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:X--^^- 
 
 
 
 iNSWERS AND SOLUTIONS 
 
 TO 
 
 Prize Problems m Arithmetic 
 
 BY 
 
 W. H. BALLARD, M.A., 
 
 Inspkctor ok Public School-, Hamilton, 
 
 AND 
 
 W. J. ROBERTSON, B.A.. LL.B., 
 
 *1athematical Master, St. Catuarinks Cclleoiatb Instituti. 
 
 '•^=:^==T^ 
 
 Toronto : 
 W. J. GAGE it COMPANY. 
 
 i 
 
Entered according to the Act of Parliament of Canada, in the year one 
 thousand eight hundred and eiq-htv-ax, by W. J. Gage & Compant, in 
 the office of the Minister of Agncmmre. 
 
 1 
 
HINTS AND ANSWERS. 
 
 1. (1) 1760, (2) 7000. (3) 57(30, (4) 4S0, (5)437:^ («) 
 1840, (7) 040, (8> 128, (9) 10, (10) 1000. 
 
 2. A number is divisible by 2 if the last digit to the 
 right is divisible by 2 ; by 3 if the sum of its digits is 
 divisible by 3 ; by 4 if the last two digits are divisible by 
 4 ; by 5 if the last digit is or 5 ; by if divisible by 2 
 and by 3 ; by 8 if the last three digits are divisible by 8 ; 
 l)y 9 if the sum of its digits is divisible by 9 ; by 10 if the 
 last digit is ; by 11 if the ditlerence between the sum of 
 the digits ir* tho even places, and the sum of the digits in 
 the odd places, leaves ik; remainder when divided by 11 ; 
 !)y 12 if divisible by 3 and by 4 ; by 15 if divisible by 3 
 ;ind by 5 ; by 25 if the last two digits are divisible by 25. 
 
 3. To square a number ending with 5 : remove the 5, 
 luuldply the number left by the next greater number, 
 ih?n place 25 after this product. Thus, to square 1.25 : 
 multiply 12 by 13, their product is 156, and hence their 
 >(iuare is 15625. Similarly, we find the square of 9995 by 
 uiultiplying 999 by lOOC and placing 25 after their product, 
 giving 9!M)00025. 
 
 8. 6000. 
 
 4. 
 
 The factors are 3, 7, 11. 
 
 5. 
 
 $2000. 6. 3-y, ra. 7. 177 lbs. 
 
 9. 
 
 48 rods. 10. 10. 
 
 
 11. 
 
 1. 
 
 1750. 2. 21. 3. 21 cents. 4. 
 
 5. 
 
 1.05. 
 836.50. 
 
 6. In every 400 consecutive years there are 97 leap 
 years ; the years, such as 1900, ending in 00 and not 
 being divisib'e by 400, not being leap years. 
 
 It 
 
« Hints and Answers, 
 
 7- 124, omitting Ist July. 
 
 8. 03 cents. 9. $9.00. 10. 31 in. 
 
 III. 
 
 1. 14,V 2.7200. 3. 33 and 21. 4. 999 at least. 
 
 5. Not necessarily. G. 10. 7. 13. 8. $22. 9. 88 
 10. 3448. 
 
 IV. 
 
 1. 5G. 2. 4 days. 3. $18.00. 4. 42i. 6. 10. 
 
 6. 0^. 7. 400. 8. $1.20. 9. 494. 10. $125. 
 
 1. $19.20. 2. The latter. 3. $3.75. 4. $2545 j*-. 
 5. 3800. 
 
 0. Horse, $99 ; buggy, $42 ; harness, $18, 
 
 7. $38,40. 8. 29 in. 9. $3.15. 10. The second. 
 
 VL 
 
 1. 12. 2, Butter, 18 cents ; eggs, 9 cents. 
 
 3, $0.80 in this question should be $4.80. Answer, 15 
 times. 
 
 4. More. 5. 22. 0. 13 miles, 200 yard'^. 7. $259. 
 8. The second. $5.55. 9. $2.85. 10. 6| lbs. 
 
 VII. 
 
 3. $7.04. 
 
 1. 4 feet. 2. $78.29^. 
 
 4, 103 and 51 yards over. 
 
 5. $7.20. 0. 30^ cents. 7. 2520 rods. 
 9. 3|i lbs. avoirdupois, 10. $110. 
 
 8. 20. 
 
Hints and Answers. 3 
 
 VIII. 
 
 1. 74 ft., 11 in. 2. 149 ft., 10 in. 3. £300. 
 
 4. 5 o'clock p.m. '24 miles. 
 
 5. 543^. 6. Christmas D.»y. 7. 535G800. 
 
 8. 33 feet. 9. 237000. 10. 1 18£ tons. 
 
 IX. 
 
 1. 1785. 2. $17.50. 3. 19. 4. 833. 5. 8*08.90. 
 
 6. Between 61 and 62. 
 
 7. 20 cents. 8. 32 ; 36 ; 40. 
 
 9. A, $16; B, $18; C, $20. 
 
 10. A should pay $16, B $18, and C $20. 
 
 X. 
 
 1. 10. 2. linch. 3. 9012^. 
 6. Cow, $25.20; sheep, $3.60. 
 6, 110 miles. 7. 133 tons, 250 lbs. 
 $1.54 9. $9. 10. 33300. 
 
 XL 
 
 1. £16. 19s. 0}?fHd. 
 
 2. ^1 of a half-crown. 
 
 3. ^ of ^ of ^\ ci the vessel=-5^^ of vessel is worth 
 £350 .-. vessel is worth ^s. of £350r-£19800. ^j of Jj of 
 vessel is worth -^j of iV oi 19800 =£150. 
 
 4. No. is : 18-T«5 of /j+f of 1=17^. 
 
 5. 8s. 9d. 6. £281. 33. 6d. 7. 
 
 •J 3 
 2T' 
 
 •65740. 9. 286^ seconds. iO. 4994 yards. 
 
 XII. 
 
 8. 2s. 11 LJ. ; 
 
 1, 99.751. 
 
n 
 
 4 Hints and Answeks. 
 
 2. First obtained ] runs, each of three others X run.s. 
 each of two others ji. .*. first G obtain 'H ; remainder J--' -^ 
 3«J runs. Wliole i:innber=120 runs. 
 
 :J. Rent paid in barley, £180; in wheat, £180; m 
 cash, £180. Number of quarters wheat = i;i804-48s. - 
 To <iuarters = GOO bushels. Number of quarters barlev = 
 £180^ 30s. =120 (iuarters=0GO bushels. 
 
 4. 2] ;| of half-a-crown. 
 
 5. Master owns .ij of « of >!=* of ship .-. his share will be 
 I of ;? of £25000=.^4lG(;;i. 
 
 G. C is to have 2— (;i f j])^?. ,^, of a chest. A buys « cf 
 so = A **^ ^ chest from C .-. A now has i-\-^K = i'} „f ■, 
 chest, B purchased from C ,\ of ^i = /;.-. he has now 
 # + is = rju = io of chest. C has still ,\ of 4^1=,! of a 
 chest. 
 
 7. 2^ bbis. beer=36x23,=90 gals. =720 pints. lie 
 put 5 of a pint in one to the pint in the other . . for every 
 1| pints contained in the 2h bbls., 1 pnit was placed in the 
 
 larger division, i. e., ^., of 720=f of 720=432 pints ; in the 
 
 smaller, § of 432=288 pints. 
 
 )12 
 
 8. -^1 of A's = 33. ; of B'8=23. ; difference, Is. 
 
 2-* 
 
 -^8 
 
 of 
 
 4f 
 
 ls.=k. A has now 17s. 6d. ; B has 12s. 6d. J. of s ^f 
 17s. Gd.=l]s. V of i of 13s. Gd. = 1415s. 14^ ^s.+Us: = 
 IGj^^s., and I of ^ of IG^V- =8.\,^.=foi .^'s. -" ^ * 
 
 9. The first can do f of the work in li days .-. he can do 
 the whole work in ^ of 11 = 17-^ days, He does in 1 
 day H^g- of work, and in 1.5 days ^f of work. The second 
 man does remanuler J-| of work ni 4 days .'.he can do the 
 wh»)le work in ^ !: of 4=27-ilj days. 
 
 10. Selling price is jj- of oOs.^55s. Throw off .,'. of 
 55s. -2;^.s., so receive 52] s. ..gain is 2]s. per watch. " On 
 503. gain 2]s. .-. on £100 gain is £4^. 
 
 XIII. 
 
 1. $19200. 2. $12. 3. $8.02rV 4. $3. 28 J., 
 
Hints and Answers. 
 
 6. $13. 78 J. 
 
 6. f['^ left, worth $15000. 
 
 7. JJDGi ;•'/., lbs. 
 
 8. Wheat, 1081-;^ bus. ; rye, 627] 1 bus. ; oats, 505 J, 
 bus. 
 
 9. 4 of each. 
 
 10. ^^jof ^ of .stock=j"j of stock injured. ^•"\j of .[ of 
 stock=:^'^ of stock uninjured. :^*) of stock cost §5400 .•. 
 4^^ cost $1800, and \{\ of stock cost .S7200. Received for 
 nijured goods .'. of .':<li>tiOO=.so:!<H). Total receii)ts= 
 $5400 + $U;iOO = $117<)0. Loss^.sTl'OOO - .^11700=$00oU0. 
 Merchant's 1oss = y'j of $(iO;jl)0 = $ooU18.75. 
 
 XIV. 
 
 1. loh francs. 
 
 2. A can do h work in 1 hour. B can do | of />=;,' in 
 1 hour. C can do ^ of v;ork in 20 niinutes = ^ in 1 hour. 
 A, B and C can do o-[-i' + ^=2 of work in 1 hour, or 
 whole work in i of an hour. 
 
 3. ^-}. 4. 3i days. . 
 
 5. 15 men can reap Held in 9 days /. 10 men can reap it 
 in i\''o-=12L' tlays, and ^ the held in ^ of iaA = G| days. 
 
 6. 15 pence. 
 
 7. Simplify fraction. A's income is T^Jof B's, i.e., as 
 :^21 : 700. B spends "455 of income = £3«i4. Whole 
 income ==^^V6^."^-=£800. A's income is i'o' of 800 = 
 £'3GGt^. 
 
 8. 
 
 •083 
 
 . 9. A gets ? marks. B's -2 (A's-C's). C's=3 (B's— 
 D's). D's=i(A's + B's + C's). E=.i (A's + B's + C's-D's). 
 C's = 3 (B's— Ds)=3 {B's— i (A's + B's + Cs) |=--;^. B's- 
 ■J A's— f B's—:- C's.-.^ C's="-? A's—:;- B's. C\s=^i B's— 
 ■i A's. Again. B's = 2 A's-2 C's = 2 A's— 2 {■• B's-t- A's) 
 .-. 11 B's = lG A's. 11 B"s = lG times ^ of marks'.-. B's=';Jr of 
 marks. Substituting values of A's and B's in C's e(^\ia.- 
 
 i\ 
 
6 
 
 Hints and Answers. 
 
 tion, wehaee C"8 = J',. Substitutin<r in D's we 
 and in E 8 |g, therefore E is first and B second. 
 
 10. See Arithmetic. 
 
 get 
 
 3Q 
 
 XV 
 
 1. £44. 17s. 8.]2*d. 
 
 2. A's wages for 351—22^ days=B'8 wages for 22i 
 
 days.-.A's wages for 38i days=B'3 for ^^^x38i = 59i} 
 days. 1G| ^ *"• 
 
 3. G times. 
 
 4. A in 2 clays does as much as B in 3 .-. A in 9 dava 
 does as much a« B in .;! x \)=m days. B in 5 days does 
 as much as C in 4 days .-. B in 13i days does as much as C 
 in 1 of 13^-10_^ days. 
 
 5. First number in 3 hours mow 4 acres, or 1^ acres in 1 
 hour feec.nd number in 5 hours mow 8 acres, or !■} acres 
 in 1 hour. Together they mow li+r»=2[* acres in 1 
 hour they mow 11 acres in (lH-2}i) x il=.3| hours. 
 
 C. Togetlie- A and B have 4 times as much as B has. 
 iJ wins i of 3=1^ times what he had at first, and now has 
 2^ times what he had. A must win back h of what B had 
 at hrst, or ^-^2^=^'^ of what B now has. " 
 
 7. $462^. 
 
 8. A does f in 4 hours, or ^ in 1 hour. B does | of I 
 -J m 1 hour C does remaining ^\ in 20 min., or i in 1 
 hour. Together they do HHi=i1.=5of ^ork in 3 
 hour .-. do all in 1^ hours. 
 
 r>. 
 
 £504. 
 
 10. Part left in each hour is \-^=\\ of cistern .-. whole 
 cistern will be filled in 3^^^ hours. 
 
 XVI. 
 
 1. £5. Os. liad. 
 
 2. B Sf^d. ; C 29fd. 
 
Hints and Answees. 
 
