hi 148 KEY. [Elkm. Abitb. . (4) 10 X 100 1000 6 : 10 :; 100 : Ans. ;= p- = — = 166^ days. 6 6 (5) . 13J : 4i^ :: $12-90 : Ans. = $12-90 X 4-,% -h 13J $12-90 xetx 3 = $12-90 X n X -h =•■ = $4-0514 ' 16 X 40 (6) 80 : 100 :: $7149 : Ans. $•7149 X 10^ ~2J.^aii = $8936-25 1000 : 16-714 :; $18 -To : Ans. = $312551-80 8(S| $18-70 X 16714 1000 1000 = $312-5518 (8) U X 7149-70 $1 : $7149-70 :: 1| : Ans. = i=:l| X 7149 -70 = 12511 -975 018. = $125 -11975 (9) $7194-60 X 1 5:1:: $7194-60 : Ans. = ?• = $7194-60 X ^ = $16787-40 (10) Qtri • \o*T " f24 9 7 465 11 -^v ^1-1 1 2 3 ' X--X_x-X — X-X-X-X-X--X~ ^ * ^ ^ ^ !( W !( t JWX^(^X«|HXI^^X ^«5IS| X ?^ X ^^ X >t^ X 81 .. ^<^ 9 ^ M r-. ^ i , ^ sj — _j^^j men. i 158 [fitiic. AmfR. (14) : : 60: Jins. 9 lbs. 6 oz. 4 dwt : 11 lbs. 11 oz. 17 grs. 7s. 8Jd. : lis. 4id. 3 U -91 «{l^ X 68657 X%X^ 3 X 68657 X 91 18743361 ^^Hii^ X m 4568 37 4568 X 37 169016 = noie8H forks. Note.— 9 lbs., 6 oz.. 4 dwt., = 64816 grs. ; 11 lbs,, 11 oz., 17 grs. = 68657 grs. 7s. Sid. = 186 half-pence ; and lis. 4id. = 273 half-pence. 4 : 27 60 : 200 (15) 279 : Jns. =; 9 10 279 X 5^7 X W 25110 4 «J«lX4 = 6277i bush. (16) 23 : 48 27*9 : 16-5 11»4 : 9'4 16 6-5 : :7'3ac's: 7-3 Xi^lSlXl«5-^X9-4 23X^7-5^X W-J| 9-3 3-8 6038 •56 ~ '^UU\ acres. Q10. IV. ABIfH. : 60 : Jlns. 18743361 169016 . oz., 17 grs. 44d. = 273 10 6-5 \ X %\'^ \ 3-8 Bxerdse 69.] 11 : 16 11 : 16 8 : 6 4 .• 6 2 : 4 8 8 2i 10 8 H : m KEY, (17) $ni.ll ijins. $28444 '16 121 159 lUl-llx 16X16 iTxTT $236-07ifi^. 8550 ; Jlns 76950 10000 ; jlnsz= = 19237^ lbs. (19) _ 10000 X iq X {Si X !^ ^ X ^ X !^i = 10000 lbs. (20) 14 X in X 1? 14 oz. : Jlns. = — - ^ ^ 14 88 10 X 2{ 2 A* »8 10 /5 9v 1 S 7 \3 4/ _2!x!f ^ ^ 4__1408 i^ i) 15 Q9I3 ^. 160 KEY. [ElIH. ABITff. If 847 : 981 (21) : 2043f yds. : jSns,= 2043?XlfX981 14304 2^ X 847 8 981 /7 847v x-x — -^l-x — I 5 1 \3 1 / 8 4 n 14304 8 981 3 1 336773376 ^ 6 1 7 847 "" 207515 = 1622Hf^ffyds. (22) 14 n __»■? X 14 X 3iX9f 8 X 4 X 7| = ¥ x-S^xlx V-f-(!x!x¥) 7 9^ ^^ 7 47 1 1 3 670173 = — X — X - X — X- X - X— = 1 1 i^ 6 8 4 23 3680 = I823Vft3o- acres. (23) 450 X 1!^ X 97 $43650 : 450 : Ans. = — — ___ 4 : 12 24 : 97 4X 2H 2 = $5456*25 8 (24) 24 : 29 9 : 27 54 : Ans.=z = 1951 bush. 27 ^ ^^ X 29 X %X 4 783 4 Exercises 69, 60.J ^^y. (1) 161 EXBRCISB 60. 50 c. I \ I 229 at $2*75 2 25 c. I \ $629*75 60 c. 25 c. 6 c. Ic. (2) 743 at $3 -81 3 2229 371-60 185-75 37-15 7-43 $2830-83 50 c. I \ (3) 7ll4at$97.86i jog i i 97 49798 64026 690058 3557 25 c. \ 1778-50 10 c. f 711-40 1-ic. \ 88-926 ic. \ 17-786 1696211 -61 5s. Is 3d Id. i (4) 699 19 213ati;216s4d 2 426 vx 1 106 10 ill 53 5 hi 4 13 6 3 li 17 9 162 KEY. [Elbh. Abith. Is. Id. i li. u 50 c. 20 c. 321ati;ais. lid. 9 2889 16 1 1 6 6 9 8 10s. i 2s. 2d. i i 4. • Je2906 14 6i (6) T147 at i;i2 12 2| 12 85764 3573 10 714 14 59 11 2 14 17 n 7 8 m i:90134 1 m 0) 217^ at 914- 70 914 3 868 4)2744- 10 217 1953* 686-025 198338 108-50 43 -'40 686-025 $198175-025 x-. ^ercise 60.J lOlY. (8) 50 c. 20 c. 618^ at $42 '711 .42 4 1236 9)170-87 « 18 -9818 25956 309 1 ik 123-60 i i 6-18 i 1 3-09 l-54i 18 -981 163 $26418 -40,^ 60 c. 25 12i 5 m 9Q1{i at $16-93 16 11' 6442 907 12)186-23 14512 453-50 226-75 113-37i 45-35 4-53i 15-5lti 15-51ti $89-40 X -0625 = $6-5875 (4) $2998-40 X -176 = $524*72 (5) 204a. 2r. 14 per. = 204*58 75a.; 204*5875a. X *085 = 17-3899375 acres 17-3899375 acres = 17 acres^ 1 rood^ 22 p. 11 yds. 7 ft. 25^1 in. (6) 29 bush. 2 pks. = 29*5 bush. ; 2^5 bush. X -001 = -2065 busb. -2066 bush. = 1 a&h 2 ats. 1*216 uta. = 1 gal. 2 ^t. 1-^g^f pts. Exercises 60, 6? ] KEY. 173 . 429 lbs. n oz. %dwt. = 429-9416 lbs.; 429-9416 X '0072 = 3-09558 lbs. 3-09558 lbs. = 3 lbs. 1 oz. 2 dwt. 22|ff grs. 227 wks. 4 dys. 11 hrs. = 227-6369 + weeks _ 227-6369 weeks X '15 - 34-145535 wks. = 34 wks. 1 day 26-99 + minutes. (9) "^^^ ^^^- ^^^- = -£93-73125 : ^^93-73126 X -0^ = ^5-623875 = £5 12s. 6,^3,d. $2947-40 X -29 = $854-746. c (11) ^ 'il^J^^V ' ^^^^'1^ X -29 = $11-3593 $47-U4 — $11-3593 = $35-6807 (12) ^ *^^r«!r^^«i ^1129 X .11 = $124-19 - «« «.« f f ^'^^ ^ *^^^ = $226-8735 ^ ' $6 636 + $124-19 + $226-8735 = $357-6995 (13) $^429 X -09 = $ 668-61 = « « '^ $U29X -30 = $2228-70= " u ^l (14) 227 X -20 = 46-4 acres wheat 22V X -18 = 40.86 « grass 227 X .17 = 38-59 « peas tt u 227 X •19 = /*,3-13 " 00»7 v^ 4;a - - ii oats root crops 22tx -18 = 40-86 « fallow 174 1147 X '23 1147 X '07 KBY. [Elbh. Abith. (IB) 263-81 = 263^ killed or wounded. 80*29= 80t^ taken prisoners. EXBROISB 63. (1) $79*80 X '045 = $3-691. (2) $916*80 X •0776 = $71'052. (3) $10800 X -015 =$162, (4) $8877*66 X •0326 =$288*52396. (5) $678*90 X •06 = $33-94J. (6) $6719-60 X •0876 = $587-95625. <^) $47*80 X '26 = $11*96. (8) $7654*32 X '045 = $344*4444. (•) $234*66 X *28 = $65*6768. (10) $555*66 X '1875 = $104*165625. (ID 617 bush, at ii*'70 = $1048*90. $1048*90 X '125 = $131*1126. , Exercises 63-64.] ket. 176 (12) $1122-30 X •33§=:$3Y4-10. (13) $8765-40 X -0375 = $328-7025. (14) $7800 X -07 = $546. (15) $907-80 X -15 = $136-17. (16) $7-87j X 7400 = $58275-00. $58275-00 X -0825 = $4807-6875. (17) $7450 X -025 = $186-25. (18) $1140 X -03375 = $38-475. EXBROISB 64. (1) $789-46 X -0275 = $21-71015. « (2) $8167-50 X -022 =$179-685, (3) isSOO X -032 = $284-80. (4) $8740 X '00375 32 $32 -775. 176 KEY. [Elbm. Abith. (5) $1888 X -004 = $7-552. (6) $11247-60 X -0125 = $140-595. (7) $4780 X -01376 = $65-725. (8) $27490 X -026 = $714-74. (9) $8790 X -02125 =r $186-7875. (10) $17496-50 X -00875 = $153-094375. EXBLCISE 65. (1) $100 stock = $117-25 money or $1-00 stock = $1-1725 money $793 -^ $1-1725 = $7930000 -J- 11725 = $676-3326 (2) $100 stock = $90-50 money or $1 stock = $0-905 money " >'905 x'9476 = $b575'78 (3) $125X9 = $1125 stock = $108-375 money or $1 stock = $1-08375 money $1-08375 y 1125 = $7000 ^ $1-27 = $700000 -f $127 = $5511-81102 $100 stock = $92 money or $1 stock = $0-92 money $0-92 X 6140 = $5648-80 (9) $25X27 = $675 $100 stock = $101-25 money or $1 stock = $1'0125 money $1-0125 X 675 = $683-4375 (10) $100 stock -= $113-50 m^n.