CIHM Microfiche (l\/lonograplis) ICIVIH Collection de microfiches (monographies) Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques [ [ [ [ [ [ [ [ [ [ r Ci [ Technical and Bibliographic Notes / Notes techniques et bibliographiques iriques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. m Coloured covers/ Couverture de couleur Covers damaged/ Couverture endommag^ Covers restored and/or laminated/ Couverture restauree et/ou pelliculee Du Cover title missing/ titre de couverture manque □ Coloured maps/ Cartes geographiques en couleur □ Co'oured ink (i.e. other than blue or black)/ Encre de couleur (i.e. n D autre que bleue ou noire) Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur Bound with other material/ Relie avec d'autres documents Tight binding may cause shadows or distortion along interior margin/ La reliure serree peut causer de I'ombre ou de la distorsion le long de la marge interieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certaines pages blanches ajouties lors d'une restauration apparaissent dans le texte, mais, lorsque cela etait possible, ces pages n'ont pas ete filmees. Additional comments:/ Commentaires supplementaires; L'Institut a microf ilme le meilleur exemplaire qu'il lui a ete possible de se procurer. Les details de cet exemplaire qui sont peutetre uniques du point de vue bibiiographique, qui peuvent modifier une image reprodulte. ou qui peuvent exiger une modification dans la methode normale de f ilmage sont indiques ci-dessous. □ Coloured pages/ Pages de couleur □ Pages damaged/ Pages endommagees □ Pages restored and/or laminated/ Pages restaurees et/ou pelliculees j 77 Pages discoloured, stained or foxed/ I J Pages decolorees, tachetees ou piquees □ Pages detached/ Pages detachees Showth rough/ Transparence m □ Quality of print varies/ Qualite inegale de Time impression n Continuous pagination/ Pagination continue □ Includes index(es)/ Comprend un (des) index Title on header taken from:/ Le titre de I'en-tite provient: □ Title page of issue/ Page de titre de la I □ Caption of issue/ Titre de depart de la li ivraison vraison I I Masthead/ Generique (periodiques) de la livraison This item is filmed at the reduction ratio checked below/ Ce document est filme au taux de reduction indique ci-dessous. 10X 14X 18X 22 X 7%X X3X I y \ 12X 16X 20X 24 X 7Si ■!? V I The copy filmed here has been reproduced thanke to the generosity of: D.B. Weldon Library University of Western Ontario L'exemplaire filmA fut reproduit grdce A la gAn6rosit6 de: D.B. Weldon Library University of Western Ontario The images appearing here are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Les images suivantes ont it6 reproduites avec te plus grand soin, compte tenu de la condition et de la nettetd de l'exemplaire film6, et en conformity avec les conditions du contrat de filmage. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a i^rinted or ilSustrated impree- sion. or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or Illustrated impres- sion, and ending on the last page with a printed or illustrated impression. Les exemplaires originaux dont la couverture en papier est imprim^e sont filmAs en commandant par le premier plat et en terminant soit par la derniire page qui comporte une empreinte d'impression ou d'illustration, soit par le second plat, salon le cas. Tous les autres exemplaires originaux sont lilmis en commeri^ant par la premiere page qui comporte une empreinte d'impression ou d'illustration et en terminant par la derniire page qui comporte une telle empreinte. The last recorded frame on each micrr>fiche shall contain the symbol — ^ (meariing "CON- TINUED"), or the symbol V (meaning "END"), whichevar applies. Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Un des symboles suivants apparaitra sur la dernidre image de cheque microfiche, S('»>.on le cas: le symbole — •- signifie "A SUIVRE", le symbole V signifie "FIN ". Les cartes, plenches, tableaux, etc., peuvent dtre filmis A des taux de reduction diff^rents. Lorsque le document est trop grand pour etre reproduit en un seul cliche, il est film^ d partir de Tangle sup6rieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images nicessaire. Les diagrammes suivants illustrent la mtthode. 1 2 3 1 2 3 4 5 6 MICROCOPY RESOLUTION VEST CHART (ANSI and ISO TEST CHART No. 2) 1.0 I. 1.25 ■^iiia ti m jao r: 14.0 2.5 2.2 2.0 1.8 1.6 ^ -APPLIED IIVMGE Inc 1653 East Main Street Rochester, New York 14609 USA (716) 482 - 0300 - Phone (716) 288- 5989 - Fox (> ><«• ^I? ^ i '%^ (bJi^iUfiJ, <-^V»^ice of the Minimcr of Ai,'n<>iltute. pri<:fach. This little work is intt'iuluU t<. ai.l tc.-ieluTM in funiisliintr F,,u,-th Classes, iiifluding Entrance Candidates, with |.ractieal exercisu in Arithinotie. In the i)rej>iirati()n of the work, the general plan ..f ProrfinU Pnthlems in AiiflnnHIr has been f()ll..wt;d. If is liojM'd that the method adopted will l(.;id pnpils to deduce results from <,'eneral principles, and, hy so doint,', t<. avoid tin; tendency to mechanical work. Kn.MoNTON, Ontidlo, IS'Jjf. .1. WHITE. I'ROGKILSSIVI-: I'KOHI.HMS -IN- ARITHMETIC J. Fourth Class. Greatest Common Measure. {Indnd'nuj rrevions H'ork. ) I. 1. Resdlvc tlio fallowing uuml)M.'s e;icli into ji n;iir (.f iiite<'r;il fict(.rs: 8 ; 14; la; 21. 2. Find the leust Hnd tlu; gmitti.sfc integral factor (.f tlie follow- ing :— lf)5 ; 455 ; ^>m. .'I Find the prime factors of ."{72. 4. How many boards, each 12 ft. ;{ in., placed end to end,woidd reach as far as 21)4 hoards, eacli KJ ft. 4 in. in length f 5. What is the least and what is tlie greatest niejusme of 744 '{ C. Find a connnpn measure of 24 and 78. 7. If 4 boys in (i days earn $7.20, how many boys ought to work 7 days to earn 818.00^ 8. What prime factors are cojumon to (U* and 273 i i). Find the G.C.M. of 108, 240, an ;l,'ji1. arul 42 gal, ro.spL'ctively, a nu'rcliaiit, uses the lars^'e.sf. possible ineastiii; that will completely empty e;u-li hanel. How much does tlie measui-e hold ? 2. Find the <,aeatest number that will divide ;i«4 and 247, leaving respectively (> and *.) as remainders. 3. A wagon Ix.x 12 feet long and '^ feet wide holds exactly ] cubic yard of gravel. How deep is the box ( 4. A storekeeper, who has two barrels of sugar weighing J80 lb. and .'}()0 lb. respectively, wishes to put up the sugar into parcels all of the same weight. What is the weight of the largest parcel he can use, so that each barrel may give an exact iunul)er of parcels I 5. A person wishes to enclose a field 4(1180 feet long and 2233 feet wide with a straight raihfence 5 rails high. The raits are to be all of the same length, and the longest he can use without cutting. How many rails will he recpiire V " 0. What numl)(!r, taken from stiven billions nine nnllions three hundred and eight thousand and six, will leave a remainder exactly divisible by live times thirty tlutusand and ninety-.seven i 7. If 7 bushels of wheat are worth 10 bu. 2 jtk. of oats, how many bushels of oats are ecpial in value to 12 bu. 2 pk. of wheat '. 8. What is the least mnuber which, taken from 40()(), leaves a remainder of which 5!) is a divisor 'i 9. Find the greatest number tliat will divide 407, 701, and 1043 without leaving any remainder. 10. A wagon loaded with c(»al K' sipiare lots each containing the same number of sipiare rods. Kind the hMi<'th' of each lot in rods. FOURTH CLASS. I 1 i Least Common Multiple. (IndnliiKi Pnrioas IVork.) III. 1. Find ;i inultipiL' ' 7. 2. Find a common nniltii'Ic of .'{ and 8. .*i. A merchant purcliased .'i.S gallons of vine'^ar at 50 ccnt^i a gallon. After addini,' water, 1u' sold it at »»(> cents a «,Mllon, and gained thereby .^4.70. Ilow nuich water did he add i 4. Find the L.C.M. of 24 and 'Ml 5. What is the (I.C.M. of 10211), 1 1057, :'.22;J, and 441 1? (». What ninnber, sul)tracted 42 times from 150085, will leave a remainder of 07 ( 7. I paid §1.80 for apples at the rate of 10 for cents, and sold them at the rate of 8 for 10 cents. Mow nuich did I gain i 8. The prime factors of a certain numl)er are 17, 1'.), .'J, 2, and 7. Find the number. 9. Wliat is the least nunibi-r which, divided by :!, 7, 10 ,.r 14, leaves 2 for remainder in each case f 10. In digging a ciillar 27 feet long and 24 feet wide, a man re- moved 144 cubic yards of earth. Ifow t>:V)!>84 by ninety- nine millions six thousand seven hundred and sixteen ; tl^e smaller nuniber is 7009. NVhat is the larger 1 8 PHOGHKS.SIVE IMtOHI K\f« txr . ., wl.Ht t„„„ Will Lis 1,,.,.„L ;„„,," r •^''"« '«' l'"»l.el» eacl, year, i„ •W mn„,te«, at what rate ,,or hour rel ho.v'lk S"' '""'" ''" " '"'"'' ti.a^i;j'r;i?!.^;r;;;:;t'^;;l;-^-«.o e ,„aoo at the same ;='i s: -: .te = '-=' -:; .s t;&i™,.:s Vulgar Fractions. {Indndhuj Previous Work) V. 2. Ho. ,n.ny quarter-poun.! parcels are there in irj pounds ^ . ♦^- A fanner put 79 1)„ 'i nl- f , ^'4 i»<>'intl,s / ■nto the hu-Ko.st ,„. iV,io «; . t-,;':'tr,;';'''f" '"'■ ■ >'"<■ ••< f'-"- fruit separate. How u,.uy harrcl ''i;! h^S; ?""'""« '•■"^'' k"'-' "« How uilTpi'c^Nvte'rhSeT" ""' """ "''■""'"'^ "f J "f " f-t each. 5. Ill ;in orcliard there w^ro '^9 ,. c . trees, and each tree yiildl'l 4 hu iT ' *'''f '' ''"'^' ^•-^' ^'-^ 40 wan put into barrels, iach hold "; o ^'^ "^ ^'^'^ \ ^^^^ ^v^i•<>Ie crop >y]iat WHS t.he price per barrej ° " ^ ^'''•' ^"'•'- ^^^^^ ^'^^ |,'W i'i FOURTH CLASS. oiiy 1 Pi^. each. \\ hat « the v„i„„ of th,'. wh.,.. .um ' "'.t; r,';. ;;'„;i,!;,"; n.ain,l„r i.s 20». What L the llh-l'l.'? '""""-"" '" "™' ■"'-' '1'- - 10. H,nv ,„a„y .si,xt„e„ths „f h„ a,,,l„ ,.re there in g „f ,,„ appk ? 11. Express f in twenty-fourths. 30 ce„t.s a b„.she,. ■M:;:"::4;Y;s'r,i-, ■;,^7;,',;;r »' «- -ti. „f VI. 1. I{«l„ce ;:■';! ,m,l \i;,l; t„ t|„.i, |,„„..,, ,,,,.„,^ 2. VVhiel, i.s t!,e greatest, and which the least of ,', J ,, , cost 'of'ISet,",;';:!/,,^ I'i;: ;" ''■■''^"■^' *"*-■*'• »'''^ »'i""l- the of atr.!l'fh;:t":Jr,::t!,;e.fir'Hd;! ■' "'T'"- ""■ '--^ • -• Bq. rd., or 1280 s,,. r S Wh^f c<"i■-«"- l.-i"« 8 for appLTl'dT */ "' "■' """'"■ ■' - J -"' H-y ^ M.nv ,„a„y ^<.y tal^ln^r^ --^i;ji;;;*;»,;.f P..^t<.s in a„ ,.,„r. a sec , '■"" bushels can^ the thL'V.y: dig i,;'o;Lrr' '""""'"■• """' ""^"y 10 iM{ooRi:.ssrvi.: promlkmh i\ aimthmktk- .10. Make out the fol]nsv\w^ ],ill .- 48fM) ,,.iil.s at f^r '>:, .,..,• C • 'i9HA •neks at .1^;].5() per (^ ; 2;JH(, foot of h.n.lH... at".Sl7 " IVT '• i'J > n..ls ..f pork at i^(;.25 pur cwt.; JKUi^ poun.ls of hraJ It W:^ hri 1 ton niou. tlun tl.u first, a,..! u tlnrd i.i.in earncl as n.i.rl, us tin- first and .socon.l to,^.ether. ihnv ...any dollurs ,li,l all ..an, ' of the'i.l pj; hush.^^- ""'^ ^"^"' •'" '^'^ '^^'•^' ^^'-^ -- ^'- value VII. I. Thv (liffV-iOMce in wc-ii^lit hc'tweon two pj.r.s is l-' cwt aiHl H.o lii^htor p,. weighs 2- cwt. Wl.at is the weight J;}!;;,^; J" fn. Il ^i/'""'";^''" 'r:"^'''^ -^: '»'>«''^'I^ "f ^vlu-at at the rate of 2 hu 2 ,,k :$. A wr.nKiM lM,„^s jmpers at tlu. rate ..f 7 for ;', cents, and soils the... at t .0 .•ute of .. for 8 ee..f.s. Ff he sells 14 papei.s every .lay what p.-oht does he make ill Txjays^ ^'> "''y> 11. ()..o-half the s.in, of two .iuii,l,ers is :;:;(►, .u.d o„e-fou>lh their (lltterenee is 2t. Iniiil the inuidu'rs. 12. Make out the followiiiL; hill in proper f(.riii : 22 1).,. 12 11). of h.irh.y Ki «. 17 .. ....... ^ 12 " U " l.'i " 7 " (i " 8 '' 7 " at ")(» cents per hiisluil 15 28 14 20 12 12 15 < I. o;its h k :;() wheat (4 84 coi-.i fc b 44 i-ye U 72 I»eas n 54 hack wheat ( t 5»; timothy seed ''$1 .<;o clover seed -^5 .(50 vm. 1. One uian has ah.tof | of an acre, and another has one of ' of iUi acre. I low nmcli is the first lot la.-^rer than the second I 2 A fai-nier had 'i .,f a t..i. of hay and [....i-hf • of a ton ; he then sold l; of H ton ; how much had he left / a What will he the cost of 500 pieces of scantlin- (;ach 20 ft 4. How much must he added to ^'j' to make .'7* ? 1 , '?■. \T'\ Zl']' ^'''''^ ' ^^ ■■^'■'"'' "^ ^'"^'^ -^"^^^ <»'^ "'^'•^■■^- How n.uch lanu nad lie Jett « «. A woman bought a numhei- of hens and chickens for S.'J2 nav- n.g three times as much for a hen as for a chicken. There 'were live times as many chickens as hens, and the hens cost her (50 cents CHcli. How many of each did she huy ^ 7. Tvvo nie.i ea,-ned $45,'v in a week. If one man earned $1(U ' how much did the other earn i ^^ 8. Thi-ee ...en owned Vi of a mill ; the first man owned A, and the second owned i ; how much di.l the thi.-d man 7;J(» ; one of the num- bers IS .]b<8, and another is 278. What is the third number i 10. Vvnm a piece of ciol h (..ntaini.iir 25 vai-.ls, 4^ yards wore sf,ld uZiar"'"'" ^ '^ ^''"'^' ^" '"'"*^'"'- ""'' """»y y'"'? 11 1 M Tl. r t tl.«.-el,y «Hia (i8 cent, „„ th. ^\Xf " """""• '""1 tahfi,.;!!;:]',:?':'!:',:,'::.';'""^- "^ '-"-".^ -.• •< i-i.- t^ck «ii, „„„. for a ?