 7 
 
 4. ^^ lost in washing, ij of remainder lost in snieltinij 
 :.^jf of remainder is pure. jVr «f io "^ ^^^ >^ Pi'^e = ':'/, J) 
 puie metal. HI'.S <»f ore=500 
 
 l9G8.i;-,i tons. 
 
 ton8.-.ore=^"'Jor^''--= 
 
 5. 8T«id. G, 084. 
 
 7. Number of female adults ^j*^^ of population 
 i? of /jy— iV of p.ipulauon. Adu'.t8 = 
 
 I • 
 
 > 1 5 _ 
 . ^ f T- 
 
 5 1 fir. 
 
 Males 
 of 
 
 population -22815*^10. Population is 22815210 x i^J = 
 37,710,528. 
 
 8. 123. 0. £80. 
 
 10. 254,500,885?. square miles. 
 
 XVIT. 
 
 1. 12i thalers. ^. 1*00. 3. 132. 
 
 4. A receives 1 of £807. 15s. —£128. 5s. B receives j 
 of £807. 15s. =£508. 10s. C receives l—(H-r;;=l—^^= 
 ^y of su!n. 
 
 5. £4, IGs. G. 22. 7. 4s. 4id. 
 
 8. Difference between shares of two sons=/y — ^-^ of ]^ 
 
 =^-:I-Ii = hU-:Ui = :-ii ■■ :'^i ^^ property 13 £514. Gs. 
 8d. Whole property = -V-,,' times £514. Gs. 8d. Widow 
 receives \l of |^ = ir.{ of property — .^Hjof ■',--/ of £514. 
 Cs. 8d.=£1270. l3. 9i>d. 
 
 9. Loses I of property, retains |, recovers I- of ,\, so has 
 now 5 of ^ = 2u of original property. .Vt^ain loses h, aiid 
 retains ^ of his present property—^ of /\^ of original 
 property =4^(j. As his debts aie ^\, he can still pay thcM 
 and have ^j J-^ of original property left. 
 
 10. £4. 153. 2^ffd. 
 
 XVIII. 
 
 1. 40. 2. 120. 
 
 3. 3jV 1^- avoirdupois -^§os ijrs. =I!1<J« x ^-V^j lb. - 
 ^^VV lb. troy. .V lb. troy + ^V-"^^. lb. troy=fVT '^>- ^^''*' 
 Also similarly 1V4 1^- troy=r. ,i^'^ x 57G0 gi's. = iV4 x :;•;;;;; 
 lb. avoirdupois =iVV ^^* avoirdupois. 
 
 I 
 
8 
 
 Hints and Answers. 
 
 4. ^108. 5. 902 bushels. 6. 32 scholars. 
 
 7. 48 pupils. 
 
 8. A should receive I of 'i of 845000 = $21 000. 13 
 should rco.'ivo i^ of f' of $21000 = $15000. C should 
 receive $0000. 
 
 0. Amounts bequeathed to A. B, C and D=^ ,'.. + |4 ,'. 
 -f^ = H-; of property .-. ^V amount beciueathed to E=$550,' 
 and whole property is 24 times $550= $111200. 
 
 10. $0.i}3?. 
 
 XIX. 
 
 1. l^Vi,- pints per hour. 
 
 2. 1040, ;'iV miles. 
 
 3. 24 miles. 1 hour, 44 minutes, 10 seconds. 
 
 4. A can mow ^ of the meadow in 1 day. B can mow 
 I of the mead(»w in 1 day. T(»gether they can mow | + | 
 =/^ of the meadow in 1 day. They can mow the whole 
 meadow in V- days = l^ days. 
 
 5. 1/,. days. 
 
 6. The waste-pipe will remove ju of cistern in 1 hour, 
 while ;l^(j of cistern Hows in per hour.*. ^^^ — -u) =?!'() of 
 cistern is emptied per hour ; whole cistern in 60 hours. 
 
 7. A can mow ^ in 1 day ; B l in 1 day. Toi^^ether, 
 mow./^+i = l^- in 1 day .-.mow whole field in ^^ = 2]^ 
 days. 
 
 8. First fills I in ^ hour, or whole cistern in Ih hours .-. 
 J in 1 hour. Second fills f in h hour..^ in ^ hour, and 
 whole cistern in ]; hour, /. c, if cistern in 1 hour. Both 
 together fill I + 5=11 + i=J^Mn hour, or whole cistern in 
 ,".. of hour. 
 
 9. First fills f. of cistern in 1 hour. Second lets out | 
 
 of cistern in 1 hour. Part left in at end of 1 hour=| ^ 
 
 = if~"r2=i"2 cistern ; whole filled in 15 hours. 
 
 10. A and B can do f of work in 1 day. A and C do 
 
 _3 
 10 
 
 in 1 day. B and C do •;. T«)i,'ether they do •:' + ^^^-)_ 2 _ 
 f,;* of work in 2 days .-. whole work in 2^^ days.' A in 4 A 
 days ; B in G^/'y days ; C in IG/, days. 
 
Hints and Answers. 
 
 9 
 
 XX. 
 
 1. 9 feet. 2. 330 yards. 
 
 50 
 
 3. Width is ^2^4^ = 16 yards 2 feet=50 feet /. ^'-=15 
 widths of roller. 
 
 4. Each sod will cover 27i x 8i=226§ square inches. 
 Number of square inches in an acre = 627 i640 sq. in. 
 Number of sods = 6272640^226^=27641 sods. 
 
 5. $15.20. 
 
 G. Room is ^^=S?, yards long, so will require strips 9 
 yards long. Number of strips = 15f feet-^f yard=7 
 strips, so will require 9 x 7 = 63 yards, with ^ x 7=2^ yards 
 turned under. In second case, 6 yards m length and 1^ 
 strips, or 72 yards, with 11^ yards turned under. 
 
 7. 17| square yards. 
 
 8. Including ceiling, 121^ varda. 
 
 Area of four walls=681 square feet. Area of doors 
 i nd windows=42 + 53|=95;^ square feet. Remainder= 
 585* square feet. Area covered by roll of paper = 24 x ^ 
 =36 square feet. Number of rolls=585i^36. Value at 
 7.5c.=$12.19i8J»g. 
 
 cubic 
 
 10. Cubic contents of wood=60 x 12 x 9=6480 
 inches. Cubic contents of match='lx ^ 
 
 inch. Number of matches=6480 cubic inchest- ^Jjj cubic 
 inche8=259200 matches. 
 
 •1 X 2 ;,=j7j cubic 
 
 1. $27. 
 0, 50 cents. 
 
 XXI. 
 
 2. $126. 3. $26. 4. 
 
 7. $5. 8. $3. 9. $3. 
 
 XXII. 
 
 L5. 5. 
 10. $18. 
 
 1. $446.40. 
 
 2. $1 in 4 yejEirs at 4 per cent, will amount to 
 
 1.16 
 
 $40 will amount to $46.40, 
 
Hints aud Answers. 
 3. $22.40. 4. $209. 97^. 5. $742. 
 
 yeH;;'^tt^thtdTr'^'"'"' '^1 ^''"''^ '^' ««^«nd fur 1 
 J' rti , me tmrd for /^ year. Answer $1399 17i 
 
 7. $107.80. ' ^* 
 
 a Rate, 6 per cent. ; time, ^ year ; answer $1015. 
 9. Rate, 8 per cent. Answei- $J.10. 
 10. $2 in each case. 
 
 XXIII. 
 
 1. The rate is C per cent. Answer $440 88 
 
 2. The time is ] year .. interest w.Il be 2 per cent., or 
 
 3. $1.03. 4. $1.02. 
 
 5. Rate, 6 per cent. ; time, 73 days ; interest, $39.42 
 
 7. $81.36. 
 
 P^^ii^:r^i^^!^^^^^'^ o^e $1000; he 
 year tl.is will amount to Iso^'m V ^ ''"'^ "^ *"^' ^««"»d 
 
 owes $505.60, which ':t^'^"t„i of t'hTtf ? ^'^'^ ^^'^ 
 amount to $535.94 nearly. ^^^^"^ ^'^^^^ will 
 
 9. 20 years. 
 
 be «00, 8 per cent, musi be Sgei ""'"" '»''>' 
 
 XXIV. 
 
 cent. iVr/ero'ent f ,.°' ^ ' « P^ «"'• » A ; 12i per 
 2- m ; G ; 10 ; llj. 3, ^3,., ^ ^,,^,^_ 
 
 6. The time is 3?^ years tinri *u / . 
 mg these together we W «t"^ *^^ '^*« Toff J multiply- 
 
Hints axd Answers. 
 
 11 
 
 6. I 
 
 1"- G 
 
 8. 
 
 1 30 
 
 0. The time is 4,^,^ years 
 
 Multiply by ^f,^ and 
 
 we 
 have ;-,f(j',) : add 1 t(')"this and the required fraction is 
 l^-^'i/,^. The amount will be ^1287. 
 
 10. $10.39. 
 
 XXV. 
 
 1. Maryh 21, 188G. 2. April 6, 1886. 
 
 3 (1) March 5. (2) March 3. (3) March 3. 
 
 4. (1) March 3. (2) December 24. (3) May 25. 
 
 5. May 29 or May 30. 
 
 6. One month, 30 days or 31 days. The first two 
 would make the noie fall due on December 25, but as this 
 IS a legal holidaj , the note would be payable on the 2Gth. 
 
 7. February 22, 188G. $433.53. 
 
 8. The note is payable in 90 days, and in that time the 
 $1825 will amount to $1801. 
 
 9. Draw the note for 143 days, and make the other 
 necessary changes in the form given in question 7. 
 
 10. $396.84. 
 
 XXVI. 
 
 « 
 
 2. f 3. ]l ]R. 4. I $100. 
 
 5. The amount is {i{| of the principal, therefore the 
 principal is \^^ or 4 of the amount, and f of $70=$50. 
 
 6. $1000. 7. $10. 8. $1.09. \%^ of $1. 
 9. £\Vl 10. $500. 
 
 XXVII. 
 
 $730. 
 
 1. $250. 2. Read "24th of July." 
 3. $500. 4. $625. 
 
 5 Altogether 21 per cent., so that $100 will amount to 
 $121, or the principal is ] §V- oi the amount. 
 
 Answer $i0. 
 
■m. 
 
 12 
 
 Hints and Answers, 
 
 I 
 
 6. U- 7. $1G0. 
 
 9. 900 guineas. 10. g|^? of $1. 
 
 XXVIII. 
 1. $2.50. 2. 4 per cent. 3. 5 per cent. 
 
 for 1 yearL $730, hence the't'efes't'on'^S^ IsTu ' 
 hence the answer is 11 per cent. *^^ ' 
 
 5. 10 per cent. 
 
 6. The interest for the whole time fs SKIqa . *i, • j. 
 
 for 1 year i, »,20, hence the „rbe,*of yelrs i,"'"'"' 
 
 7. The interest for a year would he «9i on a 
 a day ; hence the interest willtVia U in 319 day^ 
 
 8. 16f years ; 12 years ; 8 years. 
 
 S,.^\J\T'''''^'^^^-^^^^^yeB^r; $1. 10 in 2 years and 
 U. 13 m 2f years, or 949 days. ^ ' ° 
 
 10. 60 years. 
 
 XXIX. 
 
 1. $90: $1800. 2. $1000 3. $2190. 4. 6|perct, 
 
 5. The interest for a year would be $3G.50, hence the 
 8 20 
 
 required timo is — of a vpar nr «o ^ 
 
 36.50 ^ ' ^^ ^2 ^ays. Answer 
 
 July 31. 
 ^- H5^ J- 7. 5 per cent. 8. |^f |. 
 9. f of a month is J^ of a year, whereas 20 davs- i, of 
 
 mo^nth^ '"'"■''' '' *® '"■" ^^ ""O"""' °' »1 fo'' every 2 
 
Hints and Answers. 
 
 13 
 
 XXX. 
 
 1. The tirst is equivalent to a cash offer of $1744 • the 
 second to one of ^IGiJO, and the third is $1G00. The first 
 offer is consequently the best. 
 
 2. $1331. 3. $12.4G. 4. $400. 5. 20 years. 
 6. 5 per cent. 7. Gh cents. 8. 8 per cent. 
 
 9. 15 per cent. 
 
 10. The interest on $1000 for a year is $G0, or $1 for 
 every days, if we call 300 days a year. This method is, 
 therefore, not strictly correct, but is sufficiently accurate 
 when the number of days is small. 
 
 XXXI. 
 
 1. Increase is 77^5 of population of 1870 ..population of 
 1880 is tl of population of 1870-^|l of 12275 = 13257. 
 
 2. 24 tons, 1840 lbs. 
 
 3. 1500 lbs., 200 lbs., oOO lbs. respectively. 
 
 4. 12 per cent. 
 