^. or $1 stock = $1' 135 money $11120 4- $1-136 = Slll5!ftfinn^<&t,«K =_ — -:. 178 KEY. fELsu. Abith. Il I, EXBROIBB 66. (1) $974 X •11 = $10M4 (2) $1678*90 X -09 = $151-101 X 7 = $1057-707 (3) $142-70 X -08 = $11-416 ; $11-416 X 16 = $182-656 (4) $80-80 X -07 = $5-656 ; $5-656 X 22 = $124-432 (5) r-49 X -025 = $1-68725; $1-68725 X 6= $10-12 55 (6)' $208-60 X -03375 = $7-04025 ; $7-04025 X 11 = $77-44275 , O) $800 X '08 = $64 = interest for 1 yaar. 4 mos. i $64 6 38 4 = interest for 6 years 1 mo. i 21 33i * * 4 mos. 10 dys h 5 33^ < * 1 " 5 dys. i 1 77| ' * 10 days. 2i dys i 88t « ' 5 « i dy i 44^ * ' H " 08f ' i « $413 86f interest for 6 yrs. 5 mos.18 dys. Exercise 60.J KEY, (8) i7gf $7400 X -0625 = $462-60 = interest for 1 6 mos. 4 mos. i I $ 462'50 i 9 year. 4162-50 = interest for 9 years. 231-26 154-161 38-54^ 19«27iV 9 -63^1 l-92if u u u tl tt tt 6 mos. 4 « 1 « 16 days. It tt $4617 29^= interest for 9 vrs.uS'^iT Otherwise 9 yrs. 11 mos. 24 days = 9.98rvprr« $462-60 X 9.98i = $l6lT.29lf ^ ''• $9680-80 X -03 = $290-424 — intArAa* f . $290,424 X 14J :tikm.?f4.°' ' ^''^' (10) (11) 2 mos. 1 mo. 15 days 10 days 2 days 1 day $1001 -26 6, $6007 •50 333 -75 166 •875 83 •4375 41- 71875 27- 8125 6- 5625 2- 78126 = in. for 6ys = in. for 4m3 = in. for 2ms = in. for Im = in. for 15ds = in. for lOds = in. for 2ds = in. for lA $6669- 43 7f i, 6ys 7ms 28ds 180 KEY. [Elbh. A&ith. t 4 i' rm li I (12) $8160 X 'OtS = $012 ; $612 X 9]^ = $5533-50/ (13) $412*90 X •048T5 =$20«1288t5 = interest for 1 year. $20-128875 X 6 = $120-TT325. (14) $12Y-40 X '126 = $15-926 = interest for 1 year. 3 mos. 3 days i<^ $15-926 3 47 -776 =:int.for3ys 3-98125 = int. for 3 ms •13270f§ = int. for 3ds $51-88895f = int. for Sys 3 ms 3ds (15) $80;63 X '0297 = $2-394711 = interest for 1 year. $2-394711 X 4-78 = $ll-4467l858 = int.for4-78yrs. (16) $106-70 X '1347 = $14-37249 = interest for 1 year. $14-37249 X 11-113 = $159-72148137 = interest for 11*113 years. El^BBOlSB 67. 1. J of 8 = 4 cents = $0-04; i of 7 = 3-5 cents = $0-035 ; i of 11 = 5-5 cents = $0-055. 2. 2 yrs. 9 mos. = 33 mos.; 33 -r- 2 = 16-5 cents = $0-165. a 1« xrva A. mnfl — 1 ftft mr\a. ! Iftfi-i- 2 ^ftfl rentfl = $0-98. )fi AAntfl Exercisea 66, 67.J KEY. 181 4. 5yrB, 11 mos. =^1 mog ; 71^2 = 35-5 cents 8. II yrs. 1 mo. = 133moa ; io.-^2 = 66-6 cents = 51>0'665. 6. 10 yrs, 10 mos. = 130 mos. ; 130 -^ 2 = 66 cents = $0'65. 7. 4 yra. 6 mos. = 63 »os I B3 ^ 2 = 26-5 cents = $0'265. i{^ T- ^ = 37 '5 cents = interest for 75 mos. 12 -J- 6 = -2 cents = interest for 12 days, 37. 7 cents = $0,377 = int. for 6 ys. 3 mos. 12 days. (9) 3^yrs. 3 mos. 3 days = 39 mos. 3 days. 39 4- 2 — 19-5 cents = interest for 39 mos. 3 -h 6 = -05 cents = interest for 3 days.* ^ 19.56cts. = $0.1955 = int.for3ys3ms3dys (10) 4 yrs. 7 mos. 10 days = 65 mos. 10 days 66 4- 2 = 27-5^ cents = interest for 55 mos. 10 4- 6 = -16 cents = interest for 10 days. 27-66 cts = $0.2766=int.for4ys 7mos lOds (11) 1 yr. 9 mos. 25 days = 21 mos. 25 days. 21 -H 2 = 10 '6 cents = interest for 21 mos. 25 -J- 6 = .416 cents = interest for 26 days. * t i\ ^ 0\n j% -X. XV ^xo CIS = ^u ■■ iuy I6=mt. for lyr 9ms 26ds Si M 182 KEY. (19) [Elkm. Arits^ 2 yrs. t moB. 1*1 days = 31 mos. IT days, 81 -r 2 = 15 "6 cents = interest for 31 mos. . 17 ~ 6 = '283 cents = interest for IT days^ 15 • 783 = $0 • 1 5783 = int. for 2y3 T mos lTd». "•J *\ <5 M . ,\ EXBRCISB 38. (1) Interest of $1 for 7 yrs. 9 ms. = 93 cents -i- 2 = $0-466 $0-465 X 1904 = $885*36 (2) Interest of $1 for 4 yrs. 11 ms. =59 cents-f 2 =$0295 $0-295 X 274*80 = $81-066 <3) Interest of $1 for 'J- v^3 2 ms. 12 dys. = $0*132 $0-132 K a: i-90 = $88*6908 (4) Interest of $1 for 3 yrs. 3 ms. 3 days. = $0*1955 $0-1956 X 213-27 i= $41-694285 (5) Interest of $1 for 4 yrs. 4 ms. 4 days = $0-260f $0-260f X 49-73 = $12-96295^ (6) Interest of $1 for 6 yrs. 5 ms. 5 days = $0-3258i $0-3258^ X 619-80 = $201*9615 O) Il^t^rest of $1 for 6 yrs. 6 ms. 6 days = $0*^f|} $0-391 X 27*60 = $10-7916 li. Aritb^ Eiercises 67, 68.] :)S l*ldB. : $0-465 $0-295 132 1955 260f 3258i ym 8) lb3 Interest of r for 1 year. 7 ma. 7 days = $0-4561 P-456^ X 47-32 ^ S21-58680I ^ (9) Interest of $' for 8 yrs. 8 ms. 8 days= $o ^2U $0-52Ii s 222-22 = $116.86069* * (10) Interest of $1 ''or 9 vra q .»« n j $05865 X 345-67 = $202-735456 (11) lufceiest 0f$l for 10 =. inr«c. ia a ^0 651§ X 7 >3 X $514-31488^ ■ >*^J*;iJv (12) Interest of$l for 11 vm n «,« n j (13) 5 Interest of$l for 3 yrs. 24 days = $0-184 $0-184 X 207-40 = $38-1616 (14) Interest of $1 for 1 yr. 28 days = $0.0r a $0-064i X 98-20 = $6.35026f ' (15) interest of $1 for 2 yrs 7 mna i r ^« «A !«»,«/ K * -^^ ^*^^ = $0-1575 $0-1575 X 76-42 = $12-03615 (16) Interest of $1 for 2 yrs 5 m« on ^„ dh. ^.