*^'» '" *^''' ''"' "'■"' "■''••" '".V »"" --'• »"« .uuch ,li,l I |„,y I!. Fifty l)ll^'.s, <'.liOl li..l,|ii|., 2 liri •' ,,l- I „..I ,'ii , 7. What .sun, tuku.i fi-,„„ .«<| IH 7, ,,.||| |,,.,,,,^ ,,|(HI ' ' •J- If 4 Mien e;in do us iiiucli work- in •> ,^■t^r ..^ <» i i Tom',,!!" wmM^?^ ''^' ''''"", '"rlf ^' i' ^ ^^'" S'-'™ T"". m;i. and orlw,,'i:f:,lZ';n5l!^''7;;:;';;;-^;;.;;5;«'<'2«2.a„d t,. product X. tl. thir HAmto huliisfcpen^ol,tmt<,rlu..secoua;.t„,l i of it int., the ml VVliat part of lus flock did he put into tho fourth pe? poiTiiTi! rr.ASi^. 13 2. As lot is 'i oj an m'vo l.ii-cr fliai, ]\\ hut only .', ..f h.i aero larger than C s ll.nv much is I'.s smaUcr than C'n / " .'{.Two |.oiv)us startf.l fn.in the same place an.I travelk-a in opposite .hreet .h ; at the viu\ of on,. h..iir they wen; 7 mi "HO id apart; had they traveUe.l i„ die siuik; .liicction tor one hour, thev wouki have been 1 mi. 4(» rd. apart. Mow far did each travel por 4 Smith's farm contains 17}? acres more than Jones', but S'i acres less than IJrmvn s, which contains KMI^ acres. How many acres are m the three farms I 5. Three bins contained IH^-'^ bushels of wheat. The tirstand second together contained 2()4:|! busiiels, and the second and third t..gether contained 20<),'„ bushels. Mow many bushels were in each 0. What number nudtiplied by 7, the product increased by U the sum divided by 7, an1 f J galh.ns. Wnat was the capacity of the sec.»nd can ? 11. A grocer paid .'JO cents per pound for butter, and sold it at M cents a pound. Mow much did he lose on every doUar he paid 'i 12. The sum of three fractions is 2=} ; the first is 5, and the second IS >^ greater than the hrst. What is the third i XL 1. How much nnist I add to the difTerence between \}, and I to give a result ecpial to the sum of I and | / 2. The quotient of two numbers is 1805, and one-seventh of the less number is I001> ; what is the gn-ater < 3 A andB start from the same place and travel in the same d„.ect.,on. ( n the first day, A goes 27^ miles, and B .{2^ nnles; on the second day, A goes 31^ miles, and B 2O5 miles. Mow far are they apart then 'i 14 PUOfiUKSHIVR PHOIJI.KMS IN AIMTHMKTIC. 5 A vill.yo l.,t lb r<».iH l.m- uii.l ;M) foot vvi.lo w.is fc-McT.! with 2? ] 1 1^^'!',;',} V.'I'", ''T' /;'"^*i""/l'«*. ■""»• 'j- '"M"l I., the «„,„ of -«5/;, iJH' 'm«i i>7 to luuko tlio result an mto^'or ? vJu,'\ '^"'^'^',1 t''V'''""".,*^'""'"^'""" ('''i.tuiinMl .SO()l„.Hr(l feet h!^^yi '"'"" " '"'■'"' ^"'^^' '^'"^ •' '"^'"^■•'^ ^'''^'^^- ^^''-r ^vas the «..,,?/./'""; IV'"«V'^. ^•'•«t .«!127<;:{. Tlio first est $21401 the secon.l vvu.it (iKi the fourth co.st ( ov-^w^i. Jj. If 21 l,u. a pk. ..f oats ost .«2.{)r) more than 14 hu 1 ,.k 1 gal., how much would ICK) bu.shels cost ^ ^ 10. A woman spent $.'{.12 huyin-r e.^u.-il .nmntities of te-i and •sugar ; for the tea she paid 45 cents per potni. , and ^. ^8,1^7 cents per pound. H<.w nn.clylid shL spend on tea ? ^ ^ f<>r2^nI'^^,T^T^T^ ""A " '^ ^I*'- ''^'^""^ ^'"1"^ «^<^'""»«e •1 111,'- ' ''^- "^ '""''•i^«es ; h<.w many traUons, etc of coal oil should she receive for (; gal. 1 .|t. of nudas^^e^ / ' 12. What will he the cost of carpeting a room 21 ft. Ion- and KJ ft. 4 ,n. w.de, w.th carpet 2 ft. 4 in. wide, at (m cents per y.-u-dV XII. 1. Find the value of 25 pounds of tea at $^\ per lb. Srf 'of^th!?wr^ 1 ' '""'i ^ r.V'\"'^^^ ^''^'^ '^^'^y 5 of what he had. What part ot the whole cake did he give away I 3. Wy selling a farm at J?75 per acre, the owner rrained $Vi'>0 ";1 1;: -V'ti:: S,iT- "^'■"' "•" ""'"" ""^^ ■"^' *"«" "- "-y part ;/th':f ",.,:i;;:r.:e"il f' " " "^"' ""''• • -^ "- »"-•"• ^^'■'" 6. Wliiit ,,art<.t a ,l„ll,ii- will a i)ouml,,„f boof est, at «,\ ,,or lb. ? (i. It cost S22.40 to cavpet a room 17 ft. hi. by 10 ft fi in w.th carpet 21 „,. ,vi.l„. What did the carput cost pi yanl^ ' Hor^,^,cf ShrS,:!.!,';;;":;;!?,! r*""'^- '''""' '« -"'« '- '"• 8. How much must ho added to ? of J to make thu sum of | and J? KOI ; inn cLASi.s. 15 I U. I'l'IlH WnlMl r>0 ffllts |H!1- ImIsIu'I, .Itlll ...ifs WOltll .{() CflltM JJOf IhihIicI well' mi\r.l in ciiual <|ii;iiititiis ; iio l.usliols of the mixtiin' Wi-n- cxcliJiiiLjtMl foiwlic'it uml l.uilfy in i<|iihI <|ii;nif it ii-s fit Ta rt'iit.s and 45 ocM.tH |Ki- Inishfl reH[)t'ctiv. ly. ||.,w nii.ny ImisIk-Is of ijuh kind of !j;r!iin wcro lucuivod f HI k 1 10. A l»oy h.is 4,\ pounds of oandiua ; wluit is tlio loust (juiinfity Hi nnist, Ituy so i?* to huvo nn exHct nuiiihur of pounds i 11. A ni;in l)oui,dit .'U l.u. 1 pk. of Lnrlrv, .ind sold it for 815, guMuni; J:i!2.5()on the whoh- (pi.-mtity. Whjit did the l.uHey eost hini pur hushul { 12. I houLcht U'i yjirds of tweed at «)2.\ cents j.er yard, und 24! yanls of cotton at lOJ, cents a yard. Ho\v"iniu;h n»ore\lid the tweed cost inu th.m tlie cotton / XIII. 1. How nnieli is 4 times s of .'i5 i 2. I'lie seed for a fiehl of the z acconipjinying shape and size cost 2 I.S4.20 when wheat was worth (iO :": cents per bushel. How many l»ushels were sown to tlie acre ? '0 nxlH. s. r>!M-;• twenty-eii,dit times, 4. A woman paid .^.'^.72;! for a pound of tea and PJ'^f yards of flannel. If the flannel cost her 24.1 cents a yard, what dur.she pay for the tea :' 5. It recpiired i;]20 feet of lumber to build a ti^dit board fence around a lot 24 yards long and 10 yards wide. What hei.dit was the fence i ° 0. One-iifth. of a certain number is 14ji. N\ hat is the number / 7. A man .sold 7] bushels of wheat at §!2.', ])er bushel and 02 tons of hay at $?8-J per ton. He paid a debt of >^h{i':l (,ut of the nujiiey he received, }I<.w many dollars had he left i 8. It co.sts 811). 14 to cover a room 10 ft. (J in. scpiare, with carpet at 58 cents per yard. What width is the carpet i 9. What number added to 4 times ;] of 25 will make 100 ? 10, If 4 tons of h.-.y 1m. vvortli ,'30 bu.shels of wlioat, and 20 bu.shels of wheat worth 5 pigs, how many tons of hay can be bou^dit for the price of ()0 pigs ? in PHOriKKsSlVK I'llOMLEMS IN AltlTIlMKTiO. -A yHi.lH to u„ ,„,,a„n, .{j^'yanls t«. anntluM-, un,l L>.'. vanls t., u Ihini l~ A Cisdrii is It tec- iii'iiiy .idditiujial cuWic ft. long, ft. wi**«, rtiul I ftwr. witlo, jukI 7 foot (loep. How -Hi'tli iiiuU |j«. rum.)vc'tl to iimko it 7 XIV. 1 . A PyrHou !. ..fiijht 10^ hushols of chrrriuH, at $1 j.er l.ushel and Imd ^t 3 left. U..*, ,„<.nv .lollars ha<> H>- -f luty at $7 a ton, and (]817 Ih. of poiK wjj was the pork vahied at per II). / 7. A goes :ij-^ n.iles and It 2Jj;| miles each day. If thev trivel in oppoMito clnoctions for :q days, how many nxiles'^^vil! . he^'bl ajivrt" -^ggt ^^ *' '^"'''" "'^'^^ '''"'^'^^ ^"^ ''"""'-'"' '"^^^<^ '^ ^^»« ^^igl^t "f one in./lot!i'esl^f'7ir9"'r^ V''"'^' ''^ '^''"'•*^'^««' ^^^^^^ l"^^*i contain- in 10 boxes of 1 bu. 2 pk. each, at 30 cents a bushel, for 10 boxes oUea, at 45 cents a pound. How many pounds of teL were in e.S' nu^a^t.^r '"'*"^ 'l*'?" ^^=8' ^^ ^2i cents a dozen will pay for 3? qu/irts of vniegar at 20 cents a (juart i ^^ * n>^ ul-'^^f' "''f r'^''l^ ^^'^^ "^■' ^'^ C'-^rried 5 miles by rail- 12. Harriet has JR"^ wii'r.>> i - ■■• ' • , Jane '^ " '"' '""^'^ "'^'^ ''''"'' ' ^'"^ '""^^^^ has ^. FOiruTii CLAMS. 17 >« XV. Imve 20 lb. ? ' ''"^^ '"""^^ 1 "•'"^ '""■^^ »'- y<^': bu ,• ho hh to 2fi4ii;)il":?S^^i,;;"«'^j^--^^^^ -if «f-f high i.niK..i wim. ^. If i of „ farm est «{HK), wlutt will ;] of it cost i 4. Divi«lu^ of 21.1 hy || of (i, J ij •. 1. niiiwjiy, tho «li8tHiK:o Ijoihj,' 21 iiiiio.s ' 6. if « |.«u,.,i.s „f „ugH.- c,«t $u. 1...W ,„„ch »m a p.„„„,„ „„, , perVard 5 ''"'' *'"" ^"' ^ "' " ^'"■'' "' •=■""'■ "'"'t Pric„ i, the cloth 8. VVhun butter whs 4 cents dtmror Mi... ..i 10. One luuulred is f of whut number / 11. What will be the cost of carpntin- a room ^i f. i..„ ft. ni. wide, witb carpet 28 inchJ. wide • t #« '"( . '. ^'. '"r'^ /*' strips run across the room, and ind cs' jt tHn'be '.'ll ' ' ''' waste 111 matchin<' ' ^ 'i^ ''^ allowed for O * XVI. 1. Ho„ many times must n bo :M.-d to j-ivo l.'ilit for „,„„, ,r5.25 ,„.. M, wh'at, was the i:ngth''ome";!:i',i.„'f,/;;r,ir;"'^"- "'"^ 18 PROGRESSIVE PROBLEMS IN ARITHMETIC. I 1 t r 5. How many s(]uare yards of plasterin<^ are there in the walls and ceilins,' of a ro in. l(jnu;, 12 ft. wide, and 9 ft. high, no allowance being made for windows and doors? (>. A man piit llli gallon.s of water into a barrel of vinegar con- taining 45^ gallons, i)nt 4^ gallons leaked out afterwards. VV^iat is the value of the remainder at 70 cents per gallon ! 7. 1 bought a sheep for $(),^'j and a pig for $^^ less than the sheep ; I sold both for ^2 more than they cost. How much did I get for them '( 8. If a carpenter spends in days what he earns in 4 days, how mudi can he save in a year of 3<»5 days, supi>o8ing he earns ^IJ in 2 days ? 9. Smith owns {^tr of a certain property, and .lones owns | more than Smith. If what both own is valued at $^10400, what is the value of the whole i^roperty '( 10. Harry bought ^- of a yard of Hannel at $j\ per yard, and 2f yards of silk at $^ i)er yard. How much less than f li did he pay for both ? 11 A farm containing 351 acres was divided among 5 sons and 3 daughters ; each son got 10 ac. 32 s(\. rd. more than each daughter ; how much land did each son and each daughter get ? 12. A man who owns ^ of a mill sells f of his share for ^2340 ; how much is the renuiinder of what ho owns worth ? XVII. 1. What will be the total cost of the following : 2| tons of bran at $12.| ])er ton ; 4.^ cords of wood at $4i1 per cord ; 3'7* yards of cotton at 8| cents a yd. ; 2.^ pounds of coffee at 272 t^tsn^ts a lb. 2. I divided apiece of land 32 rods long and 120 yards wide into lots, each 132 feet long and 00 feet wide, and sold' all for ^4(K)0. How much did 1 get for each lot 1 3. How many pounds of sugar worth fy'g per pound must be given for 1()!| i)ounds of butter worth $J^ per pound ? 4. Tom, Will, and Henry bought a foot-ball for $3.50. Will paid 25 cents more than Tom, and Henry [)aid as much as the other two. How much did each pay ? 5. H f of a cord of wood cost ^3, how much would one cord cost? How much wouhl a pile of cordwootj 32 feet long and 6 feet high cost? FOURTH CLASS. 19 I How luiiny men wore .sick ? ^ *^ ^"^ ^^''*^^'- Lt !>«■ per yard ( * """"' '""' '"""»'• '>'''^" '"^ 'L- cloth 11. A hoy is 14 years of aire, niul his sisfPi- ;« •? ,. t , ..-ny yoars wll tlu, l,.,y« age lie twice tSS hisLC™' '" '"™ la lf7i cords of wood cost $33, how much less will 65 cord, cost ? xvm. a storokt^er'r^e'ir/'^xd.'lrrforT'' '^ f '"'^ T >'""»" »'"'"" coats per M). ; cxcliaiijre for 30 pounds of butter worth 14 2. What fraction divided by J of J of oj ,,„ ^-^^ ^ ,„^ ^^^,^.^,__^, inchp,a,:;:*wf:;^;,:;;-^i:t:bi;e:i:;iV;?^t 7. Divide2|-Uby| + |oflf. length of the j.^uniey / ""'"'' ^'^ •'^*^'^*^- ^^'"^^ ''^' ^^^e {^. ^ f'<''">»(»(» i^\..fi ix ^ , less thun for the second bnf ini . ''1 ^'''"^ '"' ^'^'^'^''^ed S?ir, much did he get LrS ? mc,re thuu for the third. How 20 PIIOOIIESSIVE PROHLEMS IN ARITHMETIC. 10. To wliat number must you add | of itself and f of itself to make 14<5 { 11. Two tubs of butter Aveigh together 51^ | lb., and one of them is 3|-^ lb. heavier than the otlier. What is the weight of each ? 12. Find the cost of ])lastering tlie four walls of a room 17 ft. 4 in. long, 14 ft. 2 in. wide, and 10 ft. high, at 20 cents per square yard. I XIX. 1. A person bought 7h 1^'- <>f tea at 37 ^^ cents per lb. and sold it so as to gain 501 cents on the lot. At what pi'ice per pound did he sell it ? 2. A man owns ^ of an acre, and | of this is 41 times what his neighbor owns. How much land does his neighbor own '( 3. I was charged $1 for 2 lb. of tea and 5 lb. of sugar. If T had purchased 1 11). of each, 1 would have been charged 41 cents. What was the price of each per lb.;' 4. I of 16 acres is .j\ of what land a man owns ; how many acres does he own ? 5. A man earns $18^ a month and spends $3J of it. How long will it take him to save $185^ I 6. A farmer pk)ughs a fuiTow 8 inches wide the whole length of a field in 5 minutes, and it takes him 7 hr 30 min. to phjugh 2 ridges. How wide is each ridge '( 7. Of what number is 2| the ^th part? 8. How nmch will it cost to plaster the w'alls and ceiling of a room 13 ft. 6 in. long, 10 ft. in. wide, and 9 ft. high, at 30 cents per s(piare yard, deducting 13| scpiare yards for windows and doors ? 9. If 1 sell a lot of '^ of an acre for f 50, what is the value of 50 acres ? 10. Three bags of wheat contain 9 bushels ; the second contains 1 bu. 1 pk more than the first, but only 1 bu. more than the third. What is the value of each bag at 80 cents per bushel ? 11. A owned i^ of a farm of 210 acres. He sold ^ of what he owned to H, who sold h of what he bought to C. What is the value of (Ts land at ^40 per acre ? 12. X man who had |^ of a cord of wood, worth $4| per cord, gave f of the wood for hens at $.\^ each. How many hens did he got y Fourth class. 21 XX. 1. How mucli is ^ of 3 tons 105 11). 