 5. 1 lb. of each would cost $2.42. The three sell for 
 $2. 70. Gain on $2. 42 -^28c. Gain (,n $1. 00 is i\% x 100 
 
 6. 15 per cent. 
 
 tj 1717 =-7_ ■ IT 
 
 cost = !??o3.8()''.'cost = |ft of $253.80 = $210.00 
 
 8. Cost of 42 gals, is $258.00. Received for it $42x7 
 = $294.00. Gained },''50. Gain on $258 is $36 ..Gain % 
 ^,VV>^100=13H%- 
 
 9 Loss is 12%=7jV i>f cost. S.-P. is 22 of cost .-. cost is 
 U of $200=$227tV" Gain by sellini,' for $250 is $22x\. 
 Gain per cent. =(22t\^ '-^27 A) / 100 = 10%. 
 10. $7200 amount for which sold : $0400 cost. 
 
 XXXII. 
 
 jl of cost is the sellino: price. |^ of 
 
 I 
 
 1. Cost of 8piuts=$3.25x 75 =$243.75. Gain=6%:= 
 
I I 
 
 14 
 
 HiNts ANr> Answkhs. 
 
 »..M..Uj, feei.,„j, ,„.,^.^. |„,^ s{al.=SL>r,5.!(;t,;4-(ir,=#:i.ii;ij 
 
 J5 of c,«t* Cost Si; of V.^5ol te w;;- """""'' ■"■'™ '' 
 
 3. '^^°' 
 
 4. Deduct 5%=^V of niarkocl price .-. i » ,>f marked nrice 
 = sellinnr nripp — $!7 loi at i j • a*) "''>'•«•« ^t.(i price 
 $7.50 P"''*'-*"-^-^ Marked price=j'0 of $7.J2A = 
 
 co^ •^f"i?'^ false weigl,t=-V of ost. Received H? <,f 
 
 6. 5 tons, 8 cwt. 
 
 oJoo^ATK^ ^^l^^, 'T^ ''r'r ' «f <=««t, as he throws 
 " ,f «^^ J.;!^"^' '« «' of marked price • marked price is 
 4 ot 5- J of cost, or an advance of 5(»/ 
 
 /o • 
 
 8. 35f per cent, advance. 
 
 9. 
 
 10% =$(143. 
 10. 2^«-%. 
 
 of cost = 8117 .-. cost = $130. Selling price to gain 
 
 XXXIII. 
 
 1 Cost of fish is 20%=^ cost of clams and oysters • « 
 cost of fish and oy8ter8=$59.40. Cost of clams and 
 C^stTf h'^'' $oa40=$49 50, and cost of fish is l9"o 
 So r,?.^ «^'"»«=/oV cost of oysters .-. | -; cost (,f oy8ler8= 
 clats=m50. <^y''-^--\i'i <'f $49.50=m ^Cost of 
 
 2. ?80. 3. $3000. 
 
 clothe^-l28S-*T'^?^^^rl^^ '^f^^'-- V «^ cost of 
 clo^thes_|280. Cost of clothes, $127 j\ ; of jewelry, 
 
 fl,L^/^"1'S?oj''^^''^^'' ^0%' each could have357 t e 
 the defeated 3o%, the elected 05% • successful candidate 
 received 6o per cent of 120=78 votes ^<tnaiaate 
 
 ! 
 
HiNis AND An.sw/:ks. 15 
 
 6. 200 lbs. cotton, 480 lbs. wool. 
 
 7. nii.OO. 
 
 8. IVdIit is ^ of co3t = 2 of 3s. 4d. =23. Gd. .•.profit on 
 3(10 yards = :i(iO times 2s. (id. = £45. 
 
 1). Coat of (U) s-als. ("} 7k\ =$4.50. Received for 40 
 ^';ils. C<t^ '.yy, $:{.75 ; for 20\m18. r..' H\c. , 5?1.<)5. Gain is 
 iir5.40 - $;4.uO=^yOc. .-.gain per cent, is 4>yo=-^%- 
 
 10. 20%. 
 
 XXXIV. 
 
 1. Freight is 5% of .S300=$15. Cost = $315. Gain on 
 
 5 of j,'oods=27% ..selling price is {-jj of | of co3t=.iir,^ of 
 cost. Gain on remaining ^ of cost is 25% .". selling p"rice is 
 loo '^f ^ = 4 "f *^'>st. Total receipts=.\'-',Vf i <>f eost = 
 ] J-;; « of 'cost = { r,i\a of ^315 = $3!m. 27 ;. gai'n is $300. 27 - 
 |f3i5.00 = $S1.27. 
 
 2. For I of goods received I of $340 = .S22(>-;. For 
 remaining | of $340 received }f;5 of j of $340=' ^100]. 
 Total recoipts=$22Gr; +$10G]=$3321.^ .-. Loss is $7t^.^. 
 
 3. G03%. 
 
 4. Gain is G cents on 24 cents. 
 
 5. Lo.ss on |i.l4 was $1.14-$ .99|=14|j. =4 = 12^ 
 per cent. 
 
 (). $31374. 7. G5,1,;;-? per cent. 8. IGxc. on the $. 
 
 '.). Loss=^* of ,!,';,= j',;-j=:./^ of Fhcep. Remainder z} 
 of sheep = 2G4. Whole number=i;0.) sheep. 
 
 10. Decrease in 187G = ^\7 of population, leaving ^t of 
 population. Decrease in 1877— G%=:;f\, leaving ^l of f% 
 ulation .". population in 187G was ^'Ij*| of 55413 
 
 = tU 'jf pop 
 
 =:G5,500. 
 
 XXXV. 
 
 1. 12^ per cent, or ^ of cost = $5 .. cost = $40. By 
 selling for $0 m^re I gain $3, i. e., j'\) of co8t=7^ per ct. 
 
 2. Marked price = I of cost. Selling price— 85 per ct. 
 
 1. 
 
id 
 
 lllNTH AND AnSWKIM. 
 
 I 
 
 (.f I of ro8t=],',J| ,.r i;(.8t .-.Kiiiii is ,',;;^ of c mt, - .f38. tAa 
 «.f coHl=.Sii, iiii.l I ;,;; of cost^lS^-^.-W, .in.umit of hill. 
 
 .'{. Viiu'-iir JH .^ of ;i of kojr^A kou. ,'^ of A of vilioL'ar 
 in ko- IS iliawn out, |,.;iviii,- »o of A ,}\^ of ko*« of viiieuur 
 = 1;> jKT I'onf. vim'i,Mr. 
 
 4. SBI(K),()(H). it. ;;:» |.or coiit. (5, 20iH<rrmit. 
 
 7. Loss L' ||)s. l.ulliM- <iii ovi'iy 10 11)3. 1^20 pur cent, 
 
 8. llT) i;al.s. wine, !*;"» t>f water. 
 
 9. (lain oil Olio »lo/(Mi [j.ipora is oU conta-2r) coiits=J) 
 conta- .y. of cost:^ oii por cent. 
 
 10. $(;:-;. 
 
 XX\'\ 1 
 
 1. l*5!>r.00eor(ls. 
 
 2. Expectetl t(. re.-civo },', of i-osfc ; dixl ro'viv » '^'' =i7 
 of cost. DiHeiviiee j of co.st==.sr»0. Cost^^-.'jLm '^" "** 
 
 ;j. ]l of cost of mixturo-^15 cents p.,rlh. ..^tst is '" of 
 ]!)ceiits=i:{,', cents por II,. ()„ o,,,, pound of c.lree 
 coatino L>;) cents he Would lose L'ao. — l;{j', c. =1 1 • cents 
 On one 11.. chicory wiuild j^aiii L'J/jC. - 10c. =^}j'/ cents.' 
 
 Would -ain one cent on ll.s. ..i;ain Ji,', cents on 
 
 I ''j f 
 
 ■11 n ^ o - =H Jl's • proportions are 1 Ih. coUoo to 3i of 
 chicory, or 8 il»s. cotiee to 25 Ihs. chicory. 
 
 4. Speiuls, saves, and pays as interest J + j + i - 1 •• • 
 
 o'^uJf^ ^ "^ '""'•'T '''''^^' ^'*1^'^^'« *!^''^'>- f'icom?>= 
 ^40.» , 1 . A im.unt paid as interest - g'^ of ;i;<40!» ,', - {?20 ."■ 
 
 .-.7^ per cent, of debts is ^20,* • debts are ':i^jj^^^ _ 
 
 7^ "~ 
 $572i\. 
 
 5. (^ain=2percent. = ,;-;„ of cost..];)2 of c:.st=sellino 
 price. Cost ^l- of ^1.08^;^)Bl.0(J.:Jf per yard. Losl 
 o^n 1 yard of dearer silk = Sl. 12.', ^1.00,1^. - ().!<^' cents 
 l^rtin on 1 yard of cheaper siik=:0i=5-.. cent^V. gain ic. on 
 
Hints ani> An.swkks. 
 
 17 
 
 ^ . . (Jain {i^^\, on ^. .,.. X li.j'^j'.j = ^.y yards. Proportions 
 
 ari« 7(5 to 77. Nunil)or of y.mls of first is /;;"., of ^^ ^^^. ...^ 
 .:=li;'^ yanlw. Nmiiber of yards of 8oconJ=-jyj of 
 = 11' }. yards. 
 
 0. 7 1 7 por cent. 
 
 7. Cam from <ro()ds=]L »)f cost. Sollinsr price=!5 of 
 cost. Loss from had o,u<,'s-i of valuo of os^'^s. Ileal 
 value of i'i,%'8--i'; of suppostMl valuo- ^ of JJ of cost of 
 m,o(ls = cost. M cither gains nor loses. 
 
 S. li has 50 per cent, more tliJin A. 
 
 \). (loods niiirked at !? 18000, and costin<j; i? 15000. 
 
 10. In l)uyin;4, he receives | ,\ of aujount i)aid for. In 
 sellin«', he liives /'y of amount paid for.', for /„ of amount 
 paid tor, he ^^ves .',, and for 1,', he gives V=-l--^5 P'^'' ct. 
 He gains 22j; por cent. 
 
 XXXVIL 
 
 1. 18^ per cent. 
 
 2. Loss is 5 per cent., /.sellin'); price is Ifj of cost=3s. 
 Od. Cost is 47/,v pence. 4.', per cent.=.'^;,7. To gain 
 .,;;„ must 1)0 sold for H;];; of 47i",=4s. Ud. 
 
 ;{. Ueali/e 10 ])er cent. - ,V of £25=£2 lOs. Wiae 
 must be sold for £*27 10s., at ISs. 4d. per gallon. 
 
 4. 25 per cent. 
 
 5. Co8t=103. 3d. —4a. lOU. =58. 4^d. .-. gain per cent, 
 is 00 j';!; per cent. 
 
 0. Profit per lb. (m tea =4(1. On 100 lbs. =400d. 
 
 Profit per lb. (m sugar Id. On 100 lbs.--100d. Total 
 
 pr )tit ^500 pence. ^Total cost -^3050 pence. Gain= 
 
 sj)o^ — «l'_^14w*V7. 
 nOsO — TT — ^*7T/o* 
 
 i 
 
18 
 
 Hi:*T« AND Answers. 
 
 7. Cleared 2 oi co3t ;. V of cost = lis. 
 by selling at ISa. Gd.=5is.=C8^%. 
 
 8. Ordinary trade price=] ^J} of coat. 
 £o20 lOs. tAtt of co8t = i'520 103.H-83. 
 
 Cost =8f«. Gain 
 
 h:j 
 
 yj^ 
 
 
 l„,y of cost: 
 jgJJ of cost: 
 
 ig-^ of £520 10s.=.i752 lOs. 
 
 9. Loss on 250 bu8h.=7i% of 280 bu8h.=18| bush. 
 Gain on 150 bush=12^% of 150 bu3h.=.-18| bush, /.there 
 was neither loss nor gain. 
 
 10 Profit --- J I f ^ost .-. sell 21 for | of a shilling. Sell for 
 Is. I of 21, «.nd for 1 guinea 21 x g of 21=302 eggs. 
 
 XXXVIII. 
 
 1. B pavi ]i^ of first cost. C pays y^„% of what B paid. 
 C pays rV« of \h^ of £345 153. =£337 19d. 4igd. 
 
 2. B pp.ys \-,fn'^ of cost, C pays \^J^ of what B pays*, 
 *• «•» VuV* of \-Q-(j- of firai cost=j^g^- of what A paid '.A 
 paid ^f 5i? of £203 7d. Gd. = £200. 
 
 3. 4| per cent. 
 
 4. He sells 1 lb. —13 drama as 1 lb., i. «., sells 15 j^^ oz. 
 
 1 :i 
 
 Iff 
 
 oz. tjrain per cent, is 
 
 ,?.,Tis£210 33. 4d.H-97. 
 
 for 1 lb. Gain on 15f^j oz, is 
 ^2iii P^*" cent. 
 
 5. yVo of debt is £210 3a, 4d. 
 iVo is Vr of £210 33. 4d. =£208. 
 