- ^^®- ^ °^^- 20 days = $o 1481 ^viio^ X 9146-70 = $1356-7606 s^. IMAGE EVALUATION TEST TARGET (MT-3) A '**) fl I , 184 KEY. EXEROISB 69. [Elbh. Abith. (0 $1000 X -Ot = $70 = interest for 1st year. $1070 X '07 = $74-90 = interest for 2nd year. $1144-90 X -07 = $80-143 = interest for 3rd year. $1225'043 = amount at end of 3rd year. $1225-043 — $1000 = $225-043 = interest. (2) $800 X '06 = $48 = interest for 1st year. $800 4- $48 = $848 =: amount at end of 1st year, $848 X '06 = $50-88 = interest for 2nd year. $848 + $50-88 = $898-88 = amount at end of 2d year. $898-88 X -06 = $53-9328 = interest for 3d year. $898-88 4- $53-9328 X $952-8128 = amount at end of 3rd year. $962-8128 X -06 =$57-168768 = interest for 4th year. $952-8128 + $57-168768 =. $1009-981568 = amount at end <>f 4th year. $1009-981568 ■— $800 = $209-981568 = interest. (3) $900 X -06 = $54 = interest for 1st year. $900 4- $54 = $954 = amount at end of 1st year. $954 X '06 = $57-24 = interest for 2nd year. $954 + $57-24 = $1011-24 = amount atendof 2d year. $1011-24 X -06 = $60-6744 = interest for 3rd year. $1011-24 + $60-6744 = $1071-9144 ^ amount at end of 3d year. $1071-9144 X -06 = $64-314864 = int. for 4th year. $1071-9144 + $64-314864 = $1136-229264 = amt. at end of 4th year. $1136-229264 X -06 = $68-17375584 = in. for 5th yr. $1136*229264 + $68'l7375584 = $1204-40301984 = -^ umt. at end of 5th yeaf. $1204-40301984 — $CCO = $304-40301984 = int. Hzercise 69.] KEY. (4) 185 Lnn ^:'* = ^'* = '■"• «>' I»' half-year. $600 + $24 = $624 = amt. at end of 1st half-vear $624 X -04 = $24-96 = int. for 2d half-ye„ lilt V'-'' = ^'''■'' = -»• "' -* oTad hf.-y, $648-96 + $25-9584 = $674-9184 = amt. at end of 3d half-year. lluZl 1 ■»* = «2«-«9«'36 = int. for 4th half-yr. $674-9184 + $26-996»36 = $701.915136 = amt ^[ STn, «,.,„ end of 4th half-year. $V01 -916136 - $600 = $101-915136 = int. $250 + $8 . 75 = $258 • 75 = amt. at end of 1st hf.-yr imt ? .•'3« = $9-06625 = int. for 2d half-vea; $258-76 + $9.06626 = $267-80626 = amt. at enTof 2d half-year. $267.80625 X -035 = $9.37321875 = in for 3d hf vr $267.80625 + $9.37321875 = $277.17946875 =t^^^ at end of 3d half-vear $277-17946875 X-036 = $9.7o/28U0626 = mt. for 4th half-year. $2n.l7946875 + $9-7012814626 = $286-88076016626 ' — a°it- at end of 2d year $236.88075015625 - $250 = $36-88075015625 = int. -f $17-60 = $897-60 = amt. at end of ist quar quarter. $897- $897-60 -{.$17,952 = $915-552 = (Continued on next amt. at end pf 2d qr. pa«o.) 186 KEY. [Elbh. Abit&. (6) continued. $91B'552 X '02 = $18-31104 =: int. for 3d quarter. . $915*552 + $18 '31104 = $933 '86304 = amt. at end of 3d quarter. $933 '86304 X -02 = $18- 6772608 = int. for 4th quar. $933 • 86304 + $18 -6772608 = $952 • 5403008 = amt. ^t end of 4th quarter. $9lS2 '5403008 X -02 = $19-050806016 = int. for 5th qr. *$952'6403008 + $19-050806016 = $971 -591106816 — amt. at end of 5th quarter. $971-591106816 X '02 = $19-43182213632 = int. for 6th quarter. $971 •591106816+$19'3182213632=: $991 '02292895232 = amt. at end of 6th quarter. $991 '02292895232 — $880 = $111 -02292895232 = int. 0) $500 X '075 = $37-50 = int. ^^r ist year, $500 -f $37 '50 = $537 '50 =: &mi, at end of 1st year. $537 '50 X -075 = $40 '3125 = int. for 2d yenx. $537-60 +• $40-3125 = $577'8125 = amt. at end of 2d year. -. $577-8125 X -075 = $43 '3359375 = int. for 3d year. $577 '8125 + $43 '3359375 = $621 ' 1484375 = amount. $621*1484375 — $500 = $121*1484375 = interest. (8) ^ $400 X '045 z= $18 = int. for 1st half-year. $400 4- $18 = $418 = amt. at end of 1st half-year. $418 X -045 = $18-81 =int. for 2d half-year. $418 -I- $18 '81 = $436-81 = amt. at end of 2d hf.-yr. $436-81 X -045 = $19-65645 = int. for 3d half-year. $436-81 -f $19-65645 = $456-46645 = amt. at end of 3d ' half-year. $456 • 46645 X -045 = $20 -54099026 = int. for 4th hf.-yr. $456 * 46645 -|- $20 ' 54099025 = $477 ' 00744025 =: amt. $477*00744025 — $400 = $77-00744025 = int. BH. AxitB. qqarter.. nt. at end r 4th quar. l;;^ amt^ltt . for 5th qr. 1106816 = = int. for :292895232 S232 = int. Sxercuse 69.] ■ v> f Ist year. at. at end >r 3d year. = amount, nterest. r. alf-year. ear. of 2d hf.-yr. [ half-year. mt. at end ►r 4th hf.-yr. L025 2= ami. : int. KEY. 187 $714.90 X -025 = $17.8725 = int. for 1st qnarter: Add 714-90 un-: Sum = $732 . 7725 = amt. at end of 1st quar. $732.7725 X -025 = $18.3193125 = int. for 2d quar. Add 732.7725 •^., . Sum = $751.09181 = amt. at end 2d qr. $r51.09181x •025 = $l8.777294 = int. for 3d quarter. Add 751 .09181 Sum = $769 -8691 = amt. at end of 2d «. $769-8691 X -025 = $19-246727 = int. for 4th quar Add 76d-8691 Sum = $78? - l'l5r"= aat. at end 4th «r- $789.1158 X -025 = $19-727895 = int. for 5th quar Add 789.1l!!58 Sum = $808-8437 = amt. at end 5th qr. $808.8437 X -025 = $20 .221092= int. for 6th quar. Add 808.^437- ^°" = ^^^ * ^^*® = a«»t. at end 6th quar $829.0648X •025 = $20-72662 = int.for 7thquitt. ' Add 829-0648 ««^o »ai. ®""^ = ^849.7914 = amt. at end 7th qr. $849.7914 X -025 =$21.244785 = int. for 8th qui Add 849.7914 Sum = $871-0362 = required amt. Subtract $714*90 188 KEY. (10) [Elkm. Akitk $'Z94-60 X •045 = $35't5'J = int. for 1st half-year. Add t94'60 Sum = $830 -357 = amt. at end of 1st half-yr. $830-357 X '045 = $37-366066 =: int. for 2d half-year. Add 830-357 Swm = $867 • 723065 = amt. at end 2:d hf.-yr. $8e7- 723065 X '04^= $39-047537926 = in. 3d hf.-yr. Add 867-723065 Sum =$906 • 7706 = amt. requi'd. Subtract $794-60 Kemainder = $1 1? • 1 706 = int. required. EXBRCISE 70. (1) Interest of $1 at 7 per cent for 1 year = $0 -OT. Interest of $1 at 7 per cent foi 3 mos. = \ of $0-07 = $0-Ol75. Amount of $1 at 7 per cent ifor 3 mos. = $1-0175. $740 -^ 1-0175 = $7400000 -^ 10175 = $727-2727 = present worth. $740 — $727-2727 = $12 • 7273 = discount. (2) Interest of $1 at 9 per cent for 1 year = $0-09. Interest of $1 at 9 per cent for 2 mos. = ^ of $0-0^ = 0-015. Amount of $1 for 2 mos. at 9* per cent = $1 -OlS. $90 -r- 1-015 = 90000 -J- 1015 = $88-6699 = present worth. $90 — $88 • 6699 = $1 • 3301 = discount. iiJxercises 69, 70.] ■0» KEY. (3) 189 Amount of $1 for 6 months at 6 per cent = $1 -03 $250 -M -03 = $25000 ^ 103 = $242 • 7184 = present ^T OTTtil, $250 _ $242 • 7184 = $r.2816 = discount. Amount of $l for 11 mos. at 11 per cent = $I.10A «»14-20 -r l-KV, = $11420 -i- 110^ = 85T04o'^ 1321' = $648.T812 = present worth. n4.20 - $648- 7812 = $65-4183 = discount. Amount of $1 for 5 mos. at 8 per cent = $1 .OS- *'"■ - tsl;"^?.