4 oz. ? for n4nh" T" P^/'::/:^ ^''^ '""^ '•' '•"• l P'^- ' K-I. of l,arU.y b:rle;^;:;t,t/T' '"' ^■^'■^l-^'-'^- ^Vhat wus the vnluo of tl.c^ «»ll^' 'h''^''''''''''^:i'^^'"'''*".^''iM>onsattherate(.f r>f.^^ ..n.l l.v 5 '4 of 8,« 4 0' 1.,. "J. "i O,'- "». A piece of hwi.l 1 mile s.p.ure u-us divi.led int..4(K) o(iuh1 lofv, How lUHiiy acres were in 20 <,f tlie l..ts ^ ' <>. Two cisterns contained tost he added to ^ cwt. to make I ton ? room n ff'-r'" !'" ^''« ^-■'^^' '.'f Pnii.tin^^r tin- walls and ceilin.. of a lo m U ft. .i Ml. l,.njr, <} ft. 4 in. wide, and 10 ft. (; j,, hj.d, at '{ etnts per s(iuare yard / ni^fi, at .>(> J). H(nv many .yards taken from ,«, rd. will leave •' vrl for remanider ? '' ie.ive y ya. tor hal/' Viiir^ """•' ''"'' "f •'"''»'•< ■"••"■l.le.,, n,.,I Nf,I w„„ the other wn„i„i H ",'"",".'"■■ ""■"y '""" •■'« "■"• Ned Imd 12. After 12. Find the smn of Z rd., ? vd and ' in ..., i answer in yards, feet, and inches^ ^ ^ ' '"^'^ "'^'"^'"''^ ^'^"^ XXI 3. Reduce H i of (3^ - i of f ) of li - ] to its simplest f<.rm. 4 By selling cloth at 92 cents a yard, I gained ,^ of the cost Find my gam on two webs of 50] yards each. S2 Progressive problems in arithmetic. 5. A j^rocer pfvid !j?84() for a (juantity of ica, and sold part of it for $14, at 50 cents per ])ound, by which price he gained $5.60 on what he sold. How many pounds did he buy ? 6. Multiply 59 bu. 3 pk. 1 gal. 1 (it. by I. 7. After ])aying his expenses with ^ of his earnings, a workman saved $<) in Ofl days. What wages did he get per day ? 8. A boy had a journey of 15 mi. 187 rd. 5 yd. to go ; he walked 3 mi. 6 rd. 1 yd. the first liour, and 2 mi. 80 rd. the second hour ; his average j)ace of walking per hour during the rest of the journey was 2 mi. 20 rd. 3 yd. How long was he on the journey ? 9. Divide 41 tons 1 cwt. 37 lb. l)y } l- 10. How many times can a measure which holds 4 of a gallon })e filled from v| of a barrel of coal oil containing 47h galhms '( « 11. A butcher bought 4 cattle, weighing together 4300 lb. at 4 cents per lb. ; the first weighed 50 lb. less than the second, but 100 lb. more than the t/liird, which weighed 150 lb. less than the fourth. What did he pay for each '^ 12. Divide 110 mi. 290 rd. 2 yd. 1 ft. by I23. XXII. 1. What is the least fraction that must be taken from 62 to leave a remainder exactly divisible by 4| ? 2. What is the price of pork per lb. when my butcher charges me 92 cents for 6 lb. of beef and 4 lb. of pork, the latter being 2 cents per lb. cheaper than the former ? 3. A boy can hoe a row of potatoes in ^ of 1 hr. 7 min. 12 sec. ; how much can he earn in f of 17 hr. 38 min. 24 sec, at 10 cents a row? 4. A farmer employed 11 men 36 days to drain his farm. After they had worked KJ days, he concluded to have the remainder finished in 11 days. How many additional men must he employ ? 5. What quantity nnist be added to ^ of 2 tons 3 cwt. 2 lb. to make the sum of 'l of 2 tons 15 cwt. 85 lb. and I of 12 cwt. ()4 lb ? (). In the forenoon, a boy lost 4 out of every 7 of his marbles ; in the afternoon, he lost 5 out of every 9 of the remainder, and had 20 marbles left. How many marbles had he in the morning? 7. A grocer mixyu 30 lb. of tea at 50 cents a pound with some cheaper tea. and sold the mixture for $22.50, at 45 cents a pound, gaining $1.50 on his outlay. How much did the cheaper tea cost him per pound ? FOURTH CLASS. 23 4 T » ui y or ^4„ - j^ ot U) to its simplest form. fT, ^"^^'/^.f '' ^''"^' '^^''''^' ^■'^ ^ full, u person pumps :{r,().rall„„s umi then h„ds that it is ^ full. How many gallons f >'""<;«, weighing respectively (I cwt. 17 U). and I K !: ' ;; '^'"'' ''"^'''"'^ ^''•*"' '^''•^•'•"t" ^'^ ^^amonton l>y the C I> the other. Mow much did the carriage cost per cwt. 'i 11. Fmm the sum of ^ of 4 s days of 8 hours each / 1». What fraction of 1^8 is j of a cent ? at ^^Irli lb ^ - t ^^^;r'^"V" ''"'^ ^^ 1«^ • 4i lb. of coffee --"• -x •; ' ■• '."4 ">•"! ^2cc at 4 cenw pc-r ii.., i2* il) of suwirat 6 c:n : z b ' si b "f ''' '' 'f ''"^'^^ "'•' ^^ ^- ''^ ^^^-- ^' f>L u iP^ ' ^? ^^- ""^ currants at 4§ cents per lb. Make out the bill in proper form, and show to whom the balance is due 54 1'U(k;kI':ssivk problkms in arithmktk'. 11. A looin 15 ft. \) in. Ion*,', ft. 4 in. wide, .-ind 9 ft. \) in. lii^^li, liiw a (l(M>r 7 ft. 7 in. by .'{ ft., a window 5 ft. hy 4 ft., and a skirt- ing-hoard 9 in. higli ; alhtwing for the area of the window, door, and skirting-board, wliat will he the cost of jilastering it, at 28 cents l>er s(juai'e yard ? 12. In tisliing f»tr tront, a hoy lost | of his line ; he then added 11 fe(!t and found the line was ^ of tlie original length. What was the length at tirst { XXIV. I! . ill 1. 1 j)aid ^95.92 for the following: 1944 11). of harley at 44 cents per hushel, 2r)()() Ih. of coal at $(\ per ton, 3rAH) Ih. of hran at ^12 ])er ton, and a iiiniiher " the lot did he sell ? ',K When oais W(M"e wvrth 34 cents per bushel, a man fed 20 bushels to 3 horses in 4 weeks ; the first horse got 7 lb., and the second (J lb. for every 4 lb. fed to the third. What was the cost of (»ats for each horse per week ( 4. Thomas bought marbles at the rate of 5 ior 3 cents. After losing 3 out of every 5 one day, and (5 out of every 10 of the remain- der the next day, he had 28 marbles left. How much money did he spend in buying the marbles ? 5. A fence feet high casts a shadow 4 feet, and at the same time a tree standing beside the fence casts a shadow 5(5 feet. What height is the tree ? (J. A person exchanged 2| yd. of cloth worth 37^ cents a yard and ^ lb. of tea for 2^ lb. of butter worth ICrh cents a pound and ,",Y gal. of molasses worth 90 cents a gallon. What was the value of the tea per ])ound ? 7. I divided 200 apples among 7 girls and 6 hoys, giving to each girl twice as many as to each boy. How many did each get ? 8. By selling hats at 90 cents each, a merchant clears J of the cost price ; he then raises the price to 99 cents each. How much does he clear on every $27 of outlay by the latter price I 9. At 26 cents per square yard, it cost $14.82 to plaster the walls of a room 15 ft. long and 12 ft. wide. Find the height of the room. 10. A brick wail is 20 yd. long, 15 ft. high, and 3 ft. thick ; each brick is 9 in. long, 4h in. wide, and 2h in. thick. No allowance being made for mortar, how much did the bricks cost at $8 per M ? ii^Ot'KTH CLASS. 11. Divide 'i .,f 4 mi. 20 id. l> yd. l,y ,-, „f | 2.'5 mi. 127 r«l. t.aN.lIed 1 1] nules. H„w .n.my acres we,v ,n the field V ' XXV. s IS Q 4 11,.. '" '""--'»nn cue tune shar^ .iri'?f l>'^ ''' ^'''^r^y ^»at,aiul .'>. Heduce 8 chains to the fraction of 120 rd t\ iv each ho't, ;:•;,;; ;;:':•, """' '""">■ i""""'» -"i •■— --■« f^i *<> 9. A vvonian .sold y '^ ft., and tw<» windows, u.-ich <> ft. by 4 ft. PIstiiMJitinj^ ;i l)undlo of lath to cover 5 .s(i. yd., how many bundles will bo ru(]iiirod for the walls of the ro(»m ? 4. For 23 cords of wood at ^i a cord and 2? bushels of oatf^ at $,^ per bushel, a man receiveil in exciiange 4;i^ yards of cloth at $2f per yard and 2i pounds of tea. What was the value of the tea per pound { 5. .James can run around a circu! ir racecourse in 10 minutes, and John in Jo minutes. If both start from the same place at the same time, and run around it in opposite directions, in what time will they meet? (5, Five-sixths of a certain number exceeds I of the nmuber by 124. Find the nund»er. 7. If 8 men, working 10 hours a day, cut 48 acres of g! dn in 2 days, how many days \V(»uld it take ',i xiuni, working 8 lujurs a day, to cut 'M acres '( 8. For a load of hay which was weighed on scales that gave oidy l!h">0 lb. t,o the ton, a man received .^7.20. How much money was the buyer cheated ? 9. A lot IV.) ft. long contains H) s(piare rods of land ; the entire lot is covered with cord wood piled 4 feet in height. What is the value of the wood at ^tJ.20 per cord '( 10. Express 24- 2f of 1| of '3^+2^^2} - f hi its simplest form. 11. For a quantity of tea at 04 cents per lb., coffee at 32 cents per 11)., and sugar at 8 cents per lb., a grocer received §?12.80 ; there were three times as many jjounds oi coffee as tea, and four times as many pounds of sugar as coffee. How many pounds of each did he sell ? 12. A fence ^ of a mile 'ong cost $50 less than if it had been | of a mile in length. How nnich did the fence cost '( XXVII. -^ 1. How many s(piaro inches of papernvould cover the surface of a cubic yard ? 2. The difference in weight between two parcels of sugar is ;| of the weight of the lighter }>arcel, and both together weigh 9| lb. What is the weight of each ^ 3. A farmer had enough hay to last 10 cows weeks ; at the end of 2 weeks he sold some of the cows, and the hay lasted 7 weeks. How many cows did he sell ? frOUKTII Cf.ASS. 57 9| lb. 4. .I;u.,es IJrown sul.l t„ Tl.n.u.is Smith ll... fnllouinir nrtic-lps t<. Hpply on an <»ver(liiii iiooiint of $;-)(>; ^772 i|, ,,f |,:,.|..,, .,. -.,, ^r'^i i^r ':•' ';"' l^;' ^'^'^^ '^^ '- -'"^^ -• »>"•, i.i ti'^^f 'l :k .it ;^(,.J., per ewt., 48!) ^..s at Ki cents a .lo.en. Maku n.iles of nmntrv JJ;TJ'mr:!;;;;r r''"^ '' ^"^^ ""^'^ ^^-^'^ -^''---^ '^ ^-^ --^ -- ,.n '^* ■) p"/^!? '' '^i'*'^' "' -^^ '^'^>''^' '""' ^^ i" '^^^ ' ''-^ until th^ meet^U^. pint of the ditch does each man .11^ V 10. Fron, a b(,ard containin.4 !> board feet, a piece 4 feet in lencrfh WHS cut off, and the board then contained V, i,oald Lt Vlu t ^ s the length and breadth of the board at first / 1«V/ '^-f 'l""f^f ;f '' »•""[' ^«^ch side of which is .'{2 ft. long and wide, t uid the nund)er of sliiu'des 12. By selling a certain number of papers, a newsboy gained '>0 nil t,!:;:;lM:":;ia t"' """^^•"- " '^" "■" '--'^'- XXVIII. . 1. A boy can dig a bushel of potatoes in \ of an hour, and can pick ?0 bu f " '"""'"" '" '"" ^""'>' '''""•'^ -" ^- <"« -»^ • \ Four sections on a railway are (J mi. 140 rd 2 vd 1 ft d 5 mi. 318 nl 2 yd. 1 ft. o in. respectively. It takes a train 1 ' hour r '' ' ^"'■''' '*'''''' '"'• ^^''"'^ '"'' ^^'' '"'^'^ "^ ^''^ ^^'*"" per 3. When measured wich a yard measure that is l of an inch too true iengthT ''^'^'''''' ''* '°"^^"' ^^^ ^^'*^'- ^^'^^^^ ^« '^^ 98 PROGUKSSIVE PKOnLKMS fN AUITIlMETIf. •iii ■ 4. Allowin}^ tlu! Hliilliiiif to l»c wortli 24.', cunts, what will he tho amount of tlio following in (/uniKlijin in<»ney : .'{(> tons of boiler |)|jiti!s at 1*15 14h. (>(1. jua-.toii, 10 tons of holts at X*.> 12h. jkt ton, J(M> tons of stuol rails at i'14 Ms. (id. per ton, 2H tons of l>ar iron at 4'12 78. j)or ton i 5. What qnantity addedfl times to 02 tons 140.*nh. 14 o/. will give KM) tons for result { (J. Six hoys eni(a<^o to hoe a field <»f potatoes in days ; after workin*,' 2 days, 4 of the hoys leave. In what time will the field he hoean hou. A can do a work in 40 minutes, 11 in 1 hour, and C in 2 houj-s. in what time will ,ill tln-ee do it if tlu^y work toujether ? 10. Divide 20<) mai'hles anioii^' danms, Harry, and Th<»mas, so that .lames shall get 20 less than Harry, and 4 times as many as Thomas. 11. What will it cost to fence a S(piare tield '.Ui) links on each side, at Jji?! for 1 yd. I ft. ? 12. The difference l)etween two fractions is ,\ of the laryer fraction, and the sum of the fractions is 1,''^. Find the prt)duct (jf the fractions. Decimals. {Tnclmliuij Frevlous Worl:.) XXIX. 1. How many tentlis are in \ 'i 2. How many hundredths are in | ? 3. Exi)ross ^ |y as a decimal. 4. When ])eas are 15 cents per })ushel dearer than oats, a man receives 81!).20 for 20 hu.shels of |)eas and 10 bushels of oats. Find the price of .'iO bushels of peas and 40 bushels of oats. 5. Find the sum of thirty-eight thousandths, five nnd twenty- seven hundredths, and one hundred and ninety-three thou.sandtU8. 2. wood ] is ^3; rOUKTH CLASH. will inHnyu..re men w<»!», .md lH-7. than li, and three tunes as nn.cl. as C. Find tlu- share uf\.ach «. One man own« 8l>(M>7 acres, another !>H acres, a third 1-88(54 acres, and a fourth 2(M)85N; acres. How n.any acre.i ill all InvnT 10. Tom and Will w..rk in- together can hoe a patch (,f potatoes 1 r hours, and \ dl ah.ne can hoc it in 15 hours. In what n^e could lorn al(»ne hoe it ^ and ^,.fu hat then reman.ed t.. H. If H paid S2m) n.nre than A, what was the value of the foundry f 12. If 2 geese are worth as nnich as .'{ ducks ..r 4 chi(k,.ns huw nmny ducks are worth as nmch as ii geese and 8 chickensV XXX. 1. What must ho added to 2'\mH) to niake ;i(MM){> ! 2. A piece of land contains (i4 s.p rd., and is covered with cord- IS ^JjO, what IS It worth per cord ;* ^ ^3. By how much do.3s 55 exceed the ditterence l,etween "55 and hi/ ^r^"". ^'\^^- ^\ i"-.^^'">^'' 1^ ft- '-' i". wi.le, and 10 ft. 10 i„ high with a baseboard 10 m. wide, has 'A win.lows, each 5 ft. 4 by .i ft. (, ui., and 2 doors, each b ft. 10 in. by [i ft. b in H.,w manv yards of paper /, of a yard wide will be re a |ti<.!c»! of work in 40 hours, 1! in 0(1 hours, and C in 120 houFH ; A and IJ work at it 10 hourt*. In what time will C finish it i XXXI. 1. What is the least (jnantity that must he added tt» the sum of .'