 6. Rent of 150 acres @ 303. =£225. Return is 4^ per 
 cent.=2fjQ of investment .*. ^,% of inve3tment=£225." In- 
 vestment = -'i;*^ of £225 = £5000. Amount spent in repairs 
 -£5000-£4G24=£37G. 
 
 7. Cost of ^ acre @ 15s. 9d. per square yard=£1005 
 153. Total cost =£4000, Rent 9 per cent, of £4000= 
 £3G0 per annum. 
 
 8. Deduct j\, and ^^^ of original sura remain. Deduct 
 charge of 12^ per cent, of rem; .inder and I of j"^ of (.:ij<inal 
 sum remain, J of |^j of original suin=£787 lOa, .', 
 original sum is £1000. 
 
 9. Income tax, J^ of rental. Remainder, ig. Cost of 
 
Hints and Answers. 
 
 19 
 
 collection, 4percent.of ^H -^ ^^-f.J'^^'''^''^ "° "' 
 i« of rental=£400.-. rental la £o20 lbs. »ci. 
 
 "lO. Cost is as 1 to 3. On the 1 be gained y,- O" ^he 
 3 he gained^, of 3 = i J^!^^^;^^^'''' "^^ ' "^ 
 gained ^^^ .-. gain per cent. =17* per cent. 
 
 XXXIX. 
 
 1. 15?.^ per cent. . 
 
 o c I'l- i nf 6-'' of property for £100 .-. property is 
 wo'rth'l si. It had rJenVfi value, therf re | o_f 
 orTginalvalue=£288.. original value was | of £288- 
 
 £240. 
 
 ^ , „o 12 1 ftf iio.=}-i of tirst cost, or an 
 
 3 Purchaser pays |r»o 01 loo— h "^ 
 
 advance of 37^ per cent, on prune cost. 
 
 4 Sells 1 for h of a penny. Gain=5 f 5„««"*: = V>.^- 
 H of cost of 1 apple=^ of a penny .cost s^ of ^-..|d. 
 -" 1 T r,«a hv aellincx 2o for Gd.=.- d- — -5— rsT r,"- 
 ri^t^oi^l^^'-^l^^-'f-'"^'''--^^'^ P" cent. =£24 
 
 LiOSS on (CjU. — ysYo • • •" r 
 
 8s. on £100. 
 
 K T> , fr.r 100 lbs 756 pence. Receive for (100-4) 
 lb'-, OolloUrOOs'peuoo. 'oain per cent.=2D2 pence 
 
 =33 \ per cent. 
 
 Z 1 or s, « - 1 008 Dints One dozen bottles hold 
 is'pirtrrumb^ of rzer=1008;.18=56 dozen. Sold 
 
 LV5Sx3=£168. Gam=£78 = 8CJ per cent. 
 7 See Paper XXXVIi, Problem 8. £708. 
 8. Lo„ of 5 P« eer^t. en pnn,e^^st = lo.^ .V' cost. 
 
 28. 4|d. 
 
 9. Cost of tea = 74s 
 
 3d. 
 
 78. 
 
 Received for it 63. O^d. x 12=81s. 
 GaTn^ is'sls. " 3d. - 74s. =78. 3d. Gain per cent. = 
 
 — X 100 =9? J per cent. 
 743. 
 
20 
 
 Hints and Answers. 
 
 10. i*ff of CdSt of or,,()(l8= £75 .'. C08t= £83^. 
 
 of co8t= {■;»/,} of 8:Ji-i:i08 Us. 8d. 
 
 Value={;i}{ 
 
 XL. 
 
 charges 
 
 1. Railroad receiv 1 t «f tiOc. -48c. per cwt 
 = iVv of 20000=8124.80. 
 
 2. 68 "43 per cent. 
 
 3. 35 per cent. more. 4. 3 por cent. 
 
 5. I of his .share was worth 81)50 ;. share was worth 
 83250. He own^d .S2V per cent, of right, so :]2t. per cent, 
 of right was worth 83250 .-. whole right was w« 'ih /.IJ!^ of 
 83250 = 810000. 
 
 6. i of first cost = 8840.-. cost = I of 8840 = 81050. 
 Freight and in8urance=5 per cent, of cost = ^^5 of 81050 
 = 852.50. 
 
 7 Wife received 40 per cent. ; son, 35 per cent. : 
 daughter, 25 per cent. GO p.r oent.='^18(J00. . 100 ])er 
 cent =831000. Wife received |12,400 ; son, 810,850; 
 daughter, 87,750, 
 
 8. 40 per cent, of =i of interest=.^\ of his interest sold 
 foi 84800 i^ is worth 8800. Reinainder of his interest, 
 n of interest" is worth 8800 x 10 = 815200, which is face 
 of note. 
 
 0. ";\ of ? of invoice = 850 .-. invoice=8208^. Part due 
 SI ill will' bo (30 ]>er cent, of GO per cent. =2^g of invoice = 
 ,«5 of 8208^=875. 
 
 10 ii of 20 per cent, of his capital=81500 .-. 20 per cent, 
 of capital = ?; of 8150^ = 84000. Capital = ^20, 000. 
 
 XLT. 
 
 1. 144 lbs. avoirdupois-=l75 lb?. Troy, difference 31 ; 
 80 that for ditl'erence G2 we shall have 288 lbs. avoir. 
 
 2. 8100. 
 
 3. A 844 ; B $45 ; C 822. 
 
 4. 10 cubic feet of water make 11 of ice. 
 
 Therefore 11 
 
Hints and Answkrs. 
 
 21 
 
 1 
 
 of ice .nuke 10 of water, or ice loses ,'.. ^^"^^^ i« ^.^ ^''' 
 cent. 
 
 5. ^4t0. 
 
 G Question slioald read ,\. Answer 272, 170. 
 
 7 The boats are shorte.nnu the distant between the.n 
 at the rate of 2r, nnles an hour, and as hey n>eet in ^ 
 hours, that distance must have been JD miles. 
 
 48xlG^_24. 
 °* 12 X 4 X 4 
 
 9. 80 years. 10. ^0.50. 
 
 XLTI. 
 1 €?3 60 2. 18 feet. 3. 81045.44. 4. ^47.38J. 
 o' 14 days. G. §03.75. 7. ^14.02^. 8. $48. 
 
 9. $201. ()0. 10. 45 miles an hour. 
 
 XLIII. 
 
 1. George's, §25; Charles', §37.50. 
 
 2. 25 per cent. 3. The second ; 1^ per cent. 
 
 4. Out of each 8102.50 that he receives, he invests 
 §100 in tea. 5000 lbs. 
 
 5. §14,400. 6. ^9775. 7- §10093.75. 8. §157.50. 
 9. Eldest, §8100 ; each of the others, §5400. 
 
 10. 80 feet ; G3 feet,. 
 
 XLIV. 
 
 1. §20. 
 
 2 Wheat is worth | as much as barley, or §f per 
 bushel Therefore, 27 busheh of wheat can be bought 
 for §22.50. 
 
 3. §2715. 4. §36. 
 
 I 
 

 
 Vt*jff,,*:- 
 
 22 
 
 Hints and Answers. 
 
 5. "Ahas|!320" should read "A has 8310." Then 
 the G. C. M. of the three numbers is $02, the price of a 
 horse. A can buy 6 ; B 9, and C 12. 
 
 G. Find L. C. M. $1800. 
 7. $44.37. 8. 76250 men. 
 
 9. 16 per ct. 10. 35c. 
 
 XLV. 
 
 1. -1553237297. 
 
 2. If for 40 weeks' work he is entitled to $40 and the 
 8uit, then for 24 weeks' work he should receive $24 and 
 ■^^ of the value of the suit ; hence | of the suit must be 
 "worth $0, or the whole suit $15. 
 
 3. $17.00^. 4. 195. 
 
 5. I of remainder cost $1656 ; therefore 
 
 whole 
 remainder cost $2760 ; therefore 40 bbls. cost $240, or $6 
 each ; hence whole number was 500 bbl. 
 
 6. Assume that he began business with $100 ; at the 
 end of the Mist year he would Le worth $140 ; at the end 
 of the second, $120; at the end of the third, $160. 
 Thus his gain is $60 on the $160, or $6000 on the $16000. 
 
 7. $3553. 12i. 
 
 8 j-.j of cost is ^5 of selling price ; hence the cost is 
 ]-i of selling price, or 13 cents a dozen. 
 
 9. Simple interest, $144. Compound interest, $154.01; 
 difference, $10.01. 
 
 10. In 60 days A can do the work 6 times ; B 4 times, 
 and C 3 times. So that the three can do the work 13 
 times in 60 days, or .Ij} in one day. When C begins there 
 is .^a of the work still to be done, which will therefore 
 require 2^;^ days. 
 
 XLVI. 
 
 1. 20 per cent, discount off leaves $2.08, which is one- 
 third more than the buying price, hence the cost is three- 
 fourths of $2.08, or $1.56. 
 
 I 
 
Hints and Answers. 
 
 23 
 
 2. $1800. 3. 25. 
 
 4. 14 cents, cents, and 10 cents. 
 
 5 (a) 53885 lbs. (6) 205 yds. (c) 127 days. 
 
 6 m,h ^ods, etc. 7. 12i095 times. 8. $56. 
 
 Every 12 feet of the fence contains 34 feet of lumber 
 J- 2 pcZ and therefore costs 42 cents. Multiply this 
 by 7li, and add S20 for labor, and we have ^o0.03. 
 
 10. 4841 m. 200 rds. 10 ft. 
 
 XLVII. 
 
 1 181 ac, 34 per. ; 203 ac, 2 roods, 14 por. 
 
 2. A cubic foot of ico will weigh ^ of 1000 ounces. 
 Answer, 750 tons. 
 
 3. $137. 81^. 
 
 15 
 
 6. Loss $400. 6. $22000. 
 
 :. All open will nn^in^n^^ J^^^^ 
 
 whole time required is 288 imnutes. 
 
 9. 32G7. 10. $74 ; $59. 
 
 8. $217.00. 
 
 XLVIII. 
 
 1. $751. 2. 675 days. 3. $11.04. 4. $1140.25. 
 
 6 meJ'the ice melts there will be room for 21 cubic 
 feet of water, that is 21 times 6i gallons, 
 7. 6. 8. ,\. 9. 80. 10. $31.20. 
 
 XLIX. 
 I. 8 feet; 38 trees. 2. $2533. 8.21216 ft. 
 
24 
 
 Hints and Answers. 
 
 4. gO,V jrain. 5. li hours. 6. 40 bushels. 
 
 7. 038 strips ; -02208 inches. 
 
 8. John, 03 cents ; James, $1.12. 
 0. $280. 10. 45. 
 
 i-i 
 
 II 
 
 1. 9 cents. 2. Lost $1.40. 3. 2^ cents. 
 
 4 The pupils may be di.ided into groups of 6, each 
 group consisting of 5 girls and 1 boy. The boys are, 
 therefore, ^, of the whole number, or 91 ; the answer 
 recjuired is 304. 
 
 5. Annie, 55 cents ; Jane, 80 cents. 
 
 0. 4 yds., 2 ft., ins. =177 in. 
 
 177 
 
 50 
 
 "5280x12"^"" 5280x4 
 
 = 002703500 m. 
 
 _ 1 < 
 
 7. The fraction^.-?— 1-of AxVv-^^TVJ'r- 
 
 oOXs.'jT) 
 
 8. $229.50. 9. $21.72^. 10. 7 o'clock. 
 
 LI. 
 
 1. 48. 56. 
 
 2. Number of square feet in fence— 300x4 = 1440 
 square feet. Area of Hrst kind of board=12 square feet. 
 Number re(iuired = 1440-=-12=120. V;ilue=812. Num- 
 ber of sec(md kind required = 1440 ^10 = 00. Value at 
 12c. =$10. 80. Second are cheaper by $1.20. 
 
 3. 75 miles =300000 feet. Wheel turns 390000-=- 10= 
 30000 times. Burns 2000 lbs. in turning 39000 times .-. 
 burns 1 lb. in turning 39000^ 2000= 19i times. 
 
 4. One three-inch volume, two two-inch volumes, and 
 two one-inch volumes take 9 inches. Lergth of shelf = 
 30 inches.-, we can have 30 -j- 9 = 4 sets, i. c, 4 three-inch, 
 8 two-inch, and 8 one-inch volumes. 
 
Hints and Answers. 
 
 25 
 
 . 
 
 5. Number of coins =L, 0. M. of 4, 
 Vaiuc=$450. 
 
 4* 
 
 5, 6=G0 coins. 
 
 6. Diameter = jl^=^'^ ^^ circumference, fi of circum- 
 ference-./, of circumference^^! of ^if^^^^f ^"^4=^^! 
 ference = 00 yards. ,'.. circumference = 4 yards. Circum- 
 
 f erence = 88 yards. Cost of fence = b8. 80. 
 