^ *""'" ^ '"'* = ^''"*''> ^ 310t — q|5»» J '00 = present worth. $911 -40 -$882 = $20.40 -discount. • (6) Amount of $l for 4 mos. at 7 per cent = $l -02^ ^'''* ~ tese'^ito^^''''' ^ ''''^ = $201429^ 307t — !|>656 • 1206 = present worth. $671-43 ^ $656-1205 = $16-3095 = discount. 0) Amount of $1 for 2 years at 4 per cent = $i -08 $947-60 .^ 1-08 = $94760 ^ 108 = $877-4074 - present worth. ~ $947-60 _ $877-4074 = $70-1926 = discount. * Multiplying each by 12. t M If , t ^"'*^P'ying each by 3. X - Uxviplying each by a to clear of fractious. 190 KST. [Elbm. Abith. (8) Amount of $1 for 16 mos. at *I per cent = $1 '09\. $888*93 -^ 1 '09^ = $88893 -^ 109.^ = $266679 -^ 328 = $813 •0457 =: present worth. $888*93 — $813*0457 :;= $75-8843 = discount. (9) Interest of $1 for 1 year at 10 per cent = $0 • 10. Interest of $1 for 47 days at 10 p^r cent = ^^y o^ $^ * ^^ = $0-01H. Amount of $1 for 47 days at 10 per cent = $1*01H. $7146-90 4- 1-01H = $'714690 -^ lOlH = $52172370 -5- 7394 = $7056-0413 = present worth. $7146*90 —$7066*0413 = $90*8587 = discount. <10) Amount of $1 for 2 mos. at 7 per cent. = $1 '01^. $710 -^ 1*01^ = $71000 -i- lOli = $426000 -^ 607 r= $701*8121 = present worth. * $7fO — $701 *8121 = $8 -1879 = discount. ' (11) Amount of $1 for 1| mos. at 7 per cent. = $1*008^. $1100-M •008^= $1100000-J- 1008 J = $4400000 ^ 4036 = $1090*4584 = present worth. $1 100 — $1090 • 4584 = $9 • 6416 = discount. (12) Amount of $1 for 2^Tnontbs at 6 per cent. '-= $1*01^. $6714-83-5- 1 *01^ = $67l483-J-101i = $4028898 -f- 607 = $6637*3937 =: present worth. ^OQO*T.Ot%9tr ^PMMiJ S ~ iJffif S .— sg7 ^*I*T»A'i(i9 — Aiai*f\nnf. S 9 -Zirvt^ \*SWV^^**ttft V. K. Abith. 179 -f 328 It. 10. r of $0*10 I-OIH. ;521t23T0 ;h. ount. M-oii. a-s-607 »Ullt. $1-0081. )00'f-4035 sou&t. = $1-01^. J898 -i- 60Y Bxfcrcises 70, 71.J KEY. ExiBOISB 71. 191 (1) ^' iT V^7: = ''' ^""^^ = '* '»^«- = * of » year. * Of 149 = $6,126 = discount required for 46 days. (2) T /^ "*" If ^® ^*^^ = 2 "^o'**^^ = * of « year. Interest of $840 for 1 year at 8 per cent. = $67-20. i of $67-20 = $11 .20 = discount required for 2 mos. (3) 4 mos. 4- 3 days = 4 mos. and 3 days. $790 X -06 = $39-60 =intere8t for 1 year. 3 mos. i $39-60 9 -871 = interest for 3 mos. ,71-1 3-29i = " " Imo. ^^^y^Ur -32^= " « 3dys. $13 - 49iV = disc, required for 4 m. 3 dys. * (4) 2 months + 3 days = 2 months and 3 days $614-30 X -07 = $43-001 = interest for 1 year. rnna I Cjo.aai 1 mo. i 2 mos. 3 days i $43*001 7 - 1668333 = interest for 2 mos ' _ '3S8 3416 = « «« 3 days. $7-6261749= $7-6261745 = discount required for 2 mos. 3 days. i m 192 KEY. [Elbm. Arith. < (8) 1 mos + 3 days = t mos. and 3 days. $21 7 '20 X -09 = $19-648 = interest for I year. 6 mos. 1 mo. 3 days i To $19-648 9 ■ "7 74 = interest for 6 mos. 1-629 = " " Imo. •1629= " " 3 days. 1-5659 = discount required for t mos. 3 days. (6) 20 days + 3 days = 23 days. $94-80 X 'lO = $9-48 = interest for 1 year. 20 days 2 " 1 " Tff 1^0 $9-48 •526§ = interest for 20 days. •052§ = " "2 '* •026i = " "1 " '6055 = discount required for 23 dys. EXEROISB 72. (1) $7000 : $2700 :: $1700 : A's profit = = $655*7lf. $7000 : $4200 :: $1700 : B's profit = t $2700 X 1700 7000. $1700 X 4200 7000 = $1020. $655 7lf 4- $1020-00 = $1675- 7lf. " $1700-00 — $1675-71^ = $24-28f = O's profit. Exercises 7l, 72J KEY. (2) 193 $29000 : $17400 :; $904-70 : B's loss __.$904- 70 X- $174000 — " — •=$542-82. 29000 $904-70 - 642-82 = $361-88 = C's loss. (3) 21 + 17 + 47=; 85 cows. 85 • 21 •• «5n'7 . , . 1. $307 X 21 .85 . 21 .. $307 : lstshare = ^ = $75-84}f. _ 86 . 17 .. $307 . 2nd shares = $61-40 85 85 : 47 :; $307 : 3rd share -, ^^^^ >< ^^ ' '»' .ora snare ^^69 • 75-/V. 85 . (4) $4 + $7 + $9 = $20. 20 $20 : $7 : : $7493 : B's share ~ ' ^^^^ ^ "^ ^ * ■" ^ ^°*^® = $2622-55. 20 »20 : $9 :: $U9B , O's share =!!f!fiL^= 533,^.3, 20 (5) ^ li + 2i + 5i = 9i. 9i • H :: $7500 : share of 1st = $7500 x H -^ Qi _$7500 X 7 X 2 . ^ i« . 9i TTTZ, ^ = $1381.671.^. • (Continued on next page.) lU KEY. * [Blim . Annf (6) continued. 9| : 2i :: $7500 : share of 2nd = $7600 X 2i -^9i $7500 X 5 X 2 = = $1973'68Ar. 2 X 19 9i : 5J :: $7500 : share of 3d ±z $7500 X 5i -=- 9J $7500 X 21 X 2 = :s 14144 . 73^1 4X.19 (6) $8900 : $4700 :: $3200 : A's share = r= $1689-88ff. $3200 — J1689-88f I = $1510-11|^ = B's share. $3 H- $4*20 + $7-49 = $14-69. S9000 V 3 $14'69 : $3 :: $9000 = $1837-98/i»^- $3200 X 4700 8900 14-69 = A*B share. $14*69 : $4-20 :: $9000 : $9000x4-20 14-69 . =$2573-17ia|^=: B's snare. $9000x7-49 $14-69 : $7:49 :: $9000 : 14-69 . cr$4588'83T8/^y=C's share. (8) $14900. — $4250 = $10650 = total loss.* i :: $10650 : $10650 X i = $5325 = A's share, i :: $10650 : $10650 X i = $2130 = B's share, i : iV :: $10650 : fiOeda X iV=f 3195 = O's share. 1 1 1 Bxercites t2, 73.] 195 +U . 1% :: $4942 : $4942 X .'A -s- i-U _ $4942X36 '''• ^** iU '■ A% :: $4942 : $4942 x ^lyt • lu. _ $4942X66 *^XT^-riJ* ;[7~ $1618.43,^^ = 2nd part. +U : T% :: $4942 : $4942 x A = $100000 =Voduct of A's 6000 X 5 = 30000 y stock and time. $7000 X 6 = 35000 = do. B's do. Sum = $135000 $3000 X 100000 $135000 : $100000 :: $3000 : 135000 = $2222 •22f = A's share. $3000 — $2222-221 = $777-77^ = B's share. (10) $35000 X 2 = $70000 ^ 24000 X 3 = 72000 > = $182000 = A's st'k for 1 mo. 20000 X 2 = 40000 ^ $11000 X 5= 55000 = B's do. do. $4000 X 2= 8000 = 0's do. do. Sum =$245000 (Continued on next page.) Abitb^ Bxerciees IB, I4.] KEY. 8-50^^ ; of A's id time. Va do. ire. or 1 mo. do. do. (10 contmued.) $245000 : $182000 ;; $9Y00 : ^ ^^^ X 18 2000 246000 = $7206.7lf = A'ssbare. $245000 : $55000 :: $9700 : J!!!i^ ^^^^^ 245000 = $2177.66^ = B's share. $246000 : $8000 :; $9700 : .