{.072, 10, and '27 to nuike the result a whole nuniher ? 2. If horseH eat 13 hu. 2 pk. of oats in 8 days, in what time will 12 horHes eat 15 hu. 'A [tk. ( 3. Simplify :U+?|-^4-n.<'f-^^-il- 4. From the sum of 41 hundredths and .'JO thousandthH take their difference. 5. What quantity subtracted 5 times from KK) miles will leavo 28 mi. 205 rd. ;{ yd. 1 ft. for remainder '. (J. By how much does the diU'erence between ".'lO.'iand 1 exceed the sum of •(►2;{ and -28 ;* 7. In buyinif a <|uantity of tea, I was cheated HO cents by a t^rocer giving me I5j] oz. for a pound. Mow much did 1 pay the grocer for the tea ? 8. I received ^8 for tw(j loads of wood, each 10 ft. 8 in. long, 4ft. wide, and 2 ft. 'A in. high. At what price i)er cord did I sell it ? 9. With a roller 8 ft. 3 in. in width, how many sipiare rods of land will be rolled in going once around a field (50 rods long and 50 rods wide ? 10. The posts in a certain fence are 8 feet apart, and a man riding a bicycle passes 11 posts every (J second.s. How many miles per hour is he going V 11. A man hired at the rate of $210 a year. He Ixjgan work on May 11th, and ipiit on Sept. 18th. What wages should he receive? 12. .l;iii(> had .'50 chickens, and Msirv h;id 15. E=u'h girl soh.l the sanie number of chickens, and .lane had then seven times as many as Mary. How many did each syll 'i FOUHTII CLASS. :u XXXII. 1. A.M 7 OiViO tnjrt'ther twonty-fivo times. 2. A property is v.-iI.umI at !«'J.%(HM>. an.l h pors..,, uIlmuvms h rrr- t III. sli.uo of It recoiv(,H «t|«;(MM) f,,,- i of u hut he ow..J VV / V t.oM of the property di,l h. own ? * ' ' ^^ '""' *''^^'- of ,;\on""' "'" '"^"' ''"'^'''^ "^ -•*'' '"■''^'^••f ''«>'' ^«^^''' ^--'iKl'ing 084 4 "W inen A, P., nn.l C. can .lo a work in i h.Mirs • A -ilone u^e'i;\,,:v,"„:,r!';;;.";;:;„.r;' " ^" '^' - "■■» '■■-«■■!''' 5. Find the product of 0101 and OOKM. Whl; ihr'"^ of ^'round i.s 38-4 yards lon.t; and 7-84 yardn wide What 18 the area m .s(iuare yards ? ^ nerlu.^ut''^ TfiTf ^ 1 fl'f '"'^ ''!;'''^' '':^'^^'""'.^ potatoes at 30 cents per l.ushe . Ha.l he sold them at 40 cents per bushel, what fraction of the cost price would he have ^.^ained ? traction ^^a From the product of -H^,} and '098 take the product of 20 and wol!!i Aon'lf ''^ t'""'"'!: -"^ ^'^^ ^""S, 10 in. wide, an of a store sold '028 of his share. What part of the store does he still own ( 6. A man bought a load of potatoes for $1(1.20. After using 14 hushels, he sohl i.| of the remainder for ,i?8.80, gaining ^l.GO on what he sold. How many hushels were on the load ? 7. From a web of cloth containing 100 yards, a merchant sold 7 I)ieces, each 1-2 yards in length. What is the value of the remain- der at 25 cents i)er yard ? 8. If I sell a [)ound of tea at 45 cents, Tgain; if T .sell it at 30 cents, I lose ; the gain l)y the fonner price is 7 cents more than the loss by the latter [)rice. Find the cost of the tea per lb. 0. The total weight of 4 bags of wheat is 10 bushels ; .*i of the bags average 2(>4 bushels each. Find the value of the fourth l)ag at 75 cents per bushel. 10. If 8 cows and 12 iheep can be kept 3 weeks for $12, what will it cost to keep 12 cows and 5) sheep for the same time, allowing 2 cows to eat as nuich as ',i sheep ? 11. One man can do a ])iece of work in ,\^ of a day, and another can do it in yV, '^f ''i <^l''iy- It' both work together, i what time will they do the work ? 12. A certain building covers 1 ac. 15(5 s(|. rd. 13 iH[. yd. 4 s(]. ft., and is 242 feet wide. How long is it '( xxxrv. 1. The total weight of 8 equal parcels is (J0r>04 lb. Wluit is the weight of each ? 2. A cellar wall is 2 feet thick, and the cellar insidethe wall is 24 ft. long, IB ft. wide, and ft. deep. How many cubic feet of stone are in the wall ? 3. How many times can you subtract '0008 froui 977 (HM ? 4. A and B can build a wall in 10 hours, H and C in 12 hours, and A and C in 15 hours. How long will it take all, working together, to do it ? 5. Divide ()8025r. by -OL'OIJ. ('». A (piantity of chicory at 4 cents a pound was nnxed with 30 pounds of cotree at 28 cents a {)ound. If I the co.st was gained by sell- ing the mixture at 27 cents a pound, how many pounds of cliicory were used '( FOirilTH OLASS. 33 7. Kxi,res.s a link in inches and the deciniHl of an inch. B^ Uu, all the ,;; -nl'^^ ^^\.^'aTC ^'^ 1^77- cost price on the l.arlev and lost ' ..f f). \ "'"""''^ '' "^ ^''^ What was his total i<.sfo;;;li;;on^:ii /''""' ^"'""" '" ^^'^^ ^^''-t- J*. The jn-odiict of two numbers is 7-<5 vd I f^ in S?S ;v.dth of four of then, is . rd. 3 ;i.^^ ft? '^.IJ^^^t ^ J^H^^rt wS!iJS;rcr- -- chains Ion, 12. Express | - H(4i x ^ -2| x |) + | in its simplest foru.. XXXV. 1. If 2-4 lb. of tea cost 01-2 cents, how much will 275 lb. cost ? 2. What number divided by 4iL-(''x? of 1 • a\ i •^^ • «i for quotient ? "^ "^ ^s^iot^-^)-^ vvill give 2^ 3. Divide the product of 4-0004 and -0003 by •(KK)12. 4 A farmer sold p of his land for $2(MM), at SHO i.er icro Wh-.f Hhould he get tor the remainder of the land at .^0 ^^r acre ^ quiieil^T ''"'"" " ''■' '"'^ ^''^ '^•--'- '^ •^'^^'- Wl-t is the u,^ (Uys. In uhat tnne can both together plough it V ^ 8. For a certain work 18 men *M wnm<>n ..,wi o^ • i • , ^1 40 T».r ,1..,, -^r ' " women, and 2/ girls received fe««i.->. Aruvv inucn (iKi eacli earn ])or day / 12-qnf?^^'''"^',^!^lw^"''*^"^'"'^'^"^^' »» oxcavati(m27-nft lon.r 12 Jb ft. wide, and (J-.'i ft. ''^^^^ "* 10 secomls, and B in 12 34 PKOfJRKSSIVE I'UOULEMS IN AUITHMKTIC. St 11. Wlien p of ]"832 is taken from a certain number and | of •070 added to the remainder, tlie fsinn is 5. What is the number i 12. A certain sum of money has (i times itself add 'id to it, and 8 times this latter sum diminished by Jft'14 leaves a remainder of $1498. Find the original sum. XXXVI. 1. A field containing 8'35.S!)5 acres is 4(>"2<) rods h)ng. How wide is it ? 2. A man paid $50.40 for cloth, and sold part of it for $10.80, at 55 cents a yard, losing $1.80 on what he sold. At what price per yard must he sell the remaining cloth to gain $3 on the whole transaction i 3. What decimal of an ounce would represent ^{\ oz.? 4. I ])aid $14.40 for a piece of tweed which was measured with a yard measure tliat was 1 inch too short. How much should I have paid ? 6. Express 785 of a week in days, hours, etc. f). On a certain map "75 of an inch represents 10 miles of country. How many scpiare inches of the nuip would represent a township containing 7<>800 acres ? 7 How many dozen peaches, Ixnight at 3 for 2 cents and sold at 6 for 5 cents, will give a profit of $1 ? 8. By selling lambs at $2.80 each, I gain '4 of the cost ; at what price must I sell them to gain ^ of the cost ? 0. A can roup a field in 4 days of 10 hours each ; B can reap it in 5 days of 12 liours each. In how many days of hours each, would both together reaj) it 1 10. Reduce "953125 of a bushel to pecks, gallons, etc. 11. Divide $180 between two men, giving one | as much as the other. 12. For 4*4 (quarts of molasses at 81 cents per gallon and 3 spools at 24 cents per dozen, a person received 4*24 pecks of oats at 35 cents per bushel and 18*50 ounces of tea. What was the value of the tea per lb.? XXXVII. 1. A ditch 1 mile long, 4 ft. (> h). wide, and 3 ft. deep was dug for $()(>0. If each man employed dug 5 cubic yards per day, find liib daily wages. 2. Whatdecimalof a toni^SOlb.? FOURTH CLASS. 35 yar,,s ,,„.., ,,„a 40 ft. „,,,e. vvi.^t ,=''4,',;";;;!, Jirfeir'"" " '"' ^ the seeo„a',l:r^ ",'!;':':;:: '™ '-="- ■;""""« ■"» ""- »- • receive,! | as u.w.y h^XL ^U , !" {.'l^r Wh' i" "''"'' f"' '''^ «""' of Mio furiu ? «t^cona. W luit vvhh each hou's slmre 6. Ex„ros, 15 cwt 5, lb. 4 ... i„ ^w, an.. U,o decin.a, ., ,. e„t forL.lr/.::'r;i:e;irf,';r,:";,;^r'.'f ;'„"""■ » " '",- - ■""- th.m the cart a„„ „ar„.„., uJl^^uH t'lc'hStlfc 't' '" ■""''' 8- How ,„atiy times will .J contain -0(10(11 ; wm'n.of;'ij'rrer;:,'"';::i..:5 ■"' ''-^'-^ ■" ^ i-ura, ■.„„. „.»„ „,„„ 10. Expres, 2 r... 2 ,,, , ft. ., ,, ,,, ,,,^ ,,^^.. _^_^, ^^^ ^^ __ .^^ ^vide, and 3 ill. thick •mrl :,'•'''' /-■^^» l)nok was 8 in. Ioiil', 4iin the cost, of the ;S;";,!/j;j. ''''•^•^-- -— d its bulk ,V lind of "f m'S>8:^. ^'.;::^^'^&i''^^^ TI ^'^ ^^^'^-^ ^-- ^he sum tjxact number of time"/" ^^-' ''^ *'*^^^ ^^ ^^^^1 contain 7-04 an Percentage. {Including Prerioiis Work). XXXVIII. 1. How many hundredths of . numher is 1% ? 2. How many pounds of IiavivnrfT. c/*.o- ■n e-,,an«e f.,r 4 tons of ol't^^-^LM;; t.r;™,tS.'^ *"™" J- " hat per cent, of a number i, | of it ? mort '^z:'^'^jz li ^!;™ o*s;'„t«uf " ■■ ^ ,»"»■" » tnnes as much as A. How n,„cl, .lid eaci; spend' '"""■'' ""•"' ""«" 5. What fraeti.,„al part of a number is 01% ? at the IS:,;- ^,st ;:!;:;\:;t:: :;-" 'r ^-^ -.. -...wn, in length ? ""^^ ^*' l''^'^'^ tlirough a tunnel 170 yards H w 36 PROKIIESSIVE I'RORLKMS IN ARITHMKTIC. 7. What fractional part of a lunuber is 1%. 8. In 5 hr. 8 niin. 15 sec. a man walked 15 mi. 128 rd. 22 yd. How many miles an hour did he travel ? 9. How much is 5% of $00? 10. Ill a race of 220 yards, A can beat B 10 yards, and C 20 yards. What ^istanco can B beat C in a race of 140 yards ? 11. What per cent, is $3 of .^50 I 12. At what times l)etween 4 and 5 o'clock will the hands of a clock be (1) together, (2) o[)po.site, (3) at right angles? XXXIX. 1. What per cent, is 3 feet of 40 feet? 2. Two parcels of tea together weigh 12'875 lb., and one of them weighs 2"(>25 lb, more than tlie otlier. What is the value of each parcel at 48 cents per lb. ? 3. How much is G per cent, of 3 lb, 2 oz,? 4. Two men rented a pasture-field of 12 acres at $4 per acre. One man put in 3 cows for 4 months, and the other 2 cows for 2 months. Whf\t portion of the rent should each pay ] ^ 5. How much is 8^ per cent, of mi, 80 rd,? <], If 9 men, in 10 days of 9 hours each, can do | of a piece of work, in how !uany days of 8 lujurs each, can 5 men do the whole work ? 7. Wlial per cent, is 1 hr, 20 min, of 2 hr. 5 min.? 8. A man divided his farm among his three sons ; the first son got 37i acres, the second got | of the farm, and the third got as many acres as the first and second together. How many acres were in the farm ? 9. What per cent, of $5 is 25 cents ? 10. At what time after o'clock will the miimte-hand of a clock be 25 minute-spaces ahead of the hour-hand ? 11. How many hundredths of 5| cords of w(jod is ^^ of a cord ? 12. Find tlie G.O.M, of 1(5 ac. 100 sq. rd, G stj. yd. 2 sq. ft. and i7 ag. J42 s(j, rd, 1 scj. yd. 2 s(j. ft, 72 sq. in, Fourth class. 37 XL. cent ,H,U L: .'""^ ''^ "^^''^'^^^ ^^ -'"^^ it cost ,ne. Wh.t per 2. On H field of n.i acre.s '-»() l.i, zt'- ii i., , . wh,;; it It',""' ""•"■ "'" *"= t""»«l I'y -lli"« a far,,, f„r twice mort tbin the'„'l,"j;."'" '"'"""' '^" "^y^' giving one of the,,. J each, nt m cents per^^. i:. " Vf ^ ^ if ''^frT 4«^'--^""nH age, Ht what price per °,U h, " n. ust' H •"T"'^ ';^' '"•^^' ^*y l^''^'^" $5.40 on the wliole ^ " ^'''' ienuiin. A merchant boutrht ch)th if «!f jn i e^e^.,.!/ ti;;:r .t;^,: „:: t;;:'ii:: :;:: f;' ?;;• ''''"■ «'■-"' "'"'■"--= cost 'i ^ ^ "' ^"•^'^ ''^ the cow. \\ liHt ,li,l euch wi„.t „■: ,;;;;;"i,."i't':' 'H:.*r,d;':./l:i. 'r" ''"■"■ ■■"' ^j "«■ -"*• -f 4 feVt ;vi:,':':^t'';!";; ;::f;tt^;'-.'. f [-* t'" f ,";- "•" • cubic yard ? ° ^ ^ ^^' ''"• ^^ l»at did it c(».st per CO,!"- ii.r::.,::;|;',;:,r'jr;-;:''tr:',^;r *"•*• ■" -^ '-- -' «l- their h,b„r. Al ow ,^, ' ,, '" " '"S^'"'"'' "■"! receive m for shouUl tl,ey diviirthf m,ty r """'" '"""'''"« '" >"« »"■•'<• ''"- thi!;rt^e'':i!!tf ••'" ""'"■" '"'■ **-2''- « I'- -nt. i,, h,.,t. Wh.t did XLI. th^^Ai'^^'" '""' f t^^« numbers is 115-6, and one of then- i~ -i r tfte ut;ier. Find their ditlerence. ''^ ^""^^ '^^ .^n^J-g^iit sold goods to the amount .)f Sn 9 wi . commission at H per cent./ ""•»'"« '>f ^112. What was his tr R" ,18 PROCJRKSHTVE 1M10HLEMS IN AKITIlMKtKi. 4. If ji «.f .Ji.hn'.s iiionoy is otiual to 4' of Jjimus', und ^ of .Jjimes' equal to ^ of Robert's, what fraction of .John's money is e(iiial to | of Robert's ? 5. My liouse is insured for $C()0() at 2A per cent. What is the annual premium ? 0, If 2 yards of clotli IM) inches wide can 1)e made from 3 pounds of wool, liow numy pounds of wool will l)e recpiired to make 1)0 feet of cloth li yards wide I 7. A collector charged me $15 for collecting ^250. What rate of connnission did ho charge ? 8. From a tract of land containing 1202 ac. 110 sq, rd. 8 sq. yd. 3 sq. ft. 10() sc{. in., a man sold lOO ac. 11) scj. rd. 4 sq. yd. 2 sq. ft. 102 sq. in. to one person, and three tiuies as much to another. The remainder he divided into Helds containing 17 ac. lOJ) s((, rd. 25 sq. yd. 8 s(j. ft. 47 s(i. in. each. How many fields had he ? 9. I pay a premium of .