 7. Amount realized from stock=t of f3500= 82187. 50. 
 Amount realized from book debts = loo "f ^l;;^0=|.H.2.oO. 
 Amount realized from notes, etc =i of ^«,80_^o44.00. 
 Total rpceipts=--$3G<)4.00. Deduct 2 per cent._^<3 8«. 
 Net .set^=^3G20.12. Liabilities, $0404.50. Creditors 
 feceive on%0404.50, $3020.12. On $1, receive oO cents. 
 
 8. 3 oxen eat as much as five horses .'. 6 oxen eat as 
 much as 10 horses. 7 sheep eat as much as 2 horses . oO 
 Tat as much as 10 horses. oxen, 5 horses, and oO sheep 
 ea as much as 31 horses. 31 horses in o weeks eat o tons 
 hay. 31 horses m 3 weeks eat 3 t^- W- ^ -^ -^^ 
 be put in to eat as much as 31-7 = 24 horses, i. e., o* 
 
 sheep. 
 
 9. Total cost of apples and barrel :;=$2. 50. Value of 
 am)les = S2.50-$ .15-^2.35. A received value, J>2,.iJ 
 T2=V.m. He paid §1.50 .". B owes him 32^ cents. 
 
 10 Valut'of one 25 cent piece, four 10 cent pieces and 
 twelve 5 cent ,ne(es = 25 + 40 + 00 = $1.25. Value of same 
 nmnber 17 of 25 cent piece. -i?4. 25. Ditference in value 
 = $3 Number of c..ins==(30-3) x 17-204 divided m 
 proportions 1, 4, 12. There were 12 of farst, 48 of second, 
 and 144 of third. 
 
 LIL 
 
 
 2. 045 cents. 
 
 3 When 1st receives t'l, 2n(1 receives m :. 1st receives 
 \=i of £12 10s. 8a. -£4 10s. 3d. 2nd receives i,M>f 
 112 IGs. 8d.=-£8 0s. 5d. 
 
 4. Number of acres in each is G. C. M. of numbers 
 =91 acres. Number of farms=27, 32, 43. 
 
 i 
 
-^ 
 
 26 
 
 Hints and Answers. 
 
 5 Divide total capital and gains in proportions 0, 5, 4. 
 Capital, S2400, S2000, and $1000 ; profits, $300, $250, 
 $200. Rate per cent. =12i per cent. 
 
 C Gain=50 per cent.=^ cost .-. selling price=:^ of cost 
 =.;| of $75.00=$112^. 30 gal. @ $2 per gal. =800. 
 \uiount to be received for remainders S112. 50— $00 = 
 $52.50. Price per gal. = $52. 50 -^ 25 =$2. 10. 
 
 7. 70 per cent of cost is 8140 .-.cost =$200. Selling 
 price to gain 5 per cent. =$210.00. 
 
 8 Loss on one is 25 per ct. =i of cost .-. selling price =i^ 
 cost 'i cost =$800 .-. cost=$1000§. Gain on the other j 
 cost .-.f cost =$800. Cost=i of $800 = $G40. Cost of 
 two=$170Gj. Realized, IIGOO.. Loss =$1005. 
 
 9. $200. 
 
 10. Receives for goods | of cost = f of $G.00 = $", 50. 
 Threw oti" 20 per cent, of marked price .-. | of marked i ice 
 = $7. 50. Marked price, $9. 37^. 
 
 LIII. 
 
 1. Cost of 8 lbs. of 50 cent tea and 5 lbs. of 37 cent tea 
 is $5.85.". cost of mixed tea is 45 cents per lb. Soils 
 
 45 
 15 75 oz. for 45 cents ..sells 1 lb. for ^ ^ x lG = 4oJc. 
 
 XO t o 
 
 Gain per lb. = 5 cents .'. gain per cent. =12/; per cent. 
 
 2. Amount of gold -If of )Z.=4Voz. Value=--4\x 
 84 = 378s. =£18 18s. Amount of alloy = ] of oz.=l.t ..z. 
 Value, l^x3 = 4s. 6d. Value of metal = £19 2.. Od. 
 Value of Jrnament=A of £19 2s. Od.=£25 lOs. 
 
 3. Area of field=^150 chains, width 10 chains .-. length is 
 15 chanis. Perimeter is 50 chains-^50 x 22 x 3=3300 ft. 
 Number of trees=3o00^ 11=300 trees. 
 
 4. 4 men can do -ff in 1 day .'. 2 men can do g\ in 1 dny. 
 5 women can do /- in 1 day .-. 1 can do ^l^; and 4 can do 
 ..*.j in 1 day. boys can do ,\ in 1 day.'. 1 can do ^i-j 
 aiid 5 can do ^^^ in 1 day. » girls can do jV i" tl'iy-. - 
 men, 4 women, 5 boys and 8 gals can do .u +^3^ + -ii'^ "^ 
 ^jY in 1 day =^ 1*5 in 1 day .'. whole work in 15 days. 
 
Hints and Answers. 
 A, B and C can earn »240 in ' ..or 840 in 1 
 
 27 
 
 tl;\v 
 
 5. A, B ana U can eaiu «.^-xv. ". - - . , ^, 
 
 i„"rda".'B"ea;,fs 8:2 ;:' day^. A earns $18 per day. 
 
 «. Le,„th of road=18xn60. ^^^^^l^^ 
 yards = 1»M7C0x 33 .-.number of acres - -g^^Q ^ 4 
 =210 acres. Value =$5.07 x21G. Value in £ sterling 
 
 $5.07 X 210_/$5^7^>i^ .^ 240 V. •• number of acres in 
 
 §4.80-- 
 
 rteld _!^^^ X no X A, X i=53;^tg acres. 
 "^^""" $4. 70s 
 
 7 Length or ditcH around pU.t = 580 feet Len.*^f 
 
 ^r::::rt,=eS".TxV=»*05°ouliefeH=U48Jcubio yards 
 
 which at 54c. - 55181 10. 
 
 8 15 miles-7'.)200 feet. Number of ^folf ^o"!'.^*^ 
 8. 10 mues Hmd wheel makes obOO 
 
 'li::ot«0«';«rl in 10 .niUs.-.makes 1 turn in 7»20O 
 14400=18 feet. Circumference of huid wheel is 18 feet. 
 .) Cubic cntents of block =4x3x2 1'-5=25 cubic feet. 
 Cubic feet of "■ater=i;, of 25=22^ cubic feet. Nun.ber 
 „"sals.=(224 X 1728)^277V=140 gals. 
 10. Duty en 1^0 .al.=50 per^cent. of y^ue +7o<=._^x 1-20 
 
 = K'-^25'-4!i=S135"Vae\ S270, o^r .2.25 per 
 
 «'''• LIV. 
 
 1 103 lots, and a remainder of 51 square yards. 
 
 „ n ;. 10 varda Ion", it yards wide. | is contau.ed 
 • % ?;Tims th'eewUb^l^ strips 10 yards lon«, or 
 SoVirds Cost per yard=S100^120=83ic. per yard^ 
 
 3. Ihhd. «»--'-^^^*tfhhV'^lntT30*b tUe.: 
 ^3_1(38 bottles ot wme in 1 hna, or in ^, ^^" 
 
 
28 
 
 Hints and Answers. 
 
 4. Coet of 8yrup=$3x40 + S3.50x30=$225. Sells 
 OO^-tJs for$225 + .s45 = 8270=$;3pergal. Gain on ^225 
 ~Ho.. gain per cent =^ x 100 = 20 per cent. 
 
 5. 1 furlong, 15 poles, 1 yard, 1 foot. 
 6- T.-5 8-f-oiy. 7. TT?^^ of a 1000. 
 
 8. Amount of flOO for 4 years @ 6 per cent.=8l24.-. 
 
 $1 is amour.t of ^^^^ and ^496 is amount of ^ll^^ii5^- 
 
 *iJ4 ^224 ~ 
 
 $400. Amount of $100 of second sum for 4 years at g 
 
 per cent. =$132 .-.$1 is amount of !i^%d $1288 -8496 is 
 
 ^ ^ $792 X 100 
 amount of ^^— = $000. 
 
 9. Cost of 30 lbs. oftea=.50cx20 + 30c.xl0=$13.00= 
 43.1c. per lb. Gam when sold at COc.=lG'Jc =i«^=Jio 
 =^8,^^%. Loss -.vhen sold at 35c. = 8\c =-^^4 - ^*^' - 1 u^» 
 percent. "^ ' 4 3«— i.jff — -i.:^j;j 
 
 10 X of a lemon is worth /^ of an orange : i lemon is 
 
 LV. 
 
 1. At 9 o'clock the minute-hancT is 45 min. spaces 
 behind hour-hand. It must ,.ua 45-7 = 38 spaces, or 
 4o 4- 7=02 spaces. Minute-hand goes 12 spaces in 12 
 
 mZl"\ ' J^' h""V^"^' ^^"^ 1 "»"• «P^^«« i" 12 minutes: 
 Minute-hand gams U min. spaces in 12 minutes .-. gains 
 
 38 X 12 
 38 spaces in - .^^-=41,^ minutes ; gains 52 minutes in 
 
 ^^V\ /tm''''V.i^^*^''f^"^^ ^^'rr minutes after 9 
 o clock (2) 48,V ^nd iO-, niiiiuies after 9 o'clock. 
 
 2. £18 Os. 10= «d. 
 
 3. A B and C can cut 100 rails in 2 days, or 50 in 1 
 day. A and B can cut JOO in 4 days, or 25 in 1 day.-.O 
 
 f-^ 
 
Hints and Answeiu. 
 
 can cut *i5 per day, or 350 in 14 days. B and ^ san cut 
 100 in 5 days, or 20 in 1 day . . A can cut 30 in 1 day, or 
 350 in 11^ days. A and C can cut 30 + 25=55 in 1 day 
 .'. B is a hindrance. 
 
 4. On Isi gain i cost ;. cost = i? of selling price=| of 
 $2000 -81333^. On 2nd lose 20% =\ of cost ;. co8t=| of 
 $2000 = ^2500. Cost of 3rd=-$'i000-.?50= $1950. Total 
 cost = $5783 L..gain=$G000- $5783^ =$216$. Gain per 
 cent. =3rj|a percent. 
 
 5. 2nd builds \2h rods. Length is 32^ rods. 
 
 6. L. C. M.+G = 366. 
 
 7. Gain --f of cost .".selling price =^ of 2 =2| cents for 
 
 5 
 5 eggs .•. 1 cent for — and 14 cents for 14 x 5-^2|=25 eggs. 
 
 8. Cubic contents of tank = 8 x 5\ x 4^ = 192 cubic feet. 
 Weight of water = 192 xl000=19'JO0O oz. =12000 lbs. 
 Gallon of water=8 pints==10 lbs. .•. number of gallons— 
 1200. 
 
 9. T'ain must go length of bridge and length of itself = 
 35 rods. Runs 15 miles=4800 rods in GO minutes. Runs 
 1 rod in J f go min. ..runs 35 rods in ^^V =Tff niins.= 
 2G| seconds. 
 
 10. Cost of cow = £216.v 6d.=£2l^-^=$4.86| x£21i§= 
 $103. 78^ .-.gain is $3G.21|. 
 
 LVI. 
 
 1. A can do 3 times, B 5 times, and C 6 times the work 
 in 1 day. Together 14 times the work in 1 day, or (vhole 
 in 1^ of day. 
 
 2. Costof first = f of $150=$125. Cost of fcecond=| 
 of $150^- $187. 50. Total cost=$312.^0 .-. Loss of $12.50. 
 
 12i- 
 
 Lobs per cent. =^r '^ 100 = 4 per cent. 
 
M 
 
 30 
 
 Hints and Answer^. 
 
 'I 
 
 3 Dealer pays 8200 for coal. Cst is ft4 50+ 50 -«5 00 
 per ton .-. he gets 40 tons = 40 x l-40 II..: ' Sella' '>C)OUIIm 
 
 for •^G.oO.-. sells 40x2240 lbs. for '^^' "^ ^ "^^ "" "-j^ _ 
 
 1:000 ~ 
 
 $291. 20 .-.gain is $01.20. 
 
 4. 4C per cent. 
 
 1 ^' J?n *^^.^^ ,*^''' ^ ^'^'^ 20 cents per lb. • on 50 lbs I 
 lose 810. On the 70 cent tea I Ji,. 10 ce,. « per lb 
 gam 810 on 100 lbs. Must mix .n 100 Jbs. ^ 
 
 ^180 three times what C ffets=88'0- siso <■•,»/ 
 gets 8220 ; 13, 8200 ; A, 83G0. -^^^^- <'uU. C 
 
 7 L?" 2'rr\^'' x^'"',- C":-""f«''^-»ee of wheels- of 
 480 times? ' "" "^ ievoluti..ns=105(;0 .22= 
 
 a In 4* seconds goes 8 rods .-. goer, 20 miles per hour. 
 