^^^^^ X «QQO 245000 = $316.73fi=;C's share. EXBRCISB 74. (1) From 70 cents the selling price ' Take 62 J cents the buying price The remainder 7*" cents = the gain per jard n cents X 209 = $15,671= whole gain. (2) Prom $1.42 the selling price Take $1^ the buying price The remainder $0 • 13 = the gain per bushel $0-13 X 8900 = $1157 = the whole gain. (3) From 16 cents the buying price Take 12i cents the selling price The remaindAr ^i /.o«*« ^u- » 3i cents X 780 = $27.30 ..the whole loss. :fi| 200 KEY. [Elbm. Abith. (4) From $5 '47 the selling price Take $4*92 the buying price The remainder $0 • 55 = the gain per 1000. $0*55 X 1142 = $628 '10 = the whole gain. (5) lY cwt. 2 qrs. 11 lbs. = 1761 lbs. ; also at $23 per cwt. it is 23 cents per lb. From 23 cents the selling price Take 18 cents the buying price The remainder 6 cents = the gain per lb. 5 cents X 1761 = $88*05 = the whole gain. ^ (6) $13*60 per cwt. = 13^ cents per lb. From 13 i cents the selling price * Take 11 cents the buying price The remainder 2| cents = the gain per lb. 2^ cents X 1143 = $28*67| = the whole gain. a) From $17*43 the buying price Take $12*94 the selling price The remainder $4*49 = the loss per ton. $4*49 X 63 = $282*87 = whole loss. (8) From $4*17 the selling price Take $3*3 7i the buying price The remainder $0*79i^ = the gain per sheep ■ 79i X 47 = $37*36i = whole gain. Exercises 74, 75.J KEY. 201 ExiBoiSB 75. (1) I want to gain $10 on $100, or 10 cents on $1. Hence selling price $1-10 x 293 = $322-30. (2) $17 i)er $100 = 17 cents per $1. Hence selling price = $1 -17 x 890 = $1041 -30. (3) $1 -23 X 630 = $774-90 = whole buying price $8 per $100 = 8 cents per $1 ; $i ^ s cLts ' $o 92 Hence selling price =$0-92 x 774-90 =$772 908 (4) 44 cents X 960 = $418-00 = cost of Whole. $33 per $100 = 33 cents per $1. $1 -33 X 418 = $666-94 = selling price. (6) $12-50 per $100 = 12J cents per $1. $l-12iX 2146-42 = $2413.6976. (6) $2-80 X 512 =: $1433-60 = whole buying price $16 per $100 = 16 cente per $1 ; $i ^ 15 ce2= $0 85 $0.85 X 1433-60 = $1218-56 = selling price O) 1 cents X 64980 = $4648-60 = whole buying price $24 per $100 = 24 cents per $1 " $1*124. V AKAo.on tmm^.^ -, " " •24 X 4648-60 = $6640-264 = selling price. m KUt. (8) [BLSlf. ABltfi. f 5*22 X 908 = $4739 "te = buying price. $1| per $100=^1 cents per $1 ; $1—1^ cents=$0*98i. $0'98i X 4739* te = $4668-6636 = selling price. EXBBOIBB 76. <1) $26*26 — $24 = $2*25 = gain on $24. $2-55 X 100 $24 : $100 :: $2*25 : . = 9f per cent. 24 <2) $17*80 X 279 = $4966*20 = whole buying price. $5570 — $4966*20 = $603*80 = whole gain. 603*80X100 $4966*20 : $100 :: $603*80 : 4966*20 r= 12]fcafl8«^ = gain per cent. ' , (3) $2*30 X 212 :s: $487-60 = whole cost. $600 «-$487*60 ST $112*40 = whole gain. 112*40X100 $487*60 : $100 :: $112*40 : -: 487*60 = 23t|?^ per cent. (4) $7*40 X 93 = $688*20 = whole cost. $688*20 — $651 = $37*20 = whole loss. 37*20 X 100 $688*20 : $100 :: $37*20 : = 6t*jS^ per cent. 6S8*ZU Bxercises 76-77.J KBt. (8) 203 $93.40 X 205 = $19147 = whole- cost. $20987 - $19147 = $1840 = whole gain. •lAi^fr ^ 1840 X 100 $19147: $100:: $1840 :___ = 3^^j^p,^^, (8) $7400 - $6250 = $1150 5t whole lo«. $7400 : $100 : : $1150 : '''' ^' ^^^ ^ ,,,. ^ , 7400^ "" ^^ ^V^^*- EXBBOISB 77. (1) $100 + $18 := $118 $118 . $100 :: $1.70 : = $1.4406M 1»18 *^^ (2) $100 4. $29 = $129 «i9o . «iAA «.« $324 X 100 $129 . $100 :: $324 : • = $251.1627ff 129 (3) $100 — $11 = $89 f89:,.o,::,n«o..i"«''xxoo^ 89 = Whole buying price. $2000 --366 = $5-6179^ per bushel. 204 KEY. [Elih. Aritb. $100 — $14 = $86 8-^0 cents X 100 $86 : $100 :: S^^ cents : 86 = lOif cents = buying^ price. (6) $100 4- $43 = $143 $9490 X 100 $143 : $100 :: $9490 : $6636-36 143 = buying price. (6) T2 X '20 = $1*344 = commission on each barrel, $6-^2X100 * $111 : 100 :: $6-Y2 : - = $6-06406 111 = original cost per barrel. $6-06405 + $1 -344 = $7-39805 = total cost per brl. $100 -f $9 = $109 $146 X 100 $109 : $100 :: $146 : = $133 -02151^ 109 = buying price. (8) $100 -). $31 = $131 $12 X 100 $131 : $100 :: $12 : = $9-ie03T|T 131 == buying price. Exercises 77, 78.] KXY. V 205 EzBRoisi 78. O) 11 cents X 207 = $22-77; $22-77-^ 34| = $45-54 4- 69 = $0-66. (2) 10 cents X 293 = $29-30 = price of eggs. 18 cents X 47 = $ 8-46 = price of raiins. 14 cents X 9 = $ 1.^6= « loaf sugar. 6 cents X 23 = $ 1-38 = « rfce ^ $8.46 + $1.26 + $1-38 = $u.ao = Price of raisins, sugar and rice. $18-20 ^ $008 = 1820 -^ B = 364 lbs. . (3) , $24-5? 4- $0-43 == 246» ^ 43 = 67,% ^s. (4) • - ••, $33T0 X 9 = $ 303-30 = worth of cows. $303-30 ^ 84 = $3-61A = price of a sheep. (6) «,«« J^'''l ^ '® = *'*»■" = ■^""' of silk. %r5*3ri2r.!.iS-='r/^ '*-»'' «•--• IP o 04 . jd «. $6-75^ = worth of cloth per yd. (6) $4-90 per cent = 4^^ cents per lb. $29-7^^ ''^o ""Tl ^'^'^^^ = ^^^*^ '' pork. *^9-743 + 409 = JRO'0'7^i9A ^v « . *^ - , -- ^—ios — viurta oi caeese per lb. 206 KEY. (T) [Elim. Abith. $1-35 X 420 = $567 = worth of wheat. $567 — $207-50 = $359-50 = cost of flour. $359-50 -i- 11983^ = $1078-50 4- 35950 = $003 =: 3 cents per lb. 3 cents x 100 = $300 = cost of a cwt of flour. («> ■ Hi cents X 423 = $46-63 = worth of sugar. $46-63 ^-$0-23 = 4663 -^ 23 = 202304^ quarts. EXIBOISB 79. $714-93 X i = JE178-7325 = JE178 14s. 7fd. (2) $914-90 X f = Je365-96 = £366 19s. 2gd. ^-•'-^^^^ . ■ (3) . ;:...,.. $611-20 X i^ff = £183-36 = £183 7s. 2|d. <4) $43-92 X § = £17-668 = £l7 lis. 4]ftd. £293 17s. 4d. = £293-8666 ; £293-86 -^i = $11 76-463. (6) £294 lis. Hid = £294-597916; £294-597916 — 1 = $786-594. 