^51 on a house insured for $.'5400. What is the rate of insurai^" '^ 10. A person has enough oats to feed 8 liorses for 10 weeks; at the end of 4 weeks lie sells 2 of the horses. How long will the oats last 1 11. For collecting a note at 4 per cent, commission, a man was charged $7. What was the amount of tlie iKtte ? 12. By selling 0^ lb. of coffee at the rate of G lb. for $2, a grocer gained .34 cunts. What did tlie coffee cost i)er lb,? XLII. 1. A premium of $15 is paid on a barn insured at 2 per cent. For what amount is it insured I 2. Make out the following bill in jiroper form: H. Nelson sold T. Brown, Sept. 1st, 1804, .5.35 lb. of Hour at $1.80 per cwt.; 48 lb. 3 pk. (if peas at (54 cents per bu. ; 2470 bu. 24 lb. of wheat at 84 cents per bu. ; 328 lb. of barley at 50 cents per bu. ; .344 lb. of potatoes at 28 cents })er bu. On Sept. 4th, 1894, the account was paid in full. Write out the receipt. 3. A storekeeper who failed in business can pay (mly 30 per cent, of his debts. How much will a creditor lose on a debt of $640? ^ 4. A^an do a piece of work in | of an hour, B in 1 hour, and C in J of an hcmr. In what time will they do it if they work together? Poiiirni CLASS. dd 5. The HHsessod value of my unnwrtv .« «ftr«nn , ., taxation ,s 15 „.ilU „u the d„n,^r'""lvi':^ ll*..': l',";', "'" "■"*" "' -ay S: n";'st"^li:!,."';i;:„t,;',;;i' ,t! .tt'^r!'"^"''"'/- "- what Ellen then has/ ' ^''''^ ^^''"*^ "'^^ ^lave j of dedLt^,^ of ™'r :;i'rfr.^s;tir"'*wir;'' "■''" ;"r.;*'^-^ ""«' u A r n 1- . ^ ^^^'^^J^ing. >> hilt amount did he collect? B.,th 8„M thoir land t tl '"," ' " '« "^ "'" "'""■" "'' ^'o y"""«or receive? ^ i'"o^i- » li.it price jier acre did they 9. A horse which cost ^f) is sold for «*»<> in \\m . gained ? ^ ""^" ^'^^ '1?J<».1(). W hat j)or cent, is what i."„,y ',;;■: ,::;' J:^,5' »■"« l-- 1--1 -... ..H it at 44 cent», fee'%\"a"°thoro i;;:i:;:f f'r '" '■"'"'""• """■ '"™y ^f-io in. Ion,, 1« in. wij^'^j;; Id i'n'^'^fi-r,"""*''"™^ '"' '■'"^■'"' "■■-'' ^^ XLin. two'n4t!S;'',4,[:;;:/;;'° '-^^ -ne in U.,,4h was h„i,t of W^rlo^f--"^- ^.-;.;-b .. .^^ .t ata left. How nmch „,„„oy 1,1,1 „e ;» ,iL ? '"""""''"•' ""^ '"•"' «54 Wh!uttt'S'ir"„,il.r "" '' "■■"•"-•■•'^ ™'-> »' «">00. remainirTn";.!"! ".K^ "' «"V",^ *'>«• » <^^'" ''■> < <4tho How long wonia^ta^jtlV ^^.^it^^'^r -■ 'i^P "' ^*^»^ ■^f: n^} 40 I'lKHJUKHSlVK PHOHLEMS IN AKITHMKTlC. iHl 7. If, by selling u hook for JjjiJ.HO, I l,.su 10 [m- cent., at what ]>rico must 1 sell it to gain 10 per cent.? H. V>y Helling a certain ninuber of cows at ^24 eacli, a dealer ]«»st i\ of the co.st on one-half of them and gained {\ of the C(>Ht on the (»ther half. If his h.ss on all was .150, h by selling a web of cloth at 72 cents a yard. Had he sold it at 56 cents a yard, he would have lost $2. What did the cloth cost him per yard ? 7. A blacksmith sold two ploughs at $18 each ; on the one he gaiiied 20 per cent., and on the other he lost 20 per cent. What did he gain or lose on both ? What was his gain or loss per cent, on both i ^. VOItRTII CLASS. 41 i.-». In wi,,., ei„. e.,;,:;;' A 'i„;;;r!,,^,!'::i'„t'r " '"""■ ■" ik 10 •'. A limn wli(, owned lOOO hnslicls of vih....f . 1 1 i r ■. wpinle iiii.i 4 r .1 • , "'ii.iMi 13 oi \\ neat sold ! (»f it oii<> ..'.^t...-. will c„„uii> i'of H ton oti™:;;;™'i V "'"" "'-"«'" "^ "'" 11. When thu I'iitG .)f tjix.itioii is « mills on tl„. ,i ii XLV. for the l,ay? ''"^- ^^ '"" I"-'"-'" 1«"- 1"" JiJ Le pay o. A new scliool-Jiouso rottiiKr ^- ^^'Lat '-»' "^ "•« 42 PUO(JUi:sSIVK PltOIU.FilMS IN AFMTIIMKTiri. H. A jiiHii IniyH milk at thu nitu of 75 cents f..r iii' ^'alh.iiH, and •sells It, at 10 cents for 2i pints. What per cent, does Ik; gain ? D Divide $170 among A, B and C, giving A $10 more than J as nnich as H, and i as nnich as C. 10. By selling an article for 81.02, a storekeeper gained 32 cents. What per cent, profit did he make i 11. John's age is now ,1 of Harry's, and in 8 years it will bo ^ of Harry s present age. How old is John ;' 12. Wliat i)er cent, does a grocer gain hy using a measure that holds 7 puits insteail of a galhm 'I ITT?; XLVI. 11 }' 4./"'"\^''^'"^'^ ^^ percent, hy selling sugar at the rate of 12^ 0). tor .^1. What ])er cent, would he gain by selling 10 lb. for |1 V 2. A man bought a farm for SOCOO. \h, gave 00 acres of it to his son, and sold 'j ,.f the remuinch'r for i?i4(K), gainiu" ^200 on what he sold. What then remained he gave to his daughter, who sold her share for $3270. What })rice per acre did the daughter get I *= 3. What per cent, does a merchant gain by selling 10 hats for what a dozen cost ? ©1 io ^r *'^^ ^"'^^^ "^ '^ ^'■^^"'^'^ "^ ^'^'"^^' ^"'' ^'"^ ^^^^^^^ i<^ cost a farmer «>110 to fence a s(piare Held. liow much was the held worth at $00 per acre ? 5. What jier cent, will be gained by a grocer giving a customer 15 oz. of rice for a jjound ? How much will the grocer gain on an outlay of $30 ? (). A piece of work can be done by A, B and C in 1 hour, by A andCin U hours, an»"cli XLvn. first, m^ *7(W, what w„s liV/ ■ "''"•"'• " ■^''' '^"l"*"! »' 8 hL!^;;,!;:^rini,i:!;T"'' '^ "•'^''" '" '^ > ^- - "i„.t tf„,„e,„, -Id the g,„„Is at catal„.„„ p.-ic.. w'hat p";!.;;?; .,,','1^; ■--';"■" long w,.uK, it taki al/w'.^lt.^'.^tl.rZt'i't I" '^'' *'^'^- """ I'or cent. Tlio anr stuns at H.;jOA.M.fru,„ u n^.^^^^^ •""' '"^^ "l^-^'- ••^""^''^^•' I-'-'" walking Ht Jlu-i.ittM,f.ii nnk,s,iH|.<.ur starts fiu,,, Brainptun tu Oianm-villo ":;[;:;;i;r- ;:-s^;;^i:::7"' ^""^ ■"^"- ^"^'''--- '-^>^-' «- ••!. What will l,„ ilu, intcvst „„ grW) f,.r 1 yc,,.- at « ,,or cent.? „. t'- '''rr '""" ""»■'«•''• t" '•" a coi'toiii w(.ik ill 12 li„ur« • after n. Kind the interest „ii *XO0 f„r 1 year at 5J per cent. V «. In « weolis, ., men, !) women, and 14 licys earned $44(i 40 • Th^yrv^T^ '" """•'' T ' ,""""•"• '""' -<=l"v<-um •« mu h as' z i)()>s. b ind the wagos of uach per day. cunt i^r an,:;" 1" ''" ""^'^ '"'^^^^^ "" ^''^^ ^-' ^ ^^^ '^^ H per H The circumfercniic .)f a vvlioel is :}1 times tlu' diameter -uul a >.cycle wheel makes 2880 revolutions' in ru in 't^^o [11^00 cent ' shnnh?i''V;! ^f^^ T ^""""^^ •^"^' '^ y^''''' ^^"^^ « "^'^"ths at 6 per cent, snuple interest. How much interest wis received for it ? FOjrKTir CLASS. liscouiitH of II a Hiini of 45 U. A Villagl! U'itll H |)..|»,ll;iti,,tl «,f 'UUii .• . . 1. Find tho siiuplo intoreMt at 7 i)ur cunt, purunninii. 2. Th XLIX. •""^-^1!M> for ly.H,H months n,lay^ n-ou nu-n fjinuMl "^21 in a wooW T». « . any as tho Mrst and second to^.et ' r Fi ; / ,"T^ ' "' '""^■'' '•'^•'• Q t , n^inci. J^ind thcdady wagt'sof ouch at 5%. *'"'" "'" ''""''"' '••' *■-'» f M^ucl, 4th to Dec.,,,..,. 2Ut fi. A woman hou<'-ht a .in.ii.f.-f,, r «u,,,,„»e,l to contHin 14 1 0,0^.' ■■"'«,'"■ I"" "'' »' l'"'™"" I""^! t„ he 14 oz. too li,,i,t" ,f' .she o'i'.f'ils"?- "If '"'""' «"^'' mucli Mimiey w,m she ehenfeil ? ' * '' ""-' ""«"'■• '"'W forlw"^,;- i';:;;;.^;;L^,,rr.T;ni:T,'.':''' \""^ -^ ■ ^ '"■ "- """•■'■• j."ut re;:ca;:''''j,''rz,.r;-r'''''f' r"' '■"' ■'■" '"■•""• '^ I«'U.-.s. I„ what ti„,e vi t e L •')" "Z" ', "^^'V "'"l'^-*" " '" l^ opened «t the »,.me ti,„o ? "'«'•'"!-'" h. .1 when nil three nre it on offiySI^Z^,wtf^;■:::;;,^;'';7J^^^^ ^^^-f- ™'i re,«i,i nepay? ' " ""^^Hst at 4%. What amount did m'"« tirtr" ^uHt'ZZ't^T^ '"'i !' ""■' -'^ 21 ,.,i,e« fiuW. at the same time ' "^ S'™ B i„ (i miles, so a., ,„ What i)er cent, does he a. .„ .... i ; . . ... . ''^ 18 cents a gallon. ui on Jii.s outlay V 12. If 3 sheet) '"id 5 Iambs r(mt Mjeep c^n be bought for $700 ? I M h 46 PROOKKSSIVK I'KOHLKMS IX ARITHMK'l rjc. p If «' 13 i- •' : ■ i L. that the one Inul tnivull,.,! •( ,7.^ •"""•'""' '"'""• other. Find the '.te'^t "id. '„:[• h,,,',';:'^' ""'■ ' '-"-■ "'■■'" "- B togotlier received. Wliut did each f KOKii .^t i- / • . interest. For what time was it lent ? "* ''■^ """1''^ 12. A can do twice as much work as IS in 11 dav •,..,] 1. n . a corta 11 work in 2'' rliis T„ 1. 1 ^' "•'"' '"'"' <=■■"' » r«i.I November amoimlij;,"/ """''■'•• """'■^'»' '" "i" - l-' -'»""■■ What ;« t^^ FOURTH CLASS. 47 e ttinount simpiJiuJrest?"'"" "'" ^''-"'» ■■'"—" '" «14,I4 ,.t BJ percent. hout,l„st.Thi,,tt,hc:;.''':.r;'ii,;": '""'••^■'v«-vi' ^^ '™ -„ i„ 5 what time c„„la eact alone dlJi^ '•"■'"'" ''''^'' '" -" '"•"'■^- I" the whole quantity. Ho. ,r:^t£t were irl'^ri^'nT'' *' "' «476:2rl1tr6',',':onri "'"'"•' '"'--'• -" S^BS an.ount to inJrlSvais''/:;5';;,t: i:!fj:!: '7/ "r' -^■■' ^-^ -"-. was day, how „,„ch WHS the e^t i^, cubic yard f '""" '"'"""^ «^ P"' an^Junrt',', V3«!yr* '" '"'"""* '"'' -^" ''•''y" '" " I'"-' oont, will LII. 1. What amount will be due Oct 7 1SQ9 drawn Feb. 25, 18»2, with intercut atli^ii'L^t'.'^errmun^*"''' cents for ^ So .anVi'S Z' '"TT ''" «" ^'•""■■'' W"« ^ each did he buy t " "' ^'"^ '"'"'' ''•™»»- How iany of wiAr;i;t^r:Litir:l,;;:i ^ti;rpri;^pZ"™ '"-^ ^"^ , 4. An ice-house 22ft. by 15 ff ^.1..^ ...o- -1 , form size to till it to the height of ' 12 fr .}' ',•:;' 'if ' ^^'^ Z^^- ""'" mches long and 1(; inches wfde, what l«-tt"lueknr^^ '^"'' " '' 48 PIlOG.fEssiVE PROBLEMS IN ARITHMETIC. in m year,'''"' "'^'' ^""^ """■ ''""''"'^ '""'^^•''' ™i" *-'?40 double itself the wheat per bushel ? * ' ^* '"" "•"' "'" ™l"e of interest did I pay ? * ° ">i7d.bO. What rate per cent, simple rovlttnfi::^iHr.?.'eS'/ I ^'^" --umference makes 1800 be made ^^r£l^^^Z J^^^mfT-'''''-^ revolutions would ing the same field ? ^ ''"'^ ^^ ^'"^^ "^ circumference in roll- it^f, ^J!Zi::^::^^:i^:^ 7^ t-^ ^----^ ^^ ^-^ times Wh!t umoir^^I^Sf "^^^^^^""^^ ^^^ ^^^ P- -"^- —-ion. LIII. 1«cn ^\'»'"»/\^"I><>«'ted $051.25 in the Savin-s Bank on A.ur 9« 18JU, and withdrew it with intere^ at 4/ on\uril 4 IH u ^F i the amount withdrawn. '*/o "" ^piii 4, 1894. Find 2. A cubic foot of water woiVli«j r.9 IK « ,.„ i rtide/-^?mn.^i;;r--^^^^^ not^ '^l^;Jml/l8?)4^!rr^'r"T^^^^^^^ ^-^j»- cent, per annum'^^^t ^1^ ^::l:!rr llirtJ^X^ ^ ^^^^ wait i:^ "r Ann ::;>nf - '"^f ^^^^^^ ''''' ''' i^' -^ -fter- solcl ; he then Id ^^^^^ ^^^ ^'""^^^ ^^« many acres as he farm ? ""' ^""^ "'^"^ '^^^es were in the second 1 ?• -.^ «*^'>rel^eeper sold tweed at a gain of 20 ner a^ut Tf 1 u a sold It at 8 cents less per yard. h. Sould ^^.vJ^^^i'Z^^ i ^'" ^""f M vvliat price per yard did he sell it? ^ ^ ' '^ ^'''" ^^"*^' POURTH CLASS. 49 e cow di»Unri:;;|f';tt :^^;;;«;f ■• (-:; i»^J "f its i™.u,,an,l the h per fiore i ^ " ^^ ^''^^ '"^ ^^'^ value of tlie farm at 7. A maij purchases a house for <:?'>i« < i «ionth. ^^U,a rate per ce^'tmr :.""'' ''"^' ^^' '-^t-^l^-i^O per money? ^ "-' ^tnt. per annum does he receive for his cost tl,„ farn.e!- T "^ ''* """'"=' '""■ f'"' **-'• Wl.it .lid U.o'oo, $-Vmouthy, wlrnta,,! the 1h„.1 c,,.4 "S":!;; 7""' '" '"» «"'" "» -il. A man borrower] SS> ynrds f, ;;hd :".^t M "T' '"ir^ f"" ^^'"■"'' ^^''--'^ yards per second, Jau.es a ^ r'ef ''''?' "' *''^' '•••'^'' "^ ^ when .John reached school, . Uu-ned 1. . I- ^ u" ^T '"^''"•*'' '-^"'^ fron, houu3 when they uiet ) ''''"^- ^*"^^' f'»' ^^us Jan.es LIV. .^4 20 per eord a..d 2;^ bushels ^oasr-^'l "^ T'"''^ "^ ^^"•"^ '"^t "^terest. What su.n was borrowed T ' "^ ''^' ""'^^"'^ l*^*' ''"^''-l, as ^■''o^^7^X:!'Z^J^;^^^^^^^ 1240 chests of tea at on the lot. How\nan;;;:;!.:^if .trin :;;:I^;;:i^^ ^^"^"'« ^^«^ au.-,ng the year, he had 5 f er X^u if T, ""'^ "'^^^^^ -^I'^'"'^-« the house. How much did he^;;^-f!;; it V'" '^'^ '"""^^ J>« V--1 for bod. Find the cost of niakin^ 1^ dk a"'^ ''""" ' ^^'^"^ ^-"^ the 5. On Sent 11 i«o. ,,/-." ^"^"^"^^ -^'-ts per s.unre yard hij cow not .^. On Sent 11 IStn Ti w — i'ors(p,areyard. ^->Lpt. 11^ |«JM, 1 I)ouL'ht a cow f..f «- "'>te ^ on April 18, 185)4, for Si(rJ Y^'i^^.A':''' '""•'"?■ ^ «<'M the gain on the whole transaction >!• iiJ'^O, and paid my note. \V1 Mt was my 60 PROGRESSIVE PROBLEMS IN ARITIiMETfC. H: 1 I' ij m h I- ! (>. W hen oats were worth 20 cents per Lushel less than wheat, a man l.ought a .juantity cf each kind ..f j^rrain, payin- as much f<.r 12 bushels of oats as for 8 bushels ..f wheat. What I'.rice per bushel aid he j)ay for each ? • 7. If I pay ^H\m for the use of $852 for 11 months, what must 1 pay tor the use of ^504 for 7 months at the same rate ? 8 T have a piece of ground 5i rods long and 41 rods wide, sur- rounded by a ditclv H ft. 4 in. wide and 3 feet deep. VViiat was the cost of diggnig tiie ditch at 27 cents per cu. yd.? xxn'\ '^'!j^\«""P'^ .interest on $300 for 2 years 2 months is $05. What wdl be the snnple interest on $450 for 9 months at the same rate « 10. A l)ankrupt stock, which originally cost $.3000, was imrchased at (, cents on the dollar. The buyer sold it at a gain of 5 percent (»n the original cost. What per cent, did he gain by the trans- action f '' 11. The amount of a certain sum of money loaned at interest for (.months was $(J1.50, and for 9 months it was $62.25. What was the sum ? 