 9. For 100 receives 8104 aver;;. r^^ „rieo-sl (U n 
 one turkey oss would be 81.25-SL(4i2r oJn t' O." 
 one goose gam 20 cents ..gain 21 cJnts on ••!:'';,, ,^J' 
 
 MofirO = 58?iVktyT^^ ^amberoftu.key«= 
 
 irL^T^"'"" '1 P«ges = 33(;xl000 = .3;u:000 p.,cves~ 
 10.S000 eaves=84000 shec.t«=84000-24 ., aires 'n,m 
 ouirps=rl7'i I'.^.i..,-. \\7 J. .«- . 'in'i Ls — ,>,)oy() 
 
 LVJI. 
 
 1. Mortar will add j inch to ler.c.fh, width and thicknes.. 
 
 .•-O'f.jic contents (.f bjick^8-/ ^ 4' x'^' 2571:5 
 
 "4 ' •*» ^ -.s= .,- . cub. nis. 
 
 Number of bjick.s m i ciio,,- f.,..;, . ' " 
 
 l.'.*,o 
 
 — i 
 
I 
 
 Hints and Answeus. 
 
 31 
 
 2. y (iinher of days in 40 years=3Go x 40=14000 + 10= 
 i4()10 day.-. (iain = 5U inin. X 14(110=730500 niin. =1 yr., 
 142 days, 35 vuv, 
 
 3. Cubic contents of space to be filled = 650 x 12 x 4'5= 
 :;5100 cubic feet. ^35100-- 27 cubic yaids = 1300 cubic 
 /a! ds. Cost = 1300 x 42 = $540.00. 
 
 4. Pi..fit = l03%=,l of cost..8eriino price=7 „f |3.G0 = 
 ^4.'J0 ]UM' yard. Atu.mnt abated=]2^%=L ^f niarkod 
 price.. ^ of marked price =$4. 20. Marked price = ^ of 
 ^4.20 = {i?4.80. 
 
 5. Width of both ends = 34 inches '. average width = 17 
 inches. Area of board=18 x \l=2b sq. feet, sq. inches. 
 
 0. Receivedperbbl. $32. 50-v-7 = 554.042. f of price of 
 remainintj bblf,. is .94 04=, price ia §7 42^'. Number of 
 bbls. is fe;84x$7.42l^ = ^l,\ bbls. ^'uuuer of bbls. is 
 18^5 bbls. 
 
 7. Silver should be %y^o = 2Z^^ S^^^- 6 oz. is ^K of 
 150 oz. .'. there must be 150 oz. of gold iid oz. of silver. 
 Amount of gold to be added=Tl50 — 1)82 =57a oz. 
 
 ^- h^ u> = ho of "*^^ mixture is salt. -^\j of mixture= 
 2 lbs.-, mixture = 120 lbs. Amount to be added = 120- 80 
 =40 lbs. of fre;:h water. 
 
 9. Proportions, 3 bush, of barley, of wheat, 1 of oats. 
 Cost = 02ic. X 3 + 8 1. 87^ X + 37 J.c. x 1 = $(13. 50. Every 
 time $13.50 is contained in $121.50, we have 3 bush, bar- 
 ley, () bush, wheat, and 1 bush, oats = 27 bush, barley, 54 
 bush, wheat, 9 bush. oats=l)() bu«li. 
 
 10. Nuu.ber of page8=20,000x 400 -8,000,000 pages.-. 
 
 number of reams used to make book8= 
 
 20000 X 400 22 
 
 20 X 24 
 
 ^20= 
 
 18,3331 reams. 
 
 LVIII. 
 
 1. 487 2 reams. 
 
 2. Area of satin=24 x|=:18 sq. yards .'. number of 
 yards of silk received=18-^|;=i281 yaids. 
 
32 
 
 fliNii AND Answers. 
 
 ! f 
 
 (i 
 
 3. Length of fence in lst=-400 rods. Lenj<th in 2nd = 
 500 rods •. extra cost is 100 rods @ $3.25 per rod=$325. 
 
 4. Area of field = 8100 sq. rods. In wheat, 6 acre8= 
 800 sq. rods. In vegetables, 100 sq. rods .-. remainder= 
 7200 sq. rod8=^too = & tjf field in meadow. 
 
 5. Solid contents of joist = 1000-1-200=5 cubic feet. 
 Area of end of joist—}!) x y», cubic feet = A cubic feet : 
 length=6^ 2^1=24 feet: 
 
 6. Length of walls without corners is 127 ft. Cubic ft. in 
 wall8 = 127x2x9=228G cubic feet. Allowance for cor- 
 ners is I foot. • .cubic contents of corneri. is 4 times I foot 
 x9 = 18 cubic feet. Total cubic contents is 2304 cubic 
 
 feet. 24| cubic feet costs $3. 85 .-. 2304 cubic feet costs 
 2304 X 385 ^„ 
 243 =^358.40. 
 
 7. Cost of drugs is $12.50 x 8 =$100. Number of lbs. 
 
 Value at $10.25 per 
 lb. =$157i^ . • . gain is $57;.\. 
 
 8. Time walking 1 mile = 16, 24, 32, 36 minutes 
 respectively. Time occupied = L. C. M. of 10, 24, 35, 36 
 = 288 minutes. -.distances are 9, 6, 4i, and 4 miles 
 respectively. " ' 
 
 9. f of selling price =f of cost . • . selling price=a of cost. 
 Lo8s = i of cost = lli%. ' 
 
 10. 1st boy has ^ of i«o=^il7 bush. 2nd has y»y + ^ of ». 
 =^§ of a bush. 3 is ^ of 15, therefore J of what 2nd has 
 equals what Ist has. 
 
 LIX. 
 
 . ,, . 8x1000 
 Apothecarie8= ^ =9|-i lbs. 
 
 olbO 
 
 1. 19. 
 
 2. Area of roof=20 x 15 ft. = 300 sq 
 walls=70 X 9 sq. '•t.=030 S(i. ft. Deduct 
 ft. Number o-. sq 
 909 sq. ft. 
 
 ft. Area of 4 
 
 t doorway = 2] sq. 
 
 ft. required - 030 + 300 — 21 sq. ft. = 
 
-^tjifi^y 
 
 i 
 
 Hints asi» Axswkrs. 
 
 35 
 
 * 
 
 :i 80 lbs. of fish .ire worth '* '* =r82.;">0. .SO will 
 
 ^^- $2.'. X 100 
 l.uy 100 8q. ft. of lumber. -.SS. 50 will buy " "gj^ = '^H 
 
 .,. ft. 
 
 4. Number of cubic feet in room=20 x 10 x 9. Number 
 
 20 X 10 X P _ , 
 . t cords = = 14 ,V cords. 
 
 iJo 
 
 5. Number of fnrrow8=(o00 ft.) 3«'.00 in. ~-15 in. =240 
 Distance = 240 x 500 - 120000 ft. =22 y\ miles. 
 
 0. See L\' I. and (5). 28^ ft. 
 
 7. The former by '01 of a rod. 
 
 8. Interest on 8100 for 1 yer.r @ 3.t per ^nt. per G 
 jntha = $7: for 2^ years = ^<i;>] .-. amount of ^luu = $1101. 
 
 mon 
 
 Amount of $40. GO- 840.00 X ,_^- 848. 41^1-. 
 
 110] 
 100 
 
 9. 8 . 50 per barrel. 10. 195^- ft. per minute. 
 
 LX. 
 
 1. Man can do J work in 1 day. Boy can do -^^ of |x 
 f in 1 day = .^V) '^^ wt>rk in 1 day. Together can do 4 + 2j 
 " ./„ in 1 day. " .whole work in 3^ days. 
 
 2. 2^ days. 
 
 8. Oil 820 gain is $2%. • . gain per cent, is 12i per cent. 
 4. 2iid boy runs 130 ft. while 1st runs 150 ft. .•.2nd 
 
 150 
 runs 1 ft. while 1st runs -— :-- and 10000 ft. while 1st runs 
 
 XoU 
 
 150 
 
 lOOOOx V..:; =11^40 1". ft. 1st runs 11 rounds and 54G,-.5 
 
 feet. 
 
 130 
 
 5. Gain at 30% prnfit=^^,yof cost. Gain at second rate 
 = i^(A) "f 5 of cost=i'(;\j of cost. • . stcond gives greater gain 
 
H9 
 
 34 
 
 Hints and Axhwers. 
 
 C, Number of sq. yauls carpet=^25 00-1-^1.25=20 3<|. 
 yards. Width of rto(>r=20x0--15=12 ft. 
 
 7. Sold to A 50 X 20= 1000 aq. rods ; to B (484 X 000) sq. 
 it. =1000 if sq. rods. Sold in all, 2000^ rods. Has left, 
 040 acres— 2<»00if rods = 100333;', square rods. -.has still 
 
 >00.':33irods. ,_. .,_, i • i r^ 
 
 •* = ] v>^ s' .-. J so# square mile is left. 
 
 640 acr. '''*' ^"^^ ^ 
 
 8. 196 lbs. of flour are worth 85.00. -.7 lbs. are worth 
 7 X 560c. 
 
 196 
 
 ^20 cents = value of 10 lbs. herrinef. 
 
 9. By sellini,' flour, fjain is 20 cents on ^5.50. Interest 
 on $5.50 for 6 months® 7%=19| cents. '.the forn. r is 
 the better. 
 
 10. Interest on ^oO'' for 1 year @ 6%=$30.-.$25 is 
 interest for l^ of 305 (lay8=304| days. 
 
 LXI. 
 
 Ml 
 
 1. C=:E-5. D=C hE-45-E-5 + E-45=2E-o0. 
 Br=C + D - 35=:E -5 + 2 E - 50 - 35=^3 E - 90. A=B + 
 10=3 E + 80. .•.A + B + C + D-f-E^E + E-5 + 3 F.-50 + 
 3E-90 + 3 E- 80=10 E-225 i.e., 875^10 E -i.*-.i5, or 
 10 E^llOO, E=110, C=105, D=170, B=240, A ^250. 
 
 2. 63 cents=84%. 3 cents=:4%. 75 cents=100%. 
 83 cents=:110:j%=a gain of 10;t%. 
 
 3. In one day A can do Jie work 24* times ; B 2^ times; 
 C 25 times, and D 2^^ times. Therefore, all together can 
 do the work 10 times in a day, or the work in ^jj of a day. 
 
 4. $1.80. 
 
 5. 29 cents in the dollar on $1700=^493 : hence 
 exfenses must be ^457. 7- >. 
 
 6. Total expense is 5^ cents in the do':ar Ikmi'" the iio» 
 rental is 94| cents in the dollar on i^S.woO, or .'i<7.")i;o. 
 
Hints and Answers. 
 
 35 
 
 lence 
 
 i 
 
 I 
 
 i 
 
 7. For each dollar of cost he formerly received 81.25, 
 but now receives if of ^l.'J."), or 81.42^, so that his profit 
 at the advanced rate is 42'-' per cent. 
 
 8. SI 125. 
 
 9. 81400 in Dominion Bank. 8420 in Bank of "Slow 
 treal. Total half-yearly interest, 80li.70. 
 
 10. Asks 130 per cent. ; accepts 113| per cent. ; gains 
 13^ per cent, \vhich=S317.50 ; therefore 100 per cent, or 
 cost of the farm=823(r,»JT. 
 
 LXII. 
 
 1. 14 days, 18 hour.«, 30 minutes, 12 seconds. 
 
 2. The pure gold in the ornament weij^hs j",j of 13^ dwt. 
 .■=^r^Q oz., and is therefore worth 812 Uj-^. 
 
 3. 1 ac, r., 17 per,, 23 yds., 4 ft., 108 in 
 
 4. 10 lbs., 4 dr. 
 
 5. 30 lbs. avoirdupois=43| lbs. Troy, which are to sell 
 for 83*.).o0, or 81.13f per lb. 
 
 C. Loss, on 814000 is 85250 .Joss on 83581 is 
 81342.87 k 
 
 7. 8385. 8. 120. 
 
 9. A received 32 months' pasture for 1 cow ; B 48 : 
 and C 30, hence A should pay -/j, B{'.^, and C y\ of the 
 cost, or 88, 812, and 80 respectively. 
 
 10. A has 8000 for 3 months, v,hich=81800 for 1 month; 
 and also 8450 for months ; which— 84050 for 1 month, 
 or altogether 85850 for 1 month. B has 811^50 and C 
 89000 for 1 month, therefore A should receive ^f ; B f | ; 
 
 ^ 58* 
 
 LXIII. 
 
 1. In the first case i*^ lbs. cost 81-80, oi 1 lb. costs 7 
 cents ; in the second, ^^ lbs. cost 81-50, or 1 lb. costs 
 cents. 
 
36 
 
 Hints and Answers. 
 
 1 ;: 
 
 M 
 
 2 (1) The minute hand is 20 minute spaces Khind tne 
 hour hnnd and : ' " ^ to be at right angles will requne 
 nour nana, aiiu ••" ^ „,;„„ ii otin,^«>v 
 
 tr ,nn "> snaces i'- ' .^a the minute hand gains li spa.t- 
 
 .sain 20 spaces, hence It of 20 is the answer. {S) i , ot oo. 
 (4) If of 50. 
 