0) £247 2s. 6id. = £247-121876 -5- is = $1069-09375. [. Abith. ur. $003 flour. far. [uarts. d. d. 1. 1Y5-463. 093*75. Exercises 78, 79.J ^i^. 207 £99 lis. lOir i= £8959376 = £8959375 ^ 4 = $358-37J. (9) $994-70 ^ $4-867 = £204-3764 = £204 7s. 6id. + (10) * $896-93 ^ $4-867 = £.184-28806 = £184 6s. 9d. + (11) $1020-11 ^$4-867 = £209-5972 = £209 lis. l^d + (12) $89-74 ^ $4-867 = £18-4384 = £18 88. 9d. + (13) ^29 14s. Hi = £29-746875 X 4-867 = $144-778039625. £2H 16S. 2id. = £294-810416X4-867 = $1434-84229+ er win nui^be/ llf , " " ' " " '" '"^ "^ » <="'-» number. ""'' " "'""* " *" " "" "1»'-<» 132 is as many times 10 ., 10 is contained times In 132 whicli is 13J-. Therefore 121 is H of 13f times 10. If 6 is i of a certain nnmber, 8 times 6 or 48 wiU be tlie required number. 48 is as many times 7 as » Is contained times in 48 which is 48 -f. 7 = ef . Therefore 48 is f of 6f times 7. (0) If 78 is jfif of a certain number -X- nf fho* u i be } of 78 which is 13 ' ^ ' """"""• ""' "''t^tllr''" """""" '^^ " = "' -'» - 143 is as many times 11 as It Is contained times in 143 which is 13. Therefore 78 is ff of 13 times 11. (10) Tf r. K V?^ '' ^ ' *^'° ^ ^' ^ <>f ^hat number? If ^ be l^of a number, that number will be | x 7 = i^ Therefore i^ of 25 is f of 64. 310 KEY. (11) [Elph. AsiTfig ,1 of 43 = 6 times I of 42 = 6X6] then 36 is -ft- of what number ? If 36 be T^r of » number, Vr of that number will be i of 36 which is Vs, If U be fr of a number, that number will be 11 times? U which is 79^. Therefore f of 42 is t^ of 79^-. (12) J of 81 = 7 times ^ of 81 = 7 times 9 = 63 ; then 63 is -^(j of what number ? If 68 be 1^ of a number, -^- of that number will Jbe ^ of 63 which is 21. If 21 be T^r of a number, that number will be 10 times- 21 which is 210. Therefoire f of 81 is i% of 210. (13) iV of 99 = 4 times ^^ of 99 = 4 times 9 = 36 ; then 36 is i of what number ? If 36 bn f of a number, ^ of that number will be ^ of 30 which is 9. If 9 be I of a number, that number will be 5 times 9 which is 45. Therefore -r»f of 99 is |^ of 45. (14) If 8 cows give 44 lbs. 1 cow will give \ of 44 lbs. which is 5^ lbs. ^ If 1 cow gives 5^ lbs. 11 cows will give 11 times 5^^ which is 60i lbs. Therefore if 8 cows give 44 lbs. 1 1 cows will give 60i lbs. Ezei If 9 If 11 There Ifl3( $ $19-8C cc Theref If A a: wi wo Theni an( as If A cai he c (lay! Therefor it in time i. e. ■^ \ AmvwtJ be i of 1 times Exercise 80.j hen 63 Jbe^of ) times - then be^of times 9 which nes 5^ give KEY. (16) 211 If 9 banrels cost $27, 1 barrel will cost ^ of $37 which IS «g)0< If 1 barrel costs $3, 23 barrels will cost 23 times S3 which is $69. Therefore if $27 pay for 9 barrels, 23 barrels will cost $69. (16) ^^ ^ V^l'' TV.""'* ^^'''' ' ^*^'' ^^^^ ^" cost A of $7-80 which is 60 cents. ^ $19-80 will pay for as many days' work as 60 cents is =''l^8o'l*'°'-''' ^^^'^^ ""^'"^ '' ^^^'^^ -^ ^^'^^ Therefore if 13 days' work cost $7-80, $19-80 will pay for .33 days' work. (17) If A and B can do the work in 4 days, in 1 day they will together do i of it, and if A a/one can do the work m 9 days, in 1 day he can do ^ of it. '^^^\tn ' "^.f^ - ^ = the part B can do in 1 day, and he will require as many times 1 day to finish U as f J IS contained times in the whole, i. e. 1 -^ ^iW = ¥ = 7^- days. ' • ^^ (18) If A «»° ^o the wholo in 10 da^s, in 1 day I,e can do Iff of It If B can do the whole in 7 days in 1 day d«v?° ,"/ °'." """"^ ° •="" ^0 '^0 ^"ole in 12 "lays m 1 day he can do A of it Therefore together they will do ^V + * + V. = ifj of t .n 1 day, and to finish it they will reqube as mny i « ,'.~T';r'*!'"''"""*'°^*^^""««*°ti»e whole, 1. e. 1 - its - jp. ^ 3^|_ ^^^yg^ 212 KEY. [Elim. Abith. Bzi I 11 1 (19) A, B, and can together do the work in 15 days, there- fore in 1 day they would do ^g of it. A, working alone, can finish it in 35 days and therefore in 1 day he can do ^ of it. B, working alone, can do the work in 42 days, hence in 1 day he can do i^^ of it. Therefore B and 0, working together, can do ^ -f ^J^ = ih^ of it in 1 day, and A can do -jV — ^ wJiat number is, that of. which ^ is 104? If t^ be. 104, ^ wUl TsV of 1^4 which is W>; and if ^ be Wtli« number required, will beVV^X 60=109^. (29) If I == Tpr ^^ 2, thfi,differejic§ betw,eejft i and. A mpt be 2 ; i. e. 5,— ^-fr = 2, or ^ = 2. If ^ of a number be 2, the number itself wUl be 44 tunes 2, which is 88, (30) I of H^ ^ = il^ ; Hi is i^ of the last product, hence the product in questionis ^ ~ ^^ = ^ X 4i = 36. 36 -r 3 = 12 = sum spoken of; 12 — 7 = 5 = 2nd quotient. 5 X 11 = 66 = remainder spoken of. 65 -)- 5 = 60 = f of the 1st quotient ; hence 1st quo- 60 X 8 tient = — =; 160. X60 X 4 = 640. ^J.^ 5wW«8fi QK^i 81.] rate of ilea per ilea per ference 17 willh^ IbyA, 233 = : ^ whfch ad. ifi^ =109^. A nipt 11 be 44 it, hence K = 36. > = 2nd 1st quo- J&^% EXBBOISB 81, 215 (1) = 17X17 = 289. (2) 23 X 23 X 23 =: 12167. • (3> 279« = 279X279 =77841. 81' = 81 X 81 X 81 = 631441. 6* = 6 X 6 (6) X^X6 = 1296. «' = 6X6X5X6X6 = 3126. (7> 4« = 4X4X4X4X4X4 = 4096. (8) 3^ = 3X3X3X3X3X3X3 = 2187. (9) 2 =2X2X2X2X2X2X2X2 = 256. (10) 3^ = 3X3X3X3X3X3X3X3X3 = (11) »' = ^ X 7 X 7 = 343. 19683. 11* = 11 X 11 (12; X 11 X 11 = 14641. 216 KEY. [Slim. AbithI E (13) 1 96 = 9X9X9X9X9X9 = 531441. (14) I^V^^^^^^^I • (1)" = |x^xfxtx|= ufb. II^^^H ' ^ (15) 1226« = 1226 X 1225 = 1500625. (16) 4837« = 483Y X 4837 = 23396569. |^H# (17) (4i)3 = (jf )3 = 1,1 X V X V- = m^^ = "jm- (18) 293 .. 29 X 29 X 29 = 24389. (19) (21)* = (f )* = fXtXfXf=^^^ = 50|f . i^B (20) '• 3^0=3X3X3X3X3X3X3X3X3X3 = 59049. EXBROISB 82. ^^^^B (1) (2) « 1296(36 3969(63 9 36 1 V 66)396 . 