12 Three-tenths of Mary's plums, | of .Jane's, and ^ of Ellen's are e(iual. Ihe three girls together have iVA ])lums. How many has each girl V LV. 1. A merch;int borrowed $24(10 at 5 per cent, per annum, and mvestc'd It in wheat at (>0 cents per bi.sliel. At the end of .3 months he sold the wheat at ()2 cents per bushel, and i)aid the money bor- rowed. How much did he gain on the whole transaction ? 2. By sellhig a certain number of bananas at G for 5 cents a truit-dealer gained 'AO cents more than he would have gained if he Had sold tliem at o for 4 cents. How many did he sell ? 3. The sum of |J)55 was ])orrowed on April 26, ]894 at 6 per cent. j)er annum. It was paid when the interest and princinal amounted to $<)89..'i8. ( )n what date was it paid ? Principal 4. The seed for ;i ticdd of the accompanyin<' shape and si/e cos^, $;{6.75. If 2 bu. 2 pk. were 4 sown to the acre, wh.at was the price of the seed per l)ushel ! FOUKTII CLASS. SI .t he «,„.■ f„,. ,4i4«. „„„. !.^j:'^.:ccj:::^: ij;^:'i:zf''' '■' the other in ru" ni . uT; iV 'i'"^"' So'-' revojuti,,.,, ,„„re than mile, ure theioC'.Jt;';'^'''""" '"'""■"" '"" '""■■«• ""»• "-y 7. A aiorchant nuirks his .-cixls at 'in •.,l,-.,„„„ r ..- cost, »,„1 „ll„vvs l,is cu»t„me« 1(1 „ !■ , f r ' "' ■""■ ""»'• "" price. What nei- cent ,11 1? ' '' '^"""""'>' "" 'he mai-lied 81.35 ; ^ ^""^ '■" «"'" "" ••"> '"■'■"'« wliich he selLs for What did t!,e tea e^;er;„u ',n '* '""'"' " '" -" """» "1-"'J- Bytlhnrn'u""f4" "';■"'"•"■ 'f '.'"f"^'" "f «-h«'t f"r »1200 price of wifa; he^s,' d.'"H lL''::id''d IH, ""l«";'"." t' ""^ -^' mo„th"was e,>ch empbyS" " ''" ^'■'""^'■^- ^' "'"" ™'« l'"'' foe" wttl;:u,si"r;:^3;,"r;;th:;: a ;1 1 """': ^" '' "«'"" "' « travel wqv. ^r.,.^.. i u r ? • V""^o,'^"t3 nnul l)et\veen two towns The Eet^eerThe't'n™ " ""' """ ""' »* ""^''"^ ''-l'' I''"'' "- .li.stance teke at 15 ce' , , e, d t^ l,» '""■"'«'•»"«■'' "''o «.ld a second mucli as if she had sol ho, ■ '"';"'"■'"''« 'o received for all was as many dozen ^^rel ule ietlnd'Srt"; '' ""'"" ''"' ''"^'-'- """ LVI. the ren.,!i„der at a "gai ^f" 6 , r eon'; «'" wl ,f ,''" ^'t' -"■<' gained on the outlay .( -" P'-r cult. " hat per cent, was apart, ""i? tt:rh!:?;:e:n''X:,lri;ir ^^rrr'"'-'-- "'"^'-"' « '-' have been re,/iire,l. Whit length ttli^'fencif """■" '"""" """■•• water i^'Tl^re if:;";;'.''' ''T-'"''',/"" "'T"' «' -"»• '"- ■»""'• 12A cent] ;,^r gaibu? "^ =""'"" "' "''"^ "'"' ""'«■ *"'"' 62 PR0(}RKHSIVK I'KOHf.KMH \S AUiTltNfKTrC. i 1 ^ 4 A n.an Ix.nrrht (500 doziMi e<^'^H nb 10 oentH h (l.,zen. He sold ,1 of tluM,, H, again <,f 20 piT ccmt,., 1 ..f thcM,, at, a khIu of JO pur cent., a.ul f ho n,,st at, a l<..ss of 10 ,,or cent Whai" per cent. Ud he gam «>n his outlay I ' 5. A Held c(,ntaining 4i acres is 24 rods wide. A second field tnc nrst. How many acres are ni the second Held ( 6 A person n.de a l.iryc;h> fro.n Toronto to Whitl.y at the rate ot 10 miles an hour and i.mm.diat,.ly returned at the rate of 8 rtehv";^'"; T '''"t '; ^"■- '' '"" '"•■ ^''^ ^•'"•"*' '''n- H-v far 18 vvnithy trom loronto <* 7. The owner of a farm sold it at .^50 an acre, and loaned the noney at (, j.er cent per annum. Had he loaned it at 8 per cent the interest receiv(,d each year would have been .^50 more How many acres were ni the farm i 8. Mr. Brown paid it!;{.80 for what butter and milk he used in 4 weeks. A p.Mu.d of butter cost tlire. tinu.s the price of a .,uart wel'l wl "' "Ti ^' •"""'■^ l'^ ^'''^'"' '"^""^ ' '»"'^^*'^ *'f '"ilk each week. U hat was the price of butter p(!r lb. ? J). A man built a fence 5 Ix.ards hi^rh an.und a field The bottom board was JO inches wide, each of the next three boards 8 niches, am the top board (5 inches. The Held was .'{0 rods Ion*. perM'" '*■ '■'"""'• "'"' """''' '*'^ *''^' lumber cost at $lb 10. A groccu- sold :-; of a chest of tea on Monday, ? of the remainder <,n Tuesday, an,l ^ of wh„t then remained on VVednesday^ he received *J.50 for what he had left, at 50 cents pei lb Ho^' many lbs. were m the chest ? ^ "• xio n The earth taken out of a cellar 27 feet long, 22 feet wide, and ^ yards deep, was spi-ead ,.yer a piece ,.f ground 4 rods long and 30 yards wide. To what depth did it cover it / » ^ " 12. The Mail newspaper, if spread out, would cover a space of 48 inches by M inches, and the average daily issue is al»out JJ)800 copies ; the road betwmm Brampton and ( )rangeville is 4 rods wide, and A,i days issue of the pap(>r would l)e re.p.ired to cover it How many miles and rods is it from liramiiton to Oran-eville ? t& 4 ^'•u in*)«F«!MM9 ADMISSION TO IIIOII SCHOOLS. 53 ONTARIO EDUCATION DEPARTMENT EXAMLXATIO.N J'APERS. ADMISSION TO HIGH SCHOOLS. June, 1S83. 1. What is the ohjuct of Division / WHh. r1,.i.... fi i ^- Divide 108,41il,71(;,001 by I8,748,(X«. roo^ S;;;^l"^S^fe;^,2l-y;-, ;;'-"«• ".e f„n„wii,« i» our. FinJ the weijjcht of 5(Ml,(MM) hricks at 4 11, '> .,y »..„.). i .-i ft* 375 tons iron j>late.s at £8 15s. (id. 107 £. tons l.;ir iron, .it £'11 14s. 10 tons hiili) iron, at £'10 lOs. 48 tons steel, at 418 7s. (id. 15 tons rivets, at £11 Is. 17 tons T iroii, at £M5 lOs. rods i„n^, fmllrritd'tido '/ '' """' '" '"'"" " '"»'=" "f '■•""• «3-5 6- Simplify: l-.+,v _,„,^^^.,,,^^,,, J l^l^^-5 4,'5i.f;i2„f,46. proportion of 15, .'} an.l 2. .\ oert kn 1 >.. ..,, ., ,iNu „'. .\ certain (luantitv of <• owntoeontain 20 hundre.hveight of larcoal; hnd n (juaiitity of <,'un[>ovvder is ftud also the weight of nitre and of sulpl lur It contaijis, its weiglit, 64 PHOOHRSSIVK I.ROMI.KMS IN AllITIIMKTfC. wb ria««. »17.2(., ,.„„i f„r duties ."« « " ff " " F<^\"V f"!"' f"'' ™'- truii.sHctioii / * '^ ^'"" ^'^^ <>» t'»e whole 8. Find tlic iiitcrost un u iiulc f<,r «'>"»*- at i <- i i ihh:., ,.,„i „,u,i Apni ,;, >HH,, ,:;, i ,,.t;. *a:'p"^,;,'::::;;,', •'■■'"""•■^ •'• l>ectmhe.r, JSS.i. thorn 'rsvr'.'rVo™;,!:'^ 1,'° ^""^ -^ ""-"• •■'-' -''i gain „„ „ :,.,xoVld,':;s,il;:i; sr,-, "'™ "•""" '""• ' 1>.". exactly ton ti„„« .» ,„„ch' as ti,o fo,' c^/ '" "'" '™'' "'"^ mo^ tS ^Ki^ri;:!.!:;^'' «• - "■"' A n,,.y ,.,.„ ,7. botweJ;!t'^ni;:;i'T,;Uf^'* '""' '^ "' '" *'^ ""^ '"«--™ Wi^s, to .. „sea in ;,„in, ^\;!X'o,^-t Z^I^ woiIi,t-tf'thr;;:;!;\.;;,X"t!r^>875^'*'--V"^'.''"" ^ "■« »■•"'" equal ? ortiei to make their cliaiiees it^^;;^;;s^r,rz'';r\ctn'lr:^^'!^--,^%r^f the v.-ork in .) iiuvs in..r«. H,>«, ,».,..!. ..r .i. r •,•■•/ ^'^" ""-^" rwi;^';:;,;^;^;^:"- "—!■ -f t>.o w..^ .cuho h rst man ADMISSION TO HIGH SCHOOLS. 55 I fo. c/ir- Y lejikago, :;he wliolo imi.iiy .'i, I's ; if 04 f Hii inch ro { ){ a clock eiico and md sold h did I 25 rods leii hud -nd Cost we ^7 J fFcrence sum by vulgar s to be whole 1 alone •eceive How liances ork at t man 10 Find the interest on 1?L>75.H() for 1)1 days at 7 per cent, per annum. Jviir, ISS/f. 1. The <|u<.tient is 12,4:14, fhc nM.iaind.-i' L>74;;, and th,- divid..nd Strrr'";'";;"" ni.- hundred and .K.;. (ho: sand o". dred and twenty-three. Find the divisor. 2. FinH '>"> '^-r ki oa'^ »>n' i the G. 0. M. of J)4,W5 and tHi,50!» ' ' ' "'' ^^' -^"' -''•' ""*^ of .J 1 1 '"'' ^^'" '^'"^'^■•^'"^^ »>etvveen the two to fh. decimal 4. Simplify : iA-.V"f i2r^*'^"^^^- (2). y]^ <)f^a guinea - f^ of a i*. Hs. 1(>-';^ l>a 1 o A g a n dealer bought (.4 bags of oats, weighing (inclu.ling he .lealer panl .4 cents a bushel for the oats .-.n.l sohl then, at 4'>l cents a bushel. How much was his gain ! " IK^M ^'\^'\!l '"''^'■'' •- '"'^' ^^"'^'^ ''"'' »>">'"'«''^-«l -n one sid. for lis. (.,([., at .VI. per s<,. nich. Find the weight .,f the plate suo- posmg a cubic foot of the metal to weigh (J2| pounds. ' 7. A, B and C do a work in 12 hours ; A and li can do it in ^e:z^^r ■"^" '"''• »■■» "->■ -• -- "-- ". thj 9. Find the duty on 8 hogsheads of sugar, each wei-hin.^ 1 '>()() pounds gross, at 1^ cents per pound, 10 pe"r cent. being"allowed for ■^^' /^L^'"'^ ^''"^ interest on 8225.40 for IG m.mths at 8 per cent. por HJUlUiii i^ll'o'r^' •■"."!*""*^^ "f -^ certain principal was *:{07.2() for .'} and $312 for ;}| years. Find tl le princi])al and the rate. •2 years, !|f!| 66 1^ I H SI I ' *"^»nLhMS IN ARITIIME IIMETIC. December, issjf, •:57i cents; 112 yards rfnt at ^li jL ^^ ' -•^'» >'''"*J« "annel at cents ; ;J7A yanls tvveed at |(I 12.' ^' ' "^^ ^'"•^'•^ «>'"t'ng at l?! 4. ^iin[)lify : r«)5U2^-Ml?x7i4-**l«-^'4 (^') -iix A X 0-02 X 0-45G y ^ j « of v . ot tho rcKun / •'^^'"' ^^ 'P-^--*''. What is the width *3.C0 H y,.ll„„ ? ' '""'-' "■■'* "'« ""xture may bo wortli unly CLXxlT"'^ " ""'"'^ --irOSOeoS 005904, $705(>;i7 and MDCC- 2. Si"^plify:--/7(3|+9||-)-^/^of-?-i^•l^«J2d. 16s. 2d. 3. Find thevah,eofl7-654 + 4-835 + 6-408. 11 t^a^ ;:rj: !!;!l;^:^z ^z:^^ r ^« r'' ^--^^^ -^^-^ ^t 18 ^ yards tweod at .il 50 i oi f ' ' "^ ^''^^^''^ ^'""^^^^ •'^t ^7 cents • cloth at .<^4.50 ^^'^^' ^-' ^'>^-'^^ «^^g« '^t '^1.75; 6A yards broad-' 5. A merchant t.urcljases sin^ir -.f -^^ ka WhHt Price per pou.u. n.u,, „e ^^51 it iforfer/o'^S'To ^T^^'.il ADMIS.S10N TO lll(;n SCHOOLS. 57 6. Find the simplu iiitcrcsf ..» ^k;; f, 7 per cent, per uiin uin. r 3 year.s, J) nioiitlis, at 7. In what, ti •no will any Hum of cent, .simple interest 1 «■ •*!?l,2(H)ist()l)0(livi(UHl I "i"iK-y • .At what two times 1 Find the si tare of oach lat a watch t' ..f ',",,' ",' '""i afterwards much did he spend i ^ '"^ = ''" ^''*^" ''•'^'l *l'i<>">. How Drrrtnhn; /.S'.S'J. 1. Define the foUowincr terms • ^^w.+, .. i* • 2. (a) Reduce to simplest form •— "•"'••M each i>^t,Ilr::,nt^n^:,:i;;;;':7;[z?-'' ''"-^ > '^^o „„., fortune at first. ^ '^' itrc. i^md the amount of Jiis by ^2 J'"" ''"■•'""'^ ^"^^•" f' ' J5»f 'viU ,„,.ku „ «.cMydivisiW„ 5. Express 3-74!.7« .ui„„to,H» tl.o ,loci,„al „f „ ,,„k «. What will 11.750 f„et„f ,„„.,„,, „„, ,, ^,,,.,,„ ^^.^ ^,,,,,_^^^_ /. Na,„e the u,„t« „f ,„„^,t,,, ji,„„^ ,,„j ^^^,^,,._^^^ ^^^^^___^ 8. F„„l the ™„,le interest „„ 8«,K. f,,,. ;, y,„,, ,, gj ,,„^ ^^.^^ they t„gether HU the ci'sten, / "''• '" "''"' '""" *"' ^"(.7, 7.s'»;, bythe,...i^.,,,„..„irM:'r;":;.!',:?;;L':";;^ ('>/ ihe product of i.mu- numht>f« io «>>- /--o ^., > luunber i8l2, the product of f 1.1 i , / ' '•'^' ^'"- ' ^'»« Hrst fourth. ' ^ "^""^ ''^ ^^^^ '^^^""'^ ^"^^ tl"»J i« i44. Find the 68 I'KOrJUIWSIVK IMIOHLKMM I N AUITIIMfrriC. 2. Maki! nut ;i hill of tlu) f,,|I, *>wi 2H ^■2 yinls tl.iimcl, (If i. WImt will L'lMLiiiis, nt 34.20. Htl exc;!4^u.M?;;.z^l;„?S;i;'n.i;^,rr^: -C!' r ;r" --^ li. l>ivi.l..*|,(KI((,,„|„i,.' \ H .,,„| (■„»!,« ".".■« tlm„ B, H.Hl lwico,>.s,„,,',.|,,;"c ■ ■ '* '""*■ '""■" *'0 work i»"c &t^f','Z''''wl:v"'f'''' r"- ""•' '■'"' -;,„i. how much ,Iou.s B «-i„ I **"y'<-ra race, st.'.i-t.iig oven, liy DecmUm; ISHIi. contain,!™ i',,' fifj !f" »,^:^|^' '""' "'"" ''"^ """'y '"'"-'» U'e msnlt i., muf «."'"" ""'' f"'"''''"' "f ■"•«? -»1 -0025 by the nun, of -9, -02 acre, " " """" " * ""'» ""'''. >'"- »>«"y -.ilos of it wiil ,„ake .(. per tlK.usana feet ? ° '" "'" '""'"'■'' ''"s' •" «112.50 Thet,lr;r;i;r:..';;::,T,!;'.,'',:"'fr "f •"'r ••""• °"™ f-'*2,ono. I^viee ,„ n„.e„ a.s a c,";; T:Z Zl ^L'Sf', ,;;::•„■.' '>-- -^\ nu buy : ^"°' "^^'j 'iow liuuiy cowss did ADMrssloV TO IIKIII Hciioor..s. »» «1« a.i« >t.m a yea,., ,„ Hlu.t .i,,,.. will hi. „.,y |„. „|| ,„„;„ j ...L;^.;:^^;i-'::M"i:::l;;r^---;j:tjv-^ cJt^l™,:!:;\-;y::::;L;;;'t;;^;-;;t:;:ix"''''"'- - i-"..i- "f u,tu:,- c„„ i,„ ,„,„i„ i„ .„„ ,,;„,";:::;::, i::. ',:,',t'„''' ;,■ :;;z 12. A limn h()ii!,rhtH.,i,jintif.y of feasuniw.stMl f.. 1... .i . light. H,Mv ,„ud;»i„:,i;i i7;;,;;.f;,::; I'.rr'-''"'" «■"" < """™ "- 1. What ,„„lti|,l„ „f 51.5 ,li, i,M l,y 5115 ,.ivo» as ,|„„tio„., 5»5/ r.(.-u„l'»ilH.'."' '"""' "•""" '■'"!'''■ "f «-• «•'■ n *". *><-, Sl'O, value of the wl,„l" "mestm^t f*"'"^' '""" ' ' ''"'"'■"■ ^L.-.t is tl.u 1 4. Change ,\ „f J + ~ * to a .si,u|,lo fraction. 5. What principal will anmnnt to *84() in 5 years at 4\ percent ? 6. If 1 ponnil „f tinea.! makes 3 yards of li„en 11 v-mls «-i I how n,a„y pounds wonid nmke 45 ya,l of linen I yard wide" ' w'= 60 PROORRSSIVE PIIOHLKMS IN ARITHMETIC. ni leii 1. Ton conts will 1. '"ly apploH ,iro wortl ions i 2. A December, 1887. I as nuich as u U ozon oranges and 7 dozen will a steamboat man can run 100 yar] go in oi days at tl « ill 10 seconds, Jf, 10 same rate ? w many niilea of July to the Shh of 3. Find the interest on }fi!150 from December, at 5 per cent, per annum. ^- A person borrows monev f..f a ., . o. repays at the end of the ti e t/,n • r'''"T -^^ ^^- I'«'' ^^'"t-, and much did he borrow ? Pmicipal and mterest, ^847. How ■ 5. A map is drawn to the srdo r.f J m«.^ acre, aro .„,„.„...„,„, i^];';. ::i;!:;^fi4;;;',;;'t';;,:: "f '- h... «• A merchant bou«dit 1 (MM) v.,..J. t '""1 »"1'1 S ■>? it .t a |.r,:Ht , f , ;^' tt ":TI t '? "^"*'' " >■■■"■''• the i,oui";rj:,:;;;' !;;* r^nt'iTijr^'f'v?-/? ^ ^ -' ^'- ™- -f each. ^ '^"^ ^-^^"e of the lot; tind the value of ^^-^t^tftr:^L^z^:^s.^-^^^-- water Jidij, 1888. 00,,^ ;l/'i;;;!:M,:;;:;r'i^!S;::;::;i-«f -•«? '-'..•>« -f oat, at«»i buttur at .-SrA c.„L, ... ,'„,,':, '" 't '' "I'l'l-" .'t !<:i.H:, a l„,,.,vl f„J AlnilHsfON TO MKJIt S('riO()f.S. Gl HiH tri N Wl 3. A train bniMinl. 54-Ve.t LI wh\^.^^ ^''^' ^--f '>f a sluugle;i.oingMlouS' ''^'''" -' ^^^^ ^""o'' ^l'^' 'i^-t ruu- .,f hovUo /-""'T'n'"''^"^'.'' nuiMher of men and 8 Ix.v.s • ],e tnvs +1.. Ooys .>().(,;> ;i„(l the men SI. J() ner ,].,v Tl,,. . . I, V^^ ^"^ to all was as mu-Ii as if .. 1 i i^' .' ''^V"'"""'^' ^'"^^ ^'^' I>'"tl manynKUMverrempHecir "^ '""""'•^ ^''■'' ^'^^ ^^^^^ ^ '-^v «• A held whose lei.irth ,s f,, t,s widtli -is 4 f,. 'i * • n acres, 2 roods .'{•> ro.lv • «-], * •/ "'"f". •'■■^ -* to ,i, contanis 2 , - .»us, ..^ rods , what aie its dniiensi(.ns / Mio second man's eioif.l r^ " .V '" '■'^^"*- "" '"-^ tNipital ; man's capitaW i',,iM.iii> .>.»,o. Wlmt was the first Dfcemlwi; JSSS. vocL^'^ImT "^"^^'^'^''^^'•"'•^^•"•f^^^^-tementof six weeks' .-ash it-cciprs , a