 3. 81. 4. lO.^;";, yards. 
 
 5 A crets S20 fur B's 825 or for C's $24, hence A get. 
 j«^ or 8100 : V. i:^l^o, and C 8120. 
 
 r, I am entitled to the use of ^OGO far 6 months, of 
 85700 fur 1 month, or 8570 for 10 mouths. 
 
 7 If IG men-^20 boys, 32 men- 40 boys, so that 31. 
 men and 10 boys^50 boys; and if 20 b-ys do the work n, 
 42 days, 50 boys can do it in lo days. 
 
 8. Of any two numbers the G. C. M. x L. C. ]\I.= 
 
 product of the numbers, hence i?^=30, number i. 
 quired, 
 o '^« 
 
 24 
 
 10. ~ cargo-l ship ; cargo=/o «^»P -' !' «•' ^^'^ ;:'^"^. •.' 
 divided between the cargo and the ship m the ratio ot •. 
 to 10, hence cargo-i^^ of 200,000-800,000. 
 
 LXIV. 
 
 1. The cash and credit prices may be representod bv 
 140 i.er cent. an<I 150 per cent., or by 14 mid lo, or by-1- 
 and 45, hence 42 ci'uts is the cash i>nco. 
 
 2. 32-4 28 sum of ages now. Therefore, Marys 
 age is 8 and Jane's 20 years. 
 
 3 If the water is 50 qua; ts less than half the mix 
 the'wine must be 50 (luarts more ; but the win.> is :■ 
 105 quarts more than oro-Hfrh the mixture. UwiW • . 
 the dilfertnee between \ and 1, the mixture is ^) <i'. -r. 
 makiu' 250 altogether, 75 water and 17o vviuc. 
 
Hints and Answers. 
 
 37 
 
 vv 
 
 I 
 
 4. 824(10- $000- 81800=cost of 30 per cent. /. $0000 ^ 
 cost of 100 per cent. .-. 200=uumber boui,'ht. 
 
 5. Cost and selling prices may be represented by 100 
 and 140, or by 5 and 7 •. cost is "of $1.02=-bO cents. 
 
 0. The top, bottom and sides are eiich 30 x 15, and the 
 ends 15 X 15. Answer, 15;' square feet. 
 
 7. $450 + 840=^$400=3 times cost of carriage. Answer, 
 ca/riage $10:Ji ; horse $-H0'^. 
 
 8. $05=92%-40%-52%.- $5-4% .-. $125-100%. 
 
 9. The whole interest is $15000 and the interest each 
 year $1000 ; hence the number of years is 9jJ. 
 
 10 For second horse: .^ 124. 80=80%. •.$150==100%. 
 For tirst horse : $150=130/. .-. $120=100%, 
 
 LXV. 
 
 1. She had V. left ; i.e., ]!] more than she spent .'.^^ 
 her money=$99.40.-.her money=-$119/J8. 
 
 2 In 20 lbs. std. gold there are H? of 20 lbs. of pure 
 crokl, worth Hj ot 20x240 or $4400, leavnig the alloy 
 worth 8100. 
 
 3 The second stick is on.y /., as large as the first, and 
 therefore 3(> feet of it would weigh ^ -^ 3000=900 lbs 
 but it must M-eigh 1200 lbs., therefore its length must be 
 1 -<y^ of 30=^45 feet. 
 
 4 4 lon*'er=2 shorter piece. Longer=4| shoj-ter 
 piece." Longer-f short er=5| shorter piece. 1 yjrrt-o,. 
 shorter piece. ;\ of 1 yard=shorter piece .-. ij of 1 yard 
 - longer piece. 
 
 5 At the end of months the amount due will be 
 $015. He pays $215, leaving 84! )0 still due. At the end 
 of the year this will amount to $410. 
 
 G. 90 per cent. = $0000 ;. HO per cent.=$733:'.i. 
 
 7. times the number=-804 ;. the numbov- 144. 
 
 S. Loss on $550=8200 .-. loss on $90— 8;'.2,V 
 
 M 
 

 3g Hints and Answers. 
 
 9. Weight of copper=6 X 3^=21 U.ns- 1 part=7 ton. ; 
 
 2 part8=14 ton8=tm ; 7 paits=40-uon. 
 
 ;i *v,^ fi^lrl i<* 218V rods, to fence which 
 10. Distance round the held is ^xo.j luu , 
 
 at $2.40 a rod will cost $o24.40. 
 
 LXVI. 
 
 24 X 7000 
 
 1. 24 lbs. avoirdupois=24x7000 yrains^-^g^^- -«>/'« 
 
 •^r.O r>nnces which at 80 cents an ounce will 
 L'lf ^o'S^fandX'ii lb. cost .?.'24, hence the ga.n ,. 
 
 $56. 
 
 450.000 X 3i 
 
 2. Weiglit= ^2000 
 
 3. I own 3 and sell ^ of it, therefore I have \.h f of |, 
 or J of the ship, hence my share is worth J?10,UUU. 
 
 1 He loses 1 ft. in GG ft., or 80 ft. in the mile. 
 5. He owned v\ android U oi his share, keepin,^ U oi 
 his share, and U of i\—iio' ^^^^ ^q 
 
 6 One dozen cost $10.32. '. number ^ozen=''^^^^ 
 
 7, I of $32324. 58 
 5 
 
 ■tons ; cost=450 x $5,^. 
 
 8. 
 
 7 175 
 of T:i—-7:?r > 
 
 5 
 
 2 " 34 38 
 
 175 77 ^210 
 
 -33- • 228 61 
 
 3 210 
 
 '^4 + -Gr= 
 
 "244- 
 
 9. 62| cents. 
 
 10 $33.60 + $3.3G=$3r,.0G=selling price of 1 cwt..'. 
 selling price per lb.=3GyG cents. 
 
 LXVII. 
 
 1. fifcnj of $1560.50=$14.04. 
 
 2. Silk, $26.25 ; tweed, $24.75 ; . ^S $1C4.00 ; oats, 
 $16.54 , lumber, $4.80. 
 
^^':> i.^-j^^--m-^^m m ' ^^ 
 
 "~^ 
 
 ■"^9^ 
 
 ■^"rf. 
 
 Hints and Answers. 
 
 81) 
 
 i 
 
 i 
 
 3. The tim. is 1 year, 122 days The interest for 1 
 year is 812, and for 122 days, $4.01 ; total interest, $10.01. 
 
 1. ..\ in the air=12 ft. . ' . length of pole=57^1 ft. 
 5 Area of walls-1176 ft. ; area of doors, etc. =204 ji. 
 ft. ; area of ceiling = 4;}2 sq. ft. =140 sq. yards. Cost = 
 
 "^ 6 The smaller wheel makes one revolution more than 
 thela^^aer " e in every 'AO ft., and as this distance is con - 
 [ufued 220 tunes in if miles, the required answer is 220. 
 
 7. ^l|=i?.=i'i- 
 
 8 On 885Cv; he pays 84750 ; on $1 he P^'Y^ fP?> = 
 r>r,l^ cents .-. loss ou $1-44-^, cents ; loss on $14,o = 
 
 !<('..")b.74. 
 
 .> Cash pricc=ijr <>f ^'o^t price. •. cost = ^,o of ^^^^^p^.ce 
 Jo oS. VI) = 88! 00. To hnd the credit price, add 5 per 
 cent, to 88.80 and we have $0.24. 
 
 10 8130 in 9 months at per cent, will amount to 
 8135.85, hence the ca^h sale is the more profatable. 
 
 LXVIII. 
 
 1 -heir sum is 11,100 ; their difference is 7,080 
 11 109 + 76«0=18858=^X VHIDCC CLVIII. 
 
 2. Remainder=570 ; divisar=^1728 -570^1 .72 ; div.- 
 dend=1728 x 1152 + 570=^1,901,232. 
 
 q n ^ 1 V X 1+ X 040^-1000 ac. =10 farms. (2) " "'i»;^-;i- "- 
 J2OO acVes. ^H) 200, 80 ; 10c, 100. 
 
 4. The hoop turns once in 0.2 tt... 5,, <-ou. 
 
 5 The detective is 504 miles behind the prisoner and 
 .ams 84 miles a day ; he will therefore overtake him in 
 days, or 10 days after -\e prisoner escaped. 
 
 <• K noat everv seconds is ten posts a minute, or 30 
 ,.'3 iniiLtes, le! 30 in a mile, or 3000 in 100 tutlcs. 
 
 it 
 
 h 
 
" ' .. S .,*\f^" - i 
 
 
 
 iX^ 
 
 "l 
 
 i! 
 
 40 
 
 Hints and A>'swers. 
 
 7 r r M of S8 00 and 80.80 is 20 cents.'. 43 boys 
 ,u,a»4,S. altogether, aUowi„s 42 boys anlSSginsto 
 be invited. 
 
 » If mo bnsV. nil 12.-> cubic ft., 750 busli. will reqmre 
 •r *-!, cui? " f . ami as a l>i>i 12i ft. s;,. and 1 ft. h..!; 
 wotfld cou.aiu iolii cubic ft. .-. the rcuued height would 
 
 1)37 V 
 be ryrrj, or 6 ft. 
 
 p*>9.iWe a-reuatc = 50x220 = 11000; Jays lost = 
 250 Tactual ag^^gate^ 11000-1250^0700. Average^ 
 
 1250 
 
 9750 
 
 220 
 
 = 41.7... 
 
 To li.ki.w 4 for each son's share, the mother's share will 
 b and ead. daughter's .hare 3, so that the -j- -U ge 
 12 the daughters 12, and the ru.ther b . • . each daught. • 
 iels one-te.Uh of the property (after deducUngex,.enses), 
 ;vhich would thus be $18,000, and r/^ of this = l?l», <oO. 
 
 LXIX. 
 
 1 The s,.n does .1 of the work, and would therefore do 
 it all in 24 days or 210 hours, and 5 tunes as much m 1080 
 hours, or 90 days of 12 hours. 
 
 2 >V7 oO = li of cost.-. cost = ^ of S2..50 = 2;i. If sold 
 for $3 "the gaiti would be S't, which is ..'a of cost. 
 
 3. ^oh,.s..are^^ ;. ^.ne^; 1^^^^^ 
 
 S8:Jo;^l^wmh^v^l2.Tou^.0,andAlex. 1^^^ 
 each 155 or 32, 48, 120 and 420 respectively. 
 
 4. A does i and B /,, leaving ?,;! for C, which he can 
 do in \;! -f 8 hours = 2,;; hours. 
 
 5 One man for 1 week cost $2.40 ; 1 woman, $1.80 ; 
 1 child, .$1.44.-. total cost = $12lU8. 
 
 6. f =42| bush. B's share = | V = ^^25 bush. 
 
 7. He has acres and sells ^ acre for 3050 guineas^ •^. 
 remaining ^^ are worth 20 x 30oO gunieas, or $484,939.00. 
 
-^ 
 
 Hints and Answers. 
 
 41 
 
 8. Th« hall is 35 by 21 ft Cost of carpet, $122.50 and 
 $105 ; ditference required, $17- oU. 
 
 9. He still has iH -300122 + . 
 
 10. 204. 
 
 LXX. 
 
 1. Groceries sold for 8^275, and cost ^ of |7275 = 
 So820. Boots sold f«r,f ?^2(^ and cost ,j 
 «447(J 1 - Dry-goods sold lor U^^io, ana cost t i? 
 
 ti 003 ' Tolal cost = $22300.07 .• • gain = $0799. dd. 
 
 422x4 
 
 2. 83iH per cent. 
 
 3. The time = 422 days. Interest = $204. 40 x ggg^^^QQ 
 
 = $1) 45 . ' . answer = $213. So. 
 
 4 The first gets 30 weeks pasture «<>' »""„%' *^ 
 set na V; th£ third 24 , a.^ the tou.h,^18 ^He^ce 
 
 the tirst pays t'.fo o\J*^' X\o in 
 the third, $10.80 ; the fourth, $8.10. 
 
 5. imile = 1320ft. 1320 x 4 X 2 x 3 = number ft. lumber 
 .-.cost = 1253. 44. 
 
 6. Width of zone = 43 degrees. ' . #5= answer. 
 
 7 *$27 97 
 
 a The watch ^^^/^ .''rrylooTuf t.t T/h^n 
 
 ;^;:;"r tr^^i'^i^a — s to 12 o-aoo^ 
 
 Saturday night. 
 
 ;i f fV.o wPf k the watch will show %fsh of a 
 .vetk^:r':L-thetKr:eekTthatis, 18 minutes past 
 
 12 Sunday morning. 
 
 $03.75^^21 loner tons = 12ix 2240 lbs. =28000 lbs. 
 $7.50 -^ 
 
 10. 
 
 = 14 short torn ' ■ ' price =.$105. 
 