123)369 336 36D Bxercisea 81, 82.J (8) 16876(126 22)58 44 246)1476 1876 (5) • • • 142884(378 8 67)628 469 748)6984 6984 0) • • • •244036('494 89)840 801 984)3936 3936 KEY. 217 (4) 53361(231 4 43)133 129 461)461 461 (6) • • 998001(999 81 189)1880 1701 1989)17901 17901 (8) • • • •395641('629 36 122)356 244 1249)11241 11241 216 B^f. tB&%ir/Afti«B. (^) (10) Y66-26)27-6 4 11397-4849(106*759 47)366 206)1397 329 • 1236 54*5)2725 212*7)161-48 2725 148-89 213*45)12-5949 ^^^^^H 10-6725 ^^^^H 213-509)1*922400 1*921581 •600819 I ^^^^ (12) ^m 98123'478k^(^13*246 671^4*^3(2590-929 4 ^B 61)81 H 45)271 . 225 623)2023 509)4629 1869 4581 1, 626'2)154*47 6180-9)4814*23 125-24 4662-81 626-44)29-2389 6181-82)151-4200 j^^^^Bi 25-0576 103-6364 626-486)4-181316 5181-849)47-783600 -^— 3-758916 - 46-636641 ■ . -422394 1-146959 Bzereise 82.J (13) 918*767)958 '623 81 186)1087 925 1908)16267 15264 1916-5)1003 -00 958-25 1917-02)44-7500 38-3404 1917-043)6-409600 5-751129 •658471 (14) 4291 = 429 -75(20 -7304 4 40-7)29-76 28-49 41-43)1-2600 1-2429 41 -4604) -01710000 -01658416 •^0051584 21d .« V. '^•.jai^ 220 KEY. [Elbm. Abith. (15) We Vl69 - Vl69 "^ ^^ ' ^400 = VioO "" "^^ (16) -^7^ = •6363636363' 0-63636363(-':9n •49 -ft. = ")2941176 • • • 1^49) 1463 1341 0-5294in6('t2'Je 49 1-42)394 284 1^58'7)12263 ^11109 1'44'7)11011 10129 1»594'7)115463 111629 1*4546)88276 87376 3834 lOOO (17) 428^ = 428-428571 428 -428571(20 •69& 4 40»6)28-42 24-36 41-29)4-0685 3-7161 41 -388) -352471 -331104 -021367 Biwrcise 82.] KEY. (18) 629^ = 629-8 • A • 629-800000(25*095 4 221 45)229 226 50'09)4«8000 4-6081 50'185) -291900 •250925 •040975 (19) 1127896i = 1127896»25 • • • • • • 1127896-250000(1062 -024 1 206)1278 1236 2122)4296 4244 212402)52-2500 42-4804 2124044)9-769600 8-496176 1-273424 :i.i5.^::::..d-A-: isii Kvr. (26) ,14ltltB. • • 213798 • 123700(462 •383 16 86)537 516 92 924 924 2)2198 1844 •3)364^12 277*29 •68) 76 •8337 78 •9744 924 ■ •763)2*869300 '2-774289 ! : * •086011 1 t ,' V BXBBOISB 8^. f * (1) f 32768(32 27 3* = 9 X 300 = 2700 5768 3X2 = 6X30= 180 2«= 4 , 2884 5768 s-'K;i?^if?^x?.^ r*^^ B^^#bli«fc 8^, 63.] 8« = 64 X 3^6 = 19200 8X7 = 66X30= 1680 r«= 40 20929 668503(87 612 146603 146603 m (8) 2« = 4 X 300 = 1200 2x4 = 8.X3b= 240 *' = re 1466 13824(24 8 6824 6824 W 260047 (63 216 6« = 36 X 300 6 X 3 = 18 X 30 3« 10800 640 9 34047 11349 34047 224 KEY. (6) [Elbm. Arith. 9* = 81 X 300 9 X 9 = 81 X 30 970299 (99 729 9« =z 24300 I 241299 2430 81 26811 241299 (6) 1053125 1 (125 1« = 1 X 300 = 1 X 2 = 2 X 30 = 22 = 300 60 4 953 ♦ 364 43200 1800 728 . • 12« = 144 X 300 = 12 X 5 = 60 X 30 = 225125 5« = • 25 225125 45025 iL0i'''*'i'r-^,^K.%l ■ »«*vi* v>»iav> ut/aj c , , 15813251 (251 8 2* = 4 X 300 2 X 5 = 10 X 30 52 = 1200 = 300 = 25 7813 1525 = 187500 = 750 = 1 7625 25« =: 625 X 300 25 X X = 25 X 30 1« 188251 * 188251 188251 225 (8) 48228544 (364 • 27 3« = 9 X 300 = 2700 21228 3X6 = 18X30 = 540 6« 36 3276 19656 36« = 1296 X 300 =r 388800 1672544 36 X 4 = 144 X 30 = 4320 4«= 16 393136 15 •70544 m t^mr.4m^ 6« = 86 X 300 ' 6 X 2 = 12 X 30 2« 62« = 3844 X aOOr 62 X 6 = 372.x 30 6« = 10800 = 360 = 4 iil64 E1163200 : 11160 : 36 1164396 245314376 (626 216 29314 . 22328 6986376 6986376 m 686-128968 (8-82 612 8« = 64X300 = 19?00^ 174-128 8 X 8 = 64 X 30 rr 1920 8* = 64 24184 88« = 7744 X 300 =2323200 88 X 2 = 176 X 30 = 6280 2«= 4 2328.434 169-472 4r666968 4-656968 "~1 te^|[*Be,83,} m • • 991026-973 (99- 1 729 9« = 81 X 300, 9 X 9 = 81, X 30 92 99« = 9801 X 300 99 X 7 = 693 X 30 7' 24300 I 262026 2430 81 26811 =2940300 : 20790 : 49 2961139 241299 20727:9735^ 20727-973 9'* = 81 X 300 9 X 7 = 63 X 30 7^ 97« = 9409 X 300 97 X 1 = 97 X 30 -1« (12) • • •915498611 (•971 729 = 24300| 186498 = 1890 = ^ 49 26239 =2822700 = 2910 = 1 2826611 183673 2825611 2825611 228 KEY. [Elim. Ahith. Bxej (13) J® V2I I 343_ __ ^^ _ , I 64 V"6r 9« = 9 X ( (14) 1^ = 0-916666666 • ■ • • 92 = 81 X 300 = 24300 9 X 7 = 63 X 30 = 1890 72 =' 49 •916666666 (-971 729 187666 26239 97« = 9409 X 300 =2822700 97 X 1 = 97 X 30 = 2910 1* = 1 183673 3993666 ^=■•9 2825611 2826611 •1168066 (Continued on next page.) 96* = 96 X .9 = 4« = 16 4X6 = 46« = 2: 46 X 4: fitercise 83J KIT. 22d (14 continued.) = '9 •90(J000000 (•965 729 l^VLlTso = ^-»'""- 6« = 1620 36 25956 j 166736 96* = 9216 X 300 — 9T«-» 1 day. Hence B cfn do Xi?°,F +^= # of it *»y i and to finish the whole^^rkh.^r^J °^ " '" I Bzereise 84.} KIT (20) 241 149^f = U9'2W2121 ■\- • » • • U9' 21212121(12 '2111 22)49 44 24'2)5'27 4-84 24'41)'4327 •2441 24-427) '188627 •170989 24 '4347) 1763827 1710429 53398 (21) 2000 4^ 6i = 4000 -M3 = 307 hrs. 41 min. 32^ sec. = 1 wk. 6 dys. 19 hrs. 41 min. 32xV sec. (22) iJ2l9 8s. lli=$877-78J. 1 f of 4i of f of— of 24J times $976-53 = $976-53x-X-X-X-X^ ^ ^ t t J^ = 976 '53 X 9 = 18788 •77. $8788 • 77 —$877 •781 = $7910^98i* 242 KEY. [Elim. Aritb. (23) ' 2'a • 3 /• 2^^ V^!' = ''^"'^'^ quarter-yards. 189431)^- , J'.'- = '^''^'^ quarter-yards. 18943&O0 ^ 172675 = 109. 708 4. times. (25) 33 IS^ 11 6 33 19 11 12 ' I 9i n ^"^ 6^is^^r? ^ 11 X6 X 33 2178 6 X 17 = -^-. = 2178 : 85 85 15013)27051(1 15013 (26) 65)138(2 130 2038)15013(7 14266 747)2038(2 1494 544)747(1 544 8)65(8 64 1)8(8 8 G. 0. M. = I 203)544(2 406 138)203(1 138 65 Exercise 84.] KEY. 243 (27) If 4 men can do the work in 66 i hours, 1 man will re- quire 4 times 56i hours, i. e. 226 hours, and hence in 1 hour he would do j^j of the whole work. If 6 women can do the whole work in 56i hours, 1 wo- man would require 6 times 56i hours, i. e. 3371 hrs and hence in 1 hour she would do 7^^= ^^y of the whole work, and consequently 2 women will do s^j of the work in 1 hour. 8 boys can do the whole work in 56i hours, 1 boy would require 8 times 56i hours, i. e. 450 hours, and hence ini hour he would do ^"of the whole work and consequently 6 boys would do 6 times xU which is ^ of the whole work in 1 hour. Then 1 man, 2 women, and 6 boys working together will do 7^ + ^^ + ^ - ^^a^ ^f ^^^ ^j^^j^ ^^^^ lu 1 hr. and to finish it they would require as many times 1 hr. as yff^ ig contained times in the whole, '• e- 1 -?