    i '^'^'^'' *'i'^'' 1st 2nd ;}rd 4th r)th Oth }ilOS. ! Tl'KH. ^Vki). ; Til 11. «^20.87§:}1.47 27.38: :i().()5 ii>.0() 20.70 2.'{.lt» 17.84 12. (M) Fill, .S3.'{.35 835 00 $20 Ki 28.;{!>, ;u.8;{: 27 v>7 21>.08: .S(;.10 25 4!) Sat. .^48.17 47. :m) TOTAL. 32.73 .'il.80 .'{7.011 27.84 50:, ;!5.55; 28. 10' 5;{.!M " 2(5.07 24.(M)j .•Jl.87 20. K 62 NIOOHESSIVE PnoUims m ARlTfTM^TlC. t I 'f 3. Divide $H2.0() fu.M^iHr 27 men -uwl "- i may have three tin.es us un^dnL eS boy '" '''^''' ''' ^^'''' ^'^^'' »'«» imha^;^:i^t;:Xn;u:.f ^'-^'^ ^-'" ^-'' intUtoNovcnber much per cent, will he gniii / " ^''' ^"^ ^"^"^^ ^^ I'^'ck, how grou;.(3(lr]e.^^^,:^f .^H,;-^^^^ ^^, wid. is built on a plot of "^u^-nJSl;;;;S/in^s how •> monuis at tlie same rate i r July, 18R9. »ill 1! Iiuvo g,„io wlioii ho moots A '( ""'"■*' '"'''-« 4. Tho ciicmiiforeiico of ,-i wlieol i>i 22 .,f if. i- J.4 y^i th;;ryK''ti;"t7:;r '"• ''T'-" ^" ■- -"*• tiiHt period ? "^ ' ^''''^ '^'^'^ ^^« population at the end of I>e,l!;rt!;!".r;;n:wn onat^of S^ Tf ''' '''^ ^^^^ ^->^« the townshipof Seott noa uri^j.^ ^r^^""'"'';''' 'r^'' '''' ^'''"^ '"-!> Jiow nmny acres does it ^^XinV" '" ^'"°''' ^">*' ^^ '» ^^'ItJ^; I ^•..^//"''•'^" f f^n '•■•ivc the use of JS.T. f«>,. •? ,.„„^.. . i'VMv much ft month shall I have to i,-,v f-"... n ^^1 '^^ m.intiis, ".ivc CO pay t(»r the mho of |58,750? ADMISSION TO llFOir SCfK.OLS. 63 8 th f«:t:.,;:3'";!,:;;::';^^rt:;''';'Tr'f"'' '"'■"-«'". ..."sand let V *"'"•"" ^ »''"* »'" 'l'-' l"."l.cr c,«t «t *17 per the c„„.et„c.s of the wcvk i); nddin^, ;::!. i's;;''.?!:'''' "■"' "■■"^■'' Isfc 2nd 3rd 4th 5th 6tli M«).N. $28.7'.) '• 2;]. 87 JO.iM) 29.i;i 18.47 19.02 Totals. 32.2U 2(;.73 34.45, 28.88 54.;i() 27.00 2;:"- -nimagrurHa..iJar; ;{2J poumls of 14 ' *" t to poiiiuls i:JomioeH Of bacon at 1( 111 casli. How much casli does the far . . 'f Hug;ir at IL lai.sins at 18/ cents per pound ; nee ) cents a pound ; and the bala in or receive / ^ ^«_^;^RE««lVl^rH(>HLKMS IN AKITHmEtIC. '"J.'''^''-. \Vhat(li,fjs.u th's n-u/ ' '^^^'''^>^ '^^' '^ r-.^e 5 per cent property renuuns m^sokl / ^ '' ^""'' '""* ^^'''^^ fraction of the f,n-oon crop ; 7iiU acres of .,, "t' « "^ "^'^''f ^^^ ^ 9 147 acres of "f PHsU.re ; Hnu'»i H r II --ipts; add ^: >Z.r^Z:^!t-J^':T'^' ^.'^ ^% -elP^dd^;t IS^^^^^' ^"^^ ^^^^^ 1st 2nd 3r.4I ''>H.47 57.99 <)9.2!> 80.07 4r>.8) J>.'{.r,(J <>-i.42 77.()8 '^VM).;i7;^98.i(} 07.02 51.42 82.!>i: o;j..;<; 72.12 87.311 7(>.8<>| 90. 21 1 07.0.7iK^40.7« 41.05 99.57 70.80 5(5.93 (58,77 24.071 50.()0j H7.9ij 54.821 81.79,! {>4.2(5 80.71 74.93 9(5.57 (50.8(5 ^37.59 70.2(j 91.82 3(5.03 12.72 31.87 .1^9.(51 42.51 89.70 21.90 9(5.07 76.82 (iVo mnrkH is con -* ;;| >,e aU.„„U fo. tkU ,u^.no., u,U„ 'a all tiiK work ADMISSION TO HIGH SCHOOLS. supply for four ,Uys t-xtm. JIov, mZ ., 1 '"^''"l""» "'•'y carry a way bou,„ ; aud .J f.. .el.Ll rate, ^i,!',; nlliraltU i/ ■,■; T/,', 6. On June 29, 185X) I horrniv*.*l «ui km a i 1892. ^vithi„ter;,.at4I^;";^;ll^tT;;,!;:,:;;;.t;;:rTl,::!;;r drainh'^k^gtLti'^t'^e'nts^er'r' ff'T, ""« ?,''"' '"'^ '-■ ""''^T- 6« cent:, pef acrrnL;'' ; .^1 ;:^,' , '^?,^,f X,'-''' 'j ''-'.cl», at rod. apart, and the fir.,t drain run/do tr^enSrl'of'th'rHSir ' A goes at the rate of 4 "S'a^.d B 'S i e, an .o"u " 'ii' ""f "''ti A walk before he overtakes B ( "'"'' '" *'" Deceml>eft iS90. recinf7".Ln1'r'' "'" following sUtement c,f six weeks' cash receipts ; add the amounts vertically and hori/«ntillv »ul the correctness of the work by adding your reluTts ^' '""'" m. 50: $74.08 $57.92 S78.81 73.55 05.43 81.47 80.57 91.32 (54.39 57.95 47.02 64.98 49.171 8,191 03.58 59.29 ( !K).54 70.41 42.8()i Of 04.93 71.4(; 92.78 $51.27 74.23 83.57 54.39 07.44 )3.(J9j ;i0.08 $73,281 30.19! 75.()4' 40.37 j 85.10i 79.31 €)(] pho(;kks.sivk vnoHLKMs ,x viari.MKTir. 2. A what t iH-TM.nsnH A iof his la.Hl, lU of fj itMi roiiiniiicd, aii.l pei-iicru. Find tJi •fCl le roiiiaiiider VH(1 sno fi,i- wliaf he. l.ad Uf of ujiumlKrof acvs he had at first t, at §!(;0 .3. A groClT iiouirllf () cAVi. of til ni.s(df anil sold H wh«»h' (jiiaiitiij' '(• ri'st «"-arw,r^n2.J0; he used 05 lbs ! f •^•> as to iiiakr ]! cent per 11 V much iMTlh. di.l lu> sell it f„r'? '. ju'ofit on was H,e a.LuI.t I'JiT;' ' "' "" ^""•'"'"••'- -'«!., M!«). What If tin. „..„■,.„«. s, M.,', , "";r;^ • ' , ;.'v, r',""" ' "^ "-,--.. .t. It ccst to carinif lliu Ij.ill ( ■" I ' y.inl, I,,, cliosun, ivliat will rod f..,. „i,clu.si„., thi wl,„l,-fi ,' ', ,1 " f"'-d™'in}; aiul Si,;);, a cent, mterc-ht did B pay / ^ ^1^0. Jo. \\ h^t nitu per porLid aiid n^^:!: v'pi^i.ir^f .;;r,::r'^^^: "^.r-^^^ - ^'^^ --^^ the fanner T, yds. of hrnad.lo 1 ^ a ' / *i'*^ '"^-I'chant .sells 8 cents per yd., and 44y;^;i!;';! ^^.^'r'^^.f,:^' ^^'^ ^'^ -dico at makes a pro.St of L'5 per cent u , ; , ■ .T''^^M'^'»- .y(I., and trunsacti<,n^ndhownuidi(' '' ^'"''' ^^'^' "'^^^'^ '>y the Jintr, isni. ADMISSION TO muii SCH0018. 07 c«rr„ctnoss of y„„r work b;;,i;i,:;g\;::U:u|";''''''^' "'"' '""™ "■<> l8t 2nd 3rcl 4th Otll «th Totals. Mom. ^75. 59 82.01 50.95 91.04 08.17 47.80 Ties. $02.08 79.81 49.8.S 75.10 ;M.75 81.14 Wkd. j Thir. : Fri. ! Sat. TOTAL, 859.03 §02.78 807.:{0 891341 48.79; 92.1.'} 81.78 87.171 89.04 40.98 77.03 07.19 47.85 39. ()7 85.94 49.85 : >8i 59.70 93 19 48.77: 79.08 95.79 80.97 98.99 3. Brooiihs are l)()u--• -■" <> ft. eumeut at 10 cents per square yard. '""= " "'"' *'"'■*""' "■■ ^"'di: l:;;Int oVS45':";\;^;r,f;:"?.T"^' ""-j- "> ">.»iy 34 cords of vvdod at *.l .".n bhi., 350 Ib.s. of ti <>^^\^hH. of hayatS15uer j'CT Goni, 4 biWs. of apple.s at $2.75 cents and to whom due .our at $2.50 per cut., 30 11 I- lb. Make out the- aciumV „;ary toil J l)er >«. 10 oz. butter at 10 showing the bahuice. I 68 \h\ PROGRESSIVE PROULKMS IN ARITHMETIC. Note. -Candidates .». „, otherN. TnthoHrstquostionf June, 1892. are to take the first question and our marks are to l)e allowed for F any six ^OHM Hvo umrks ,m.y be a,UIrf tr miatness ^ """'^'- ^ '""^""-n. of i«"K,>t':- ""' "" '""""''"8 account, „«,«, „„„ „,,„,„j„,y^ ._, ' »"« i)ai(i you *10 on account April 8th. ^ ll).s. tea, at 80c. ^^00 lbs. sugar, at 4|c. 45 yds. print, at lljc 24: galls, syrup, at «5c. 12A yds. towelling, at 12Ac. Ijloz. knives and forks, at $2.50. 'it lbs. cheese, at J 5c. 1 lb. 10 oz. lemon peel, at .">2c. per lb. 2. A load of wood 10 ft ln7i"<>»»■ he l«ken fro,., the .„.n of fiq- » <> . . - .065^ and zO^, »o that ,t w.n contain 6.06 an exfcf muA^Hf C f I f p II tl AbMlSSIOK TO tllGH SCHOOLS. 69 111 ^n ^i/^ ^"'J r-}'"^'^ *-^-^*' cllfcting Hoc.untH f„r h physician He was allowed 5^ per cent. ; what anu.unt ,li,l hv. collect ? tees^lvL'lM.nru''!: P'V'f""'"' '^ '^'^•^^'•'^'^.^"^ f'"- ^ir><),(KH). The trus- tecK nave rmilt a .school-houso costing i!!'l,8(X). ('0 What will the school-house cost a ratepayer whose pro- perty is assessed for !S!4,r)(M) ? ^ W NVhat would be the rafr of t^ixation per annum on the whole section if the house were paid for in six equal annual payments, without interest 1 June, 1893. coal at ^b.to per ton. Mow many pounds of coal does he get '( 2. Nathan Cmd sells you 752 lbs. of cheese at ll?c ner lb and receives the followin.r '»■ etc. Fi,ui ti,„ vHi!,l „f ;i;;:'i';„';,l'j;""' *"'"'■ "f "» vuhi,.io,. »• Write the foil, „vi„g in f,j,„r,..s: {«) Fifty tho„«.„„ „i„„ |„„„,,,;„, ,^,,_, _ (I') N,„„ |,u„,lre,| t),ou»Hn..u.„„I ,.„,! ninety „°r' W •;;■'; '■"n,l„.,I,u„l Hovent,™ nnllions ,„„. ninety-three 0. N-;'...".Ire,, .n,, nineteen t.„„.™.,,, f„n, InL.Xn,. |i>l ing liilf : '*"• '"" "' '"■■'!>- f""» ■»«' «n.l the .mount of ,.),o fo„„„. •Millie Isf,, 1894 (I \f Toronto, 488(n.us;;j6 Ibs/wl^at-^Ht'^^^^^^^^ soW to John Scott, full for paynent of aecovrnt, 2«tlf i?,ne "" "^^ ""' ^ '"^^^'i^^ "^ gal W I!:S27^ 2?/S: '-t^^^^ ^^«V -d an imperial pint of water. "^'^ ' ^"'^ ^'^^^^ weight in ounces , bian'l^j:^;^^ ^ the C<.Iun.- HcrcsTO rods IJ» yds. 7 Jee ' Th^^^^^^ "area .f 30 How many feet in length wasit? '^"'^ ""''' ^^^ ^^^«t >v'ide. of ^.3^'^K;:;;rSi: "rjJ ^,V7 ^"^^ «^" *« -^^^e a proht of 4 for 3 cents V "^ '""^^ ^^ ^ ^'^^ •* c^'its and sells a^ the rate 5. A sells goods to R at a gain of lo ^.^ ._^. =^."no goons to (T at a gain of 7l^ner c«Mit"'-^P \ guods. How much '^^ * '*. per cent., G paid aid A pay for them ? Ml sells the > for the AnMJSsrOV TO iiKiii sciloOl, n <». A <,'p;ivi;l-lHtl wliusr -,111 tuiv lias an aiva of 4 acivs contains gravel (o jin nvuia-,'.' .h-pth of <; f,..- ||,.u manv niilfs (,f n.ad JJ feut wulo can be covered fi-oin tli, vil m tlii' kul, if it Ik- spivad on fo a miif. .1 1,1 ili Afay, 18!)4, ho Witli.hvw the principal and simpii' inlcnsf at 1 per cvnt.'ptT annum VVhut finiount did he withdraw / H. A man spent ^\ of jus monry f..r a Iioiin, , -^ ,,i (hi- remainder for cattle, and the rrst for n farm. If the farm cost him 8:5r»7 1, ^h than tht! hous,. and cattle to^rethcr, what did he pay for all ! o , , ^. ,., r.-(^'^) .(\nf\)+(nni5) .>. Of) Sunpl.fy: ^V + d^ "f ^U)- (J of H^) !^ k-H"" /' IVrnlliply ;;.,(». t l,y one* and .livi.l(> tie! | rodnct J.y .(XMKL'M.). ANSWERS. Exercise 1. 1. 2,4; 2,7 ;.V,; 3,7. 5. 2,;n. 2. HJl; njH; 2,i;i. (5. 2, .'{Mr(]. •i- 2, 2, ;{, :U. 7. 9. 4. -m. 8. 3, 7. 1. 3 gal. 2. 14. 3. 9 in. 4. (M) 11.. 1. 14, etc. 2. 24, etc. 3. 1 gal. 2 (it. 4. 72. 1. G4 cu. ft. 2. 175. 3. 33(J ; (572, etc. 4. 100300. 1. 24 ({uarters, 2. 71. 3. 40 barrels. 4. (>3. 3, 7 Iff' 2ff- 1. 2. 3. 04 cents. 4. Exercise 2 5. 44020. (i. I7r.7«;. 7. IH bii. 3 pk. 8. 47. Exercise 3. 5. 11. 0. 729. 7. 70 cents. 8. 135(i«. Exercise 4. 5. 15 ft. (i. 21 lb. /. <) yr. 8. 1081. Exercise 5. 5. 81.50. «. 9.^ pt. 7. $19.50. 8. 4^. Exercise 6 5. i : f . 7. 36948; 247ni»7. Exercise 7. «;. Mill !w. 7. <» yd..') ill.; 1 v,l. L'ff. ;5 ill. ■ U). S-J rents. II. L'7. L704. "'►■ «f.\y. ;ir). 7. «lx,H', -s. Is-'. Exercise 10. r>. O-SJ I,,,.; IO(L- 1,,,.; '•/ l.ll. IOl'-' 7. '27 \i i-d. H. I.'.' 10. ^:i\;, 11. x;;;. 12. 20j^ JO. l4H-,'al. 11. 20i-i>nt,s. 12. I 7.^ 2. 12748715. 4. 4!>.'i!)j|. 1. «iir)}o 2. ^ .'1 90 ae. 4. .,1. 1. ()3.<1. 2. .S hn. 3. *185.V. 4. 02^uouts. Exercise 11. T). Ji!?:{r).io. SO' 7. h; ft. 8. ><2:»i>4 I o- Exercise 12. 5. 8,V <>. . r> ft. (} ill. «. 7M. 7. !B2: 8. 2 ft' U ill. a* 840. 10. #2.70. 11. 18., Ml. 12. S:\1.h:). ::.it. !». 20 I)u. 10. ,••<, 11,. 11. lOci-nfM. 12. i<:\Mil. 5). KJj^. 10. ;i2't..ns. 1 1. l.'i;] oeiils. 12. 108 eu. ft. A!*SWKIl.«|. n 1. ^17. 2. 9, «, cents. :i. 22 ft. 4. 12 l.oys. 1. h;^i II.. 2. «<«>. 3. $2000. 4. 4. 1. IH. 2. r»()y,l. 4. 24 i»limi8. 1. ^)5.7(5|J. 2. 1250. 3. 25 11), 4. 76ct8; $1 ; Jll.75. Exercise 14. (). 10 oiiiits. 7. 2ir>,\ mi. Exercise 15- a. 8580. 7. i!^2l 8. 20 cunt h; 10 cents. Exercise 16. 5. 70.'i NCI. y^\. <). .'{«>. 84 j. ' 7. .^l.'l^'L'. 8. !ii5|82.'50. Exercise 17. 5. .m.50 ; :i^27. 7. 2 men. 8. ()0 cent.s. 1. 48 1b. 2. n. a. $. . 81«>8(K). 10. $'i^. U. 47 ac. 112 s(|. rd. 37 ac. 80 s.i. rd. 12. «!3510. 0. 52 ft. K). (iO marbles. 11. 8yr. 12. $^8.70 J>. !B1(;5; Ji!l80;|155. 10. m. n. 23^11,.; 27-1 lb. 12. J|14. 0. ^4i(;(K<;2.20. il. $1200. 12. 3 hens. «. 2f yd. 10. :!i«i4i)0. 11. 14. 12. 5 yd. 1ft. 5|in. 76 1. «6 ; $o. 2. $20. 3. 1^. 4. $20.10. 5. 2800 1b. PROOHfiSSlVli PROIiL^MS m Altll'HMEtld Exercise 21. ?■ f? r.- - I'^- ^ ^*^- 11- ^'*'^5 *45 ; $.'39; 7. $1.50. 145 ,^- ^ '^^- 12. 9 mi. 73 rd. 2 yd. 9. 44t()n8lGowt. 41b. 1ft « i,. 10. 38. "• 2. 8 cents. 3. $1.20. 4. 9 men. 5. 8 cwt. 72 lb. Exercise 22. G. 105. 7. 30ct8. 8. 3j,9j. 9. 1000 gal. 10. 20cts. 11. 9 8q. yd. Csq. ft. 36 sq. in. 12. $12 ; $8 ; $l\. 1. 2. 3. Exercise 23. 1- If- 5. $98. X' '^^' 6- 4 papers. ?• if- 7. fy>v. 4. 84.80; $2. 80; $2. 8. 24 men. Exercise 24. 1- 775 1b. 5. 84 ft. 2- MH- 6. 48 cents. 3. 70 cents ; CO cents ; 7. 20 ; 10. 40 cents. 8. $6. 4. $1.05. 9 1 10. $1.G2 duo you. U. $17.30. 12. 20 ft. 9. 9 ft. (5 in. 10. $.308.64. 11. 6. 1*. 15 ac. 1. 45 ft. 2. 5 horses. 3. $40(K). 4. 10 rolls. s- mi fftVffij- Exercise 25. 6. 12 hr. 10. 7. 4 lbs. 4 oz. 11. 1957^ 11, H. $1035. 12 V . I. .» 9. 20 cents; 40 cents; "' "" '''' 80 cents. 1. 2. 3. 4. 1. 2. 3. 4. 1. 2. 3. 4. Exercise 26. 1. $1.62 you owe. 4. 72 cents. 2. 91 8(1. rd. 12 sq. yd. 5. 6 min. 8 sn ff Q'7 i a., li IK'J ^^' 7. 5 days. 3. 10 bundles. 8. 18 cents. 9. $435.60. 10. ion.|. 11. o ib. ; 15 lb. : 60 lb. 12. $189. ANSWERS. 7 Exercise 27. 1. 7776 sq. in. 2. 3| lb. ; 6 lb. 3. 2 cows. 4. $9.86. 5. 837.50. 6. 18 ; 30 ; 108. 7. 264 ft. 8. 36 sq. in. Exercise 28. 10. 12 ft.; 9 in. 11. 10«'J68. 12. 80 cents. 1. 3jj hr. 2. 20 mi. 3. 140iy(l. 4. $11925.28. 5. 6 tons 417 lb. 11 oz 6. 14 days. 7. 95 cents ; 5 cents 8. 8 ft. 3 in. Exercise 28. . 9. 20min. 10. 80 ; KM) ; 20. 11. 8227.70. 12. i 1- iV 2. fA. 3. 0546875. 4. |!;]8. 5. 5-501. 6. 70 men. 7. 29-9498. 8. 8360; 8320; 8120. Exercise 30. 9. 95-70236 uc 10. 10 hr. 11. 824000. 12. 15. 1. 0073. 2. 84. 3. 5005. 4. 114|yd. 5. ^. 6. 370-7042. 7. 5 days. 8. 3-993. Exercise 31. 9. 42 ct. ; 43 ct. ; 14 ct 10. 90 cents. 11. -323. 12. .70 hr. 1. -758. 2. 7 days. 3. 1^,. 4. -078. 5. 14 mi. 68 rd. 4 yd 2 ft. (} in. 6. •;}94. 7. 87.<}8. 8. 85 ;|. Exercise 32. . 9. 109 s<|. rd. JO. 10 mi. U. 178. 12. 11. 1. 176-34. 2. J. 3. 20-832 tons. 4. 12 hr. 5. -000010201. 6. 88; 68; 44. 7. mVOm sq. yd. Exercise 33. 9. -08322. 10. 32 ft. 11. 8119.04. lot 1-. jjj. 1 §tiifiK(\ 2. iit' a. 837.70, 4. 2 WGoks. 5. -715392. 6. 54 bu. 7. ^22.90, 8. 34 cents ;). 81.56. 10. 813.50. 11. ^ day. 12. 356 ft. 78 I'ROORESSIVE PUOHLEMS IN AIllTHMRTIC. 1. 7-503 lb. 2. io.-><; CU. ft. 3. 16080. 4. 8hr. 1. 104-5 centH. 3. lOOOl. 4. ^KKK). •2rd. 1. .33- 2. 70 cents. 3. •04()875oz. 4. ;|^14. 1. |il.25. 2. 04. 3. 6 ft, f) in. 4. 3-775 mi. 1. 2. 3. 4. 5. IrtA- 232(»0 lb. 40 per cent. $120; ^50; $',m. 1 Iff 1. 7i per cent. 2. J§3.72; $2.4(5. 3. 'i oz. 4. ^(i ; $12. 5. l()5ra. 1. 50 per cent. 2. iiVA. 3. 100 per cent. 4. 48 ; 30. 5. (5. 7. 8. 5. 6. 7. Exercise 34. 3-84. (J lb. 7-1)2 in. $20. Exercise 35. 1H0(M). 2=1} (lays. $0.35. 90ct.;«Oct;40ct. Exercise 36. 9. -00081. 10. 10r(1.2y(l.lft.0in. 11. $355-()2i. 12. ifA. 0. 10. 11. 12. 5. 5 (ly. 11 hr. 52 niin. 0. 48 sec. 10. 0. 1^ s(|. inch. 7. 50(l<>z. 11 8. $3.20. 12. Exercise 37. o. 0. 7. 8. 180ac.;00Hc ;30ac. 9. 15-5125 cvvt. 10 *117. ll' 25(MK). 12. *2 1-0924. 15 yd. 5-049. $27. 4 days. 3 })k. 1 gal. 2 qt. S72 ; $108. 50 cent-s. 4 men. .0078125. $12. 3-29. Exercise 38. 0. 22.iisec. 7 •■' " '• 4 00- 8. 3 mi. 9. $3. 10. 0.^yd. Exercise 39- 0. 27 days. 7. 04 per cent. 8. 175 Hc. 9. 5 i»or cent. Exercise '10. 5. 20 cents. 0. |?1 .54 7. $81 ; $45. 8. $381. 11. 12. 6 per cent. 4hr. 2l,», min.; 4 hr. o4y", min, ; 4 hr.5i\min.; 4hr. 10. 11. 12. 38 j-^ nun. 7 o'clock. 4 Hcj.rd. 1 H(j. yd &q. ft. 9. 25 cents. Hi. $.'U"».80. 11. 12. $<}« ; $5 $3.50, 1. 2. 3. W^'V AN'SWKUS. 79 Exercise 41. 2. il2-HH. 3. $i.m. 5. $150, (5. 81 11) 7. »; . 4. 5- 8. 44. 10. 12 weeks. 11. .SI 75. 12. 28 cents. Exercise 42. 1. 3. 4. 8750. S20!>5.82. •S<'>78. i>. 0. < • 8. J?0(>. 84. 5i<040. $(J0. 1. tut* 3. 4. 00 C'Mlts. 5? 1 108.80. ^1.44. 8200. 5. 0. < ■ 8. Exerc 12 mills *> 1 «> (tuvs. .92. 2(). 12 rows. 1. o 3. 4. 5 ft. 25 -X. Exercise 44. 27 ^2' o. — <»/>• 00 cents. 1- t ■ 8. .•^1.50 : 4 20 l,r. 0. '. 10. §17(M). 11. 12 < 12. KM) cu. ft. *•>. 12 cents. 10. '.J.35 A.M. 11. 33.'j per cent. 12. 20 ; 21 ; 41. ». 567o 10. 1500 11). 11. 85450. 12. 22.^ hu. 1. .822400. 2. *8.40. 3. 848.75. 4. 1 ft. 11 in. 1. 373. ^ . 2. 805.40. 3. 20 °/. 4. 824(M). Exercise 45. 5. 20 cents. 0. I 7. lOOt,^•l]l. 8. 00 ,. Exercise 46. 5. OH < ; 82. 0. 4 hr. 7. .80 ; 83.50. 8. 8 1. .'55. 0. .840 : .8.50 ; 8H0 10. 20°,. 11. 4 years. 12. 14f 0. 1 10. 10 cents. 11. 04. 12. 40 cents. 1. .8000. 2. ^y iir. 3. 3(> cunts. 4. 88«)40. Exercise 47. 5. OOij per c.Mit. 0. ^?«lHys 7- ; >• i;t I cent. 8 ^^:.0. 0. .'JO (-nnts 10. 2|lh.;.3|ll,.;2^1l). 1 1. 24 [)er cent. 12. lyOO lb. 80 PROORKSSIVE PROHLKMS IN AKITIIMKTIC. 1. 2. :i. 4. 1 1 12 mi. «46 1 S' Exercise 48- ^- $44. 0. ^140.80. C. $1.20;40ct.;20ct. 10. 102 lb.; 120 1b. 7. '«^10(). 11. 345H. 8. 2 ft. 4 in. 12. 50 II). f 257. (JO. 5. 2. 80ct.;.«!1.20;$1.50. (;. 3. ^1.08. 7. 4. 126. 8. Exercise 49. $28.80. 50 conts. $04. 8f hr. Exercise 50. 1. $15.00 + . 2. 4 mi. ; HI mi. 3. $7(H). 4. $850 ; $200 ; ;?0(M). 1. $11M).10.^. 2. 30 cents; 24 cents. 3. 4 years. 4. 3(5 lirs. ; 45 hrs. 5. $2400. 1. $140.00. 2. 10; 24. 3. 10 year.s. 4. 16 in. 1. $6(>«.88. 2. 173}^ lb. 3. $.398.51+. 4. 105 acres. 1. $080. 2. 4({Ib. 4. $18. 6. $8.44. 5. $22.()8|. 0. 7 pints. 7. 40{M». 8. 20 cents. Exercise 51. fi. 12j^'g sq. ft. 7. 7 |>er cent. 8. 1141m.; 100 bu. 114 bu. Exercise 52. 5. $24(M>. 0. 8 (lays. 7. 8 per cent. 8. 00 cents. Exercise 53. 6. (»0 ctints. (». $11200. 7. 10%. 8. 24 days. Exercise 54. 0. 40 cts. ; (>0 cts. 7. $17.(54. 8. $3a.50g. 9. $33.75. 0. $737.87 10. f mi. 1 1. 35 per cent. 12. 100 sheep. 0. $24(5. 10. (5(5 rd. 11. 3 years. 12. A33dys;li(i6dys. 0. Oi per cent. 10. 20 cents. 11. $015. 12- A. 1 2 0, Ojl per cent. 10. 2420. 11. 30 years. 12. $7('M). 0. $40. 10. $(50. 11. 70 cents. 12. 1200 yd. 10. 75%. 11. $(50. 12. Mary 30 ; Jane 12 Ellen 21. I ANSWKRH. 1. So 1.25. 2. »(K). .'1 Dec. 1, 1894. 4. 00 cunts. 6. 8. Exercise 65. ^UXMJO. 7 mi. .'iO cents. 0. ?4rH>. 10. *I8 ; 6.U 11. 22 mi. 12. 15d()z. 1- 21]%. 2. ^ mi. :i. 1] gal. 4. 14 per cent. Exercise 56. 5. 4.}, ac. «>. .'U)ini. 7. r>() lie. ^. IT) cents. 0. 81)."). 70. 10. 45 H). 11. (» in. 12. 21 mi. 80 rd. 62 PR0GKKS81VE PHOHLEMS iJf ARlTHMfeTlft. ADMISSION TO HIGH SCHOOLS. 1. Book ; 5783, Remr.5. 3080. 6. 2. 1031] t(.ii8; ^3300. 3. $!2m)27-84i. 7. 4. ^319. 37i 8. Jvne, 1883. .•$14 5 1. 'J. 441 (1 •()i\Ai)\ H»(2SS() > •37nfT- •'• W'^'+.^l- J 33/, cwt; lOOcwt; 10. 4 hr. 21 V, min. ; 13^ cwt. 4 hr. b^^ min.; $.3.56]. 4 hr. 38A min. $5.25 + . December, 1883. 1. 720300, Remr. 128] 2. $3(5.08. 3. Not so ; 9^\ times 4. $508 ; $438; $254, L.5. (). .7. 15. •0014997. $14.56. June, 1884. 8. 2931 yd. 9. I 10. $4.81 + . 1. 7070. 2. ]49()88 ; 119. 3. -00278 + . A 72 1 . 1 5. 0. 7. $8.76. 281 hr. ; 36 hr. 48 hr. December, IS84, 8. 5000. 9. $110.88. ; 10. $24.04 + .; $240; 8%. 1. 80407089. 2. 221. 3. $12().805f. 4. (a) 22H|^; {h) 5. 6. 7. 111 ft. 7 days. 25| gal. June, 1885. 8. $19.16 + . 9. 4 hr. 19i\ min. ; 4 hr. 24 min. 1. Book-work. 9 12 61 3. 28-89927017. 4. $93.39^. 5. 0. 7. 8| cents. $43.83|. I63 years, December, 1885. 8. $266i| ; $933|. 9. 3 hr. 16,4 n^iij . 3 hr. 13}^ min. 10. $90. 1. 2, 3, 5, 7, 11. 2. ^j; 28152. 3. $1890. 4. 6^. 5. 6. 7. •000372. A yard ; a day ; a sovereign. 8. $132. 9. 4hr. 1. 2. 3. 1. 2. 3. AVSWEIW. 83 1. 2. 3. 1. 2. 3. 4. 5. July, 18S6. 125t028(),V; 478'>nn 4 stld. . 'in c i $52(>.70 52 timoH, •00)1. 1] mi. 8.'i7.5(). 30 cows. •1 5rt' <). $2()0f) ; Hiu'rceiit. H. J(»"> yd «. !i^424 ; ^:U\4 ; ^212. 1. 2. 3. 1. 2. 3. 4. 1. 2. 3. 364025. 8300. 81000. 205. 2700 mi. $3.(M). 8700. Book -work. H. 5 yours. 7. 27eonts. 8. 12. , ijurs. /m/*/, /.SW7. 5. 8H85.713. 6. 12 1b. Deieniff.r, /,V,S'7. 5. 25({(»Hc. «. First m.-iii ; 827. 7. 901»,'r oz. 8. 8720. J"ui»/, /.. 14580 .sliingles. Vccemhrr, ISSS. 1. 81169.36. 2. 82.80. 3. 850.70; 825.!K). 1. 70 barrels. 2. 8117.08+. 3. 24 mi. r.s. 1. 80 ce^ 2. 80.10 + . 3- 54.^«i| mi. 4. 8349.71/y. 4. 815.07 + . 5. 83,'j per cont. 0. 3(527 cords. Jnlij, 1SS9. 4. 4^ ft. 5. l.TUO. 0. ()()480 ac. December, 1S89. 5. 8320. «• 170if!?ya. 7. 82.2f». 10. A No. is oxHctly div. I)y0ifthosinn • )f its dij^'its isdiv. by with»Mit hifiv- ini,' a romaindor. 11. 84 lb. 12. 800. 7. 8250 loss. 8. 8| months. 0. 0] per cent. 0. 4!»28cu. ft. 10. 8I2«M>; i^t.HK). 11. 77UO, gal. 7. 12 men. 8. 24 rd. by 18 rd. 0. 8l2!>;i7.50 7. 817.50. 8. 307g sq. yd. 7. 84;{.75. 8. 8448.80. 0. 81171.41 8. 84070.10,',; ^.^1 0. 20+ percent 10. 82048.78. Si rnoORKSHlVT- I'KOIJLKMH IN AKITHMETIO. July, 1S90. 1. 1H22I.S.47. 4. |, 2. 9 ytfars. !«<»«. 3. 48882 c-u. yd. r». i?«;7.20. (5. «!18.47 + 1. f24»r>.08. 2. KHhic. 3. 11 cents. 21 2 i!ji. from K. 1. $254.3.22. 2. Pi)2.40. '^. 44 per cent. 1. $.'{|.8!>A. 2. (a) ;i?.S.40/j ; (/.) 3. $4y.t)0. 1. 221>3.'{.i Ih. 2. You owe Curd $m7i. 3. 5. 4. 6. 6. 'if ml. 7. 4. 5. (). 8170.22 + . ^440. 2(KM> sheep. |!25()0 ; $30()0 ; Jw/tc, 7^.9j2f. $81.(58. $54.%. ^8. •11. JB204. 148i mi ^'i5."20 1. $2!M(5.4f)j^n. 2. 20 rf"'„V.. <;z. 3. 1087 ft. June, 1894. 4. ()2(M> oranges. 6. $.il26. (5. 27 mi. 7. 10 years. 8. «)0 (lays, y. 20 mi. 7. $23.25. 8. 5 J per cent. 9. The merchant ; 60c. 7. KHJ; 75. 8. $8(». 9. 80 cents due B. 8. $.'{«;8. 9. ((() ^54 ; (h) 2 mills on i. 7. 45 cents. 8. $1750. 9. Book-work. 7. $881.21 + . 8. $2261. 9. (a) f ; (6) 108000. Di ONTARIO EDlfOATlOX DKPAIITMENT EXAMINE TrOX PAPERS. Public school Leaving. June, ISns. 1. (a) What is meant by tho prime fiicto. mimlior ? (b) Find the prime factorH of VVSM), 22()rA 1 L'.SJi^a, ami (r) By means of the prime fact<.r.s Hiid their (}.(\M. and L.T.M. 2. A man owned !».S,!»4(> Hank Sun-k which paid.t yearly divich-nd of 4i per cent. lleMc.hl out at lOUi? ami invented the proceeds in Michij,'an Central Stock at 74,^, j.aying a yearly dividend of ;i por cent. By how much was hi.s yearly income changed i)y the transfer # 3. Find the proceeds of tile foll(»wing note: $2,4()().00, Hamilton, Feln-nnry .^rd, 1S<»2. Five months after per cent, per annum. Vance Allkn. Discount. .1 May 22n(l, 1H!)2, at 7 per cent. (Year^^Ofi days.) 4. A machinist sold two seed-drills for equal sums of money. He gained 25 per cent, on the one and lost 25 per cent, on the other. His total loss was .«9.50.25 per cwt,, charging 2i per cent, for buying. How many cwt. of pork does he buy and what is the amount of his two commissions ( B5 MICROCOPY RESOLUTION TEST CHART (ANSI and ISO TEST CHART No. 2) 1.0 I.I 1.25 4 5 2.8 ■ 50 3.6 40 1.4 2.5 2.2 2.0 1.8 1.6 A APPLIED IIVMGE inc 1653 East Main Street Rochester, New York U609 USA (716) 482 -0300 -Phone (716) 288- 5989 -Fox 8r, PROGRESSIVE PROBLEMS IN AHITHMKTIO. 0, Find the cost of the material rocjuirod to fence 2^ miles of railway (both sides), posts placed 8 feet ai)art, an 8 inch b"i.se 1 inch thick, a 2x4 rail at top, and (i strands of wire. The posts cost 12.\c. each, the lumber $14 a thousand, and the wire 4c. per lb. (A lb. of wire stretches one rod.) 7. (<') A circular cistern. 8 feet in diameter and feet in depth, is tilled with water to the heijn;ht of (} feet. How many ^'allons of water in the cistern ? {\ cubic foot of water weighs i,()(MJ oz., and a gallon 10 lbs.) (/>) If a sphere whose diameter is 4 feet is submerged in the water in the cistern, how high will it cause the water to rise ? 8. Add vertically and horizontally the following statement of eight weeks' cash receipts : MO.N. TlTRS. Wkd. Tnt'R. 1 Fri. Sat. 1 Total. 1st .... $^,m-2. !W n,'.m 76 !*(j,7(i0 (i8 .*i,m>8 91 ifl.OiK) 6.1 * 43 68 '2n(l ... ;tit(i 74 (i.nw :i7 8()4 .'{9 !>64 2( l»i7 (19 1,864 86 3rd .... i,7()8 6:i 4(i7 80 2,o:u, OH 3,10.'} (13 '191 83 78.-. 97 4th .... 3,!)78 29 .543 (K! 8th .... li)4 87 .3 8.5 7,«43 82 OS.*) 38 765 42 39 67 Total .. ■ June, ISOS. 1. (a) What is meant by a common njultiple of two or more fractions ? (6) Find the L. C. M. of 2], 3§, 3^§, 14, |. 2. Express in decimals accurately to seven places : 1 1 1 1_^ 5 X 5^ 7 X 5' 3. A boy can run six times around a circular plot of ground in 52 seconds, another })()y can run nine times round the same j)lot in 80 seconds. If they start from the same place at the .same time, and run in the .same direction, how many refunds will each make before the faster boy overtakes the slower^ 4, A clerk pays ^7.50 taxes on his .salary. What is his total salary if $400 of it is exempt from taxation and a 2h per cent, rate is levied on the remainder ? I i^UnLIC SCHOOL LKAVtsrj. 8f 5, A iiiilli^r Ixmght 20,«KX) imslicls (»f wln'ut •li.l luul it iiisurod for ^ of its cost, ut 1 j',^ I'ercent., jtayiii^ u pivinium of .^I.'}(). At wliat prictt jkt biislu'l nuiHt lie sell it to yuin "JO per eeiit.^ <». For wli.it smii imist a note he drawn on .Inne 1st, IS!»;I. pay- Jihle in !K> days, so tliat when disi;i>untt^d on ,Iimu' I4tli at .S per cent, the proceeds will Ih^ 8717.20 >. 7. I own }?*'•, 0 of iJank Stock, payinth), <>u tlu' following ledgf account : Dr. Jan. 12 Feb. Mar. 8' April 4 May 12. 1803 Feb. 18 I By Cash Ai)ril 20 June 24 % r. 100 (K) 150 00 312 00 9. A S(|uare plot of grtonid that contains ,"„ of an acre is covere) in rate per cent. 4. A storekeeper on the 1st Marcli, 181)4, bought goods amount- ing (at catalogue prices) to $840, on which he was allowed succes- sive discounts of 33.\ per cent, and 5 per cent. The account is pay- able in 00 days, after which tiuu) interest is to be charge '», for $:i()(H), pay- aide one-third cash, one-fourth on the 1st of February, 1804, and the balance on the 1st June, 1804. Find the equated tinu; for the payment if made in one siun. • (►. M invested money in 3 per cent, conscdidated stock at 05 and an e(hIs amount- lowed succes- ccount is pay- I'ged at 7 per ,'$10(), How )r ^{(KK), pay- ry, J8U4, and il time for the d stock at 05 mual dividend lollars a year liar shares of to be 6 feet ng for :\ brick cu. ft.=:24|| long and 5 ft. be capable of 2 inclies square fngth being 27