- Tf fir = -4f *^ = 46i| hours. 24 4 8 10 32 3J d (28) 400 : Ans. = 6 m --^ 3 WXl?^X3ix2lXSi I = 5 X 3iX 21 X 3 = n02i rods. (29) ^^89 14s. 81d. = £789-735416 X 4-867 •70 ^ 4-867 = $2984700 -f 4867 ^ £613 6s. Old. = $3843-6422-H 2^ KEY. [Elim. Arith. (30)^ 1800 X -045 = $36 = Int. for 1st half-year. Add 800 Sum = $836 = Amt. at and of 1st half-year. $836 X -045 = $37-62 = Int. for 2nd half-year. Add 836* Sum = $873-62 = Amt. at end of 2nd half-year. $873-62 X -045 = $39-3129 = Int. for 3rd half-year. Add 873*62 Sum = $912 -9329 =5 Amt. at end of 3rd hf-year. $912-9329 X -045 ='$41-08198 = Int. for 4th hf-year. Add 912 -9329^ Sum = $954-01488 Amt. required.' $954-01488 - $800 = $154-01488 = compound interest. (31) 1?orontOj^£^^=:^==^32 : 100 :: 1 : ^^ = 3^. Hamilton, T^m^ = TgB,, = ,i^tf = 800 : 100 :: 11 : 100 X 11 = ¥=1|. 800 Kingston, TiTOSTT = T*^ = -Sj 320 •: 100 :: 3 : 100 X 3 (32) Assu. 60 I l^l^^J^^. . 72. .80. ;88. .96. . 100 ^^^"' ^ I •- " -' «> .» 6.. V.22.'. 8.. 5 .. .. .. 11.. A- -R 1. c. m. 60 X C X 11 X 4 X 6 = 79200 Bwrclfle 84.J 5 KEY. 245 $^900; $2700 (34) $2470X^ = A's. Share. .*r9fto.:^2300 :: $24fO ^illili!"" — Pa Share. *'"'-*'''''-^«'V = *.06.70Hf = i Share. (35) = Whole gain. $956-20 ; $100 :: $44-8Q ..^ilfi^ _ 144)9146714 In. ^^^^ 8)63618 ft. 86 in. • ,m|282a_8q„arter-yds.6ft.i22,„. 233 pe, 35 q, y^^^ - 233 per 9 yds. 3 ft. 86 in. '• ^' 33 per 9 yds. 3 ft. 86 in. 246 KEY. (37) [Elix. Abith $2967-80 X 1% = Je890-34 = £890 Cs. 9^. £29 8s. Hid. = £29-447916 -M = $78-627. (38) 17 bush. 1 pk. 1 gal. = 17*375 bush. 14672 X 17-375 = 2 ;4926 bush •19704 •39408 •57632 1 -15264 2 bush. 2 pk. gal. 1 qt. 1*15264 pt. mi Exercise 84.J KEY. (80) lUd^T = 7149-272727 247 1' = 1 X 300 = 1 X 9 =: 9 X 30 = 99 = 19« = 361 X 300 = 19 X 2 = 38 + 30 = 2« = 192« = 36864 X 300 192X6 = 1162X30 6« 300 270 81 7149 -2 72 72 7(19 '26 1 6149 65i;5859 290*272 109444 218-888 11069200 71-384727 34660 36 11093796 66-662776 4-821951 (40) Since one pipe can fill the cistern in 40 and ih. «4u m 26 minutes, the one will fill A and th : he 'rS m 1 minute, and since the third pipe empties iUnVn minutes, in 1 minute it will emntv 1 T^J^^ ^ T}i«n if oil *!, . empty ^ of its contents 248 KZY. (41) [Bxiuc. Abitb. 71-413 -^ -91467 = V141300 ^91467 91467)7141300 •(78-076 640269 738610 731736 687400 640269 471310 467335 13975 (42) Prom 43 a. 2 r. 7 per. yds. Take 19 3 27 18 Diflf. = 23 2 19 12i yds. acr. per, yds. ft. in. ac. r. per. yds. ft. in. 23 2 19 12 2 36 X 8 = 188 3 35 7 2 36 10 236 11 34 1 4 72 X 7 = 1653 1 38 10 4 72 10 2362 20 15 X 3 = 7086 1 21 14 6 108 Sam = 8928 3 15 1| 4 72 = 8928 3 15 2 2 36 ISiercia* 84.] KEYi (43) 2*78 yds. 3 qrs. 1 na. 2 in. 1115 qrs. 249 4461 na. 2i 8924 lllSi 10039^ inches (44) 9i 8i ? of 3i of 6i of 8§ of of of -9 of * of -63 lU I7i ^ .9 5{ 13 13 !^!5 57 n 9 ^ ($8 — --X — X — X — X — X — X — y-lv-- ^ 4 5^ jj i^^ JJEf^'lo''^ ""lOO 4 Y _ 13 X 13 X 5 7 X 9X9 ^ T^4X4XlOXl"^ = ^^^^''^ = '^^^^^ 250 KEY. [9lik. Abith. (46) 23 a. 3 r. 30 per. at $47-80 per acre. 2 roods r I I 1 rood 20 per. 10 per. i 5^47-80 23 $1099-40 23-90 11-95 6-97i 2-981 $1144-2U (46) $100 stock = $1-08* money or $1 stock ^ = $1*08J monej. $l'08i X 2400 = $2604. ' (47) ^ 60 miles = 50 X 6280 X 12 = 3168000 inches , 2 ft. 6 in. = 29 inches = inches in 1 pace. 3168000 -J- 29 = 109241H = number of paces. (48) $100 4- $16 = $116 $7890 X 100 $116 : $100 :: $7890 : — = $680l-72U 116 ■ (49) to Int. of $1 for 7 yrs. 3 mos. 20 days or for 87 mos. 20 dys. = $0-436 + $0-003J = $0-438J $0-438J X 894-80 = $392-220! Exercise 84.] KIT. 351 (50) A can do the whole work in 24 days, hence in 1 day he can do ^ of it. , ^ B can do the whole work in 30 days, therefore in 1 day he can do ^ of it. In 7 days A does ^'f of the work, leaving ^ to be done by A and B together. Then i^y + iV = ^j = work done by A and B together. !♦ X 6 ki-i-ia^kiX^zr. = ^=:9Jdays. 3X3 ,51) 2 lbs. 3 oz. 4 dwt, = 13056 grains. 11 lbs. T oz. 9 dwt. 4 grs. = 66940 grains (52) £493 16s 4id = 237033 half-ponce £8 lis 7d = 4118 « 237033 -f- 4118 = 57ff^ J (53) ^..$..ll..l^..lti..20..1(^..l76..616..42 Assu'e 20 Assu'e 21 44.. 164.. 21 44.. ^'^ 1. c. m. = 20 X 21 K 44 = 18480 (54) $6-34 X 419 = $2237-46 = value of fiour $2237'46 X -1125 = 1251-71425 = coi^imission. 252 KEY. (66) [Elhm. AnitUi ^3 cents X 47 = $34-31 = value of barlej. $34-31 ^ 69 = 40f S cents = value of oats per bushel. (56) $4260 X -0125 = $53-125 = insurance. (6T) A = 207 X 4 2= B29 B = 109 X 5 = 545 C = 43 X 5 X 4| = 967i Sum = 23401 $200 X 828 23401 : 828 :: $200 23401 ; 645 :; 23401 : 9671 :: $200 2340i $200 X 545 23401 $200 X 9671 2340^ = $^0-75igH. = $46-57^/«3,. = $82-67|^y (68) 23 at 80 cents = 1840 cents. 19 at 75 cents = 1425 cents. 30 at 40 cents = 1200 cents. ^ at 60 cents = 2520 cents, lbs. in mixtures. 114 worth 6986 cents. 6985 cents ^ 114 = 61^,i^ cents ^ n.,-.. .^ , ,u Szerclse 84.] KEY. (69) 25^ A gets 1 share, B gets 1 share, gets 2 shares, and D gets 4 shares ; therefore they together get 8 times A's share or B's share. $1100 -f. 8 = $137-50 = A's share = B's share. $137-50 X 2 = $275 = C's share. $137-50 + $137-50 + $275 = $550 = D's share. 15 : 25 36 : 48 12 ; 8 6 : 5 12 : 9 (60) ::io:A„s.=ii^'iL^illi^iii^ 3 ^ 5 X 25 X 2 3X3X3 = 9^. THE END.