(' 
 
 I 
 
 42 
 
 HiNis AND Answers. 
 LXXI. 
 
 i A o ..f 10 acre field is 1000 sq. rods. Length oi 
 
 1. Area of 10 a^^^ "« a^ rods -40 rods. Length of 4 
 side IS sq -f «y^f^^3 "^bo t at 15 cents = S24. Length 
 8ides = 4x40=l()0rods^^ ,;;^,,_ J ^,^^1^ ^f 4 sides = 
 
 2. Block 3 ft. long, i ft. thick, cont^vms 10 cu^- ft " « 
 cubic ft. =2 cubic ft. •. breadth = 2^2-1 ft. l.u . 
 stick = 10^ (t1ix1) = 1^ ^^• 
 
 3 Marked price = 140% of cost. Selling price to friend 
 =tof 140% of cost = 112% of cost.-.gain = 12/.-^1.0«. 
 Cost = $900°. 
 
 100 X 15 
 
 Income = 5^% of $18000 = 1^090. 
 
 91)0 
 
 = S15 Tax on $990 is $15 . ' . tax on 8100- 
 $1U = 1B per cent. 
 
 5. Merchant pays ^. of cost. Last PJ^rchaser pays ^of , 
 of cost = f of cost . • . !/ of cost = ^'^0. Cost = b.O. 
 
 6 On 36 in. gain 39371 in. -30 in =3-371 in. . ' . gain 
 percent. = M^of3-371=^9i;iJpercent. 
 
 7 The slower train has a start of 50 miles. Faster 
 
 rctbX, a: uiu^tlt 15 minute spaces. «au.. U 
 smces in 12 minutes.' .gains 15 minute spaces in U-A 
 mLJcs. Answer, 16^ minutes after 1 o clock. 
 
 9. i of circumference is between "'''''»••,• i"'.?,";';""': 
 
 fei^nce = 7i inci.es . • . citcuu.ference = 41 n.ches^ .,, tn ncs 
 
 he dmmetcr=44 inches.- . drameter is 44+.!} -14in^li<-s- 
 
 t^Xof "."•■•'« '-»ir"v24'''8ift"'^ "■ " 
 
 travelled in 24 hours=44 m.X24 = «» tt. 
 
 10. 
 
 Ait 
 5 • 
 
Hi>'TS AND Answers. 
 LXXII. 
 
 48 
 
 240 acres. Kept 200 acres. 
 
 o 1 .>f his money is 82000 more than W hi^ money 
 ana ^1000.-.^ of xno.^y^ «^.-^y;^$3obo\ 
 uK.ney - .^40000. Gave his son $.0000. 
 
 3. 155 yards. 
 
 4. B spends » of l=ii of income .-. ,'o <>< ■n~™-^ 
 S55. Inci.uie is !<ijoO. 
 
 5. V bbls. ,.f Hrst a. worth 817.^^^^ 
 
 S"of s"l!"a,.e :!.fth Vr^5«raia 1 bbl. .orth *8,75. 
 First is worth $11.25 per bbl. 
 
 r ^Pllincr nrice=T of 85 cents =$1.19 per gal Number 
 
 6. Selhngprice ^ ,^,^^. u)^r^()-^. Number of 
 
 of gaUons ^«l;!=;".;:;rV85 cents=7l»4.L."' Number gals. 
 
 ■1 1 i. +„ 10 i^{ vvholo votes. Uereateu 
 7 Elected candidate gets ]o ot y^*'^^^i'^__e^ j. of 
 r 80 /:i8+--5^t = ''F> of wholevotes. Ditteience— ao oi 
 
 gets 5^ - bo + 80 ' >^o 
 
 vM )tes===5 . • . whole vote = 400. 
 
 S. in 18 seconas -in Hoes 204 yara.^,I",^lf ^^ 
 
 ^•^71 ft Cubic contents =<.3< 4X^2^* -^^ ^ 
 fT Costat2Uperft.=$258.03|. 
 
 V -sill % ':!. tr-of ^t uLH' ali^U' 
 
 sheep = togetner j\o ci-nn 
 14675 . • . cost of each = $1000. 
 
 LXXIII. 
 
 1. Difference between f ares =J^f whole capUal ^.^i 
 of capital=$3792.-. whole capital_$30Jo^. 
 $1328 ; B's, $1707f. 
 
1 1 
 
 1 
 
 &4 
 
 Hints and Answers. 
 
 • «iino • A and B receive $130. If $130 
 2. C receives $100. . A ana x> soOxlOO 
 
 be gained from $390, $100 will be gained from -^3^- 
 =$300. which is then the value of 120 yards of cloth.'. 
 1 yard is worth $2. 50. 
 
 • ™«r+l, 23of S9000 = $10350. I of first 
 
 price = n f ?„"( 05220 = 85800. Allowed J- discount on 
 rHngtr.-.-fofSgprice = «D800. Asking pnoe ,s 
 
 ^of $5800 = $7250. 
 
 rtr8i5"(5o*'fnTe7e!r.'Tof «0800=Vm Total 
 gain = $2.3o0. 
 
 6 Area of end= 4 sq. ft- Length = 16x27^4 = 108 ft. 
 Value = 108X55 = $59. 46 
 
 ltt;kedout = 63-48 = 15gals. 
 
 8 Value of wheat = 20x 2i times $1.05 = |52. 50. 
 -1 of cost • $52. 50 = I of cost. I of cost = $8_7o. 
 _5 0ituai..v post • S50 = ? of coat. (jram-?!)ivJ. 
 
 chant's Kain = l of cost. .9fou 4 
 Merchant gained the more. 
 
 o 1 4 of « sells for $2700;.ship would be worth $23000. 
 9. TW ®^ 7 ^^"* ' . * •, • s . 9-2 of former value = 
 
 |5^i;<5^'' =^12:= v/o™V2¥oyi.25000. 
 
 .^.^. ^"'-Xere.^' Sete'l^^rreJitit^Lls^t 
 Difierence = 82 per y^^^- "' ^i,„^ ■ $28.80 is the 
 
 Sand 6 P'Vrtnl $28Mx8 = «230 40 = interest at 8% 
 'n"fnd;^liiha40-|230.40 = «480 00. Interest on 
 iS tor 1 year = S28.80 .•.rate = 6%. 
 
 Gain 
 Mer- 
 
 \ 
 
 I. 
 
Hints and Answjks. 
 
 45 
 
 'M 
 
 LXXIV. 
 
 1 §130. 2. SU4.r)0. 3. 8 years. 
 
 1 1 -al milk cost 1<; cents, and is sold for 24 cents. 1 
 
 nf milk. . in o 
 
 5 Frcmi loth October to 15th Mayis 212 days. .lO^'r 
 
 tons wm be used. Cost at 80.50 = ^OoOli?. ^^ 
 
 « P«in on (me = 1 of cost . • . selling pnce=:^ of cost. ,. 
 
 OoBt ot two=$ J050. Loss IS ^oO. 
 
 . Each of Hr.t three rides twice as far .s the four.h 
 iourth pays} of cost = f of $o = 71r cents. 
 
 8 ICOO yards. '.>• 838.40. 
 
 10. Number of cubic yards in room-— ^7 " 
 
 cubic yards. Number of cubic yards per pupil = 000 cubic 
 yard3^40 = 15 cubic yards. 
 
 LXXV. 
 
 17 
 I 
 
 1 I) 1- 
 
 1 12001).)4. 2. £480. 3. 
 
 4 Paid 2d. in the £1 .".has 238d. in the Ml Iff^H^^f 
 money. Ir^, of income = £1^8 10s. . .mcom. .,.,. 
 103.=i:i80 
 
 If .addle o'^.t h of whole, the lv>rse est 
 
 of whole 
 
 • » of whole = £00. Whole cost = ^ of £00 = £ JO. 
 
 ft TntPrest on £inO for 4 years (5 2.V per cent = £10. It 
 
 principal is 10 times £oUL i^s. ^u. 
 
 .11 on L''n-i.oi4-'^4 ft =108 ft. Area 
 
 yards of paper 
 
 ^150^1 = 200 yards. 
 
 tl 
 
/ I 
 
 4C 
 
 Hints and ANswF.nrt. 
 
 10 
 
 »ofco«t = u «Hi-/.c''«.t%^:';.rT 
 
 24, ,,r OiL per doz. 
 
 ()( 
 
 
 ImustselHorAofGd 
 
 : iOd. per tl^^ 
 
 LXXVI. 
 
 1 \rea of one si 
 
 ,d„ofcube = 31xni.,-ft-=12i«1 
 
 Area of 8=x rki 
 Mte coveri'd by 
 
 r8= i 
 
 ft.. ior)<s4 s(i 
 
 aiu;.lii:)S4 8(1. in. 
 
 S( 
 
 ft. 
 
 in. 5(» sq. in. 
 are covered by 
 
 105H4^rjG-r8.=lbOgi 
 
 .>-,xt5e_ 1 V.l"- cents 
 
 ,fco'-.t- 00 cents. Cost= 
 
 Gan. i: '; = ^ of coBt;.'^*- 
 
 price 
 
 '., r -it — '-2:^ of i'''.!"=7o cents p* 
 =i of cost = . JO "I -:» 
 
 rib 
 
 revives 85 nu.ve th;u. 2..a [V->t2^=84. 
 recciveb i<^-^o ; 1st, bl.> ^•> 
 
 f^2. an 
 
 d 1st 
 
 II 
 
 il divide 
 A2]y', 2. A 
 
 4. 27 A mitiutes after ."> o'clock. 
 
 ' n 1 - '•*;->() -'-120 - Sr>. 41 ", per bb) 
 
 5. Avera-e cost i;';';; ' r;;;.;.;, ,;ents, or Ic. on ,h 
 
 bbls. On bbl of sec a y^^^ =,^ ^^^ ^^^ «eco.d = o ox 
 
 first 'to 4 of seci.n. =*..... b.b. 
 bbls. of second qualuy. 
 
 1 , f 1 oil wine • Sl.OO IS value ot y-^o 
 G. ^^•20i^valaeof 1 1^.1, ^» . .. ^ ^^^.^^ ^^ ^^^^r. 
 
 = 5. gal. of wine. Ueinaindei, « ='U. .^i 
 
 ,, • _r,oix^'> !.')=>' I <)!^3*^0. Freight, 
 7. Cost of 4 l'^P';^^^;;-,::i;.,>;);.(i:. T..tal co«t= 
 ^57.00. Duty,^ ^V. ^^ ^Jl^'Vl40l.2uV ^^57 H.7oi?.-. gains 
 |l401.2Gl. Gain=^lj|^0 .- i^ui. .. 
 
 __ 100x$iV78/73J^__j^^_j_pj,j. cent. 
 
 per cent.- — ^^^Qj^ 25H 
 
 34 bush, corn and •^•^ bu^h. nar .>, ,, ^,,,.,^ j, .^orth 
 
 cents per bush. 
 
11 1 MS ANP ANSWKKS. 
 
 4*1 
 
 , f J,. .. rh ■ -ioll-* at i?c. each /.pn. lit i- 
 H,. 1 'v L j„c. per peach. Must buy and sell ^4.^0 . ,„ 
 — 1 ■_'(!( > peaches. 
 
 10. 144^. 
 
 LXXVL 
 
 1. Area of hall = -I x l ' i^. .,- ^ 21 o=$29.1G-:i. 
 • rxi.emo of carpet will be !-1.2oX „ -J!?-^. . 
 
 *>. '20 gallons. 
 
 * +r..inq nasa over in 8 seconds v^yv.xh 
 
 3. Dl.fancc two ^^-^^"^ f ^^^'^'^^^as, tirst train ,u..^cs 
 ,l,oir eo.ubiued lengths. 1" J^^^'^^^^^ ^^^^0 yards = :i.V2 tt. 
 .- >n V- rda • in 8 seconds, moves off ^^ f."^" ^ .,-0 , -wo- 
 
 1.1 1 ,ap 4- of 5=:8ir minutcs. It 
 
 4. In 42 hours it would lose ..^ 01 o 04 
 
 will show G, 1', lo". 
 
 f <.n «^100 for 2lf years (<i> 7% is 817 \. ^l i"* 
 
 5. Interest .m $100 f >r i y ^,^^.,^^ 
 
 interest on l<J^-;.$5.87i is interest on-^^^^^^ 
 
 . c n :^ of • -icle for 3 of cost/.sold whole article for 
 
 . ;, 1 of sellin- price.-.^ of selling price h; 
 
 7. Discount IS J; ot suiui, 1 • •- ,)Q3 cents. 
 75 cents. Selling price is i' of i.> cents U4 
 
 ^ • fl of 10 lbs =S1. Cost of 10 Iba. 
 
 8. Gain=^s "^ c"^^- -^ ,k " r' '. ,^ u lb.. =97;, cts. .'. 
 _^H^-88^ cts.=8i;c. per lb. Cost^> U l^- |^ 
 
 ^Un is 2I cents. Gam per cent. -(2, . .)..)xIUU u 
 
 per cent. 
 
 oinn for n vears ^ 4 per cent, is $20.". 
 '>■ TT^Z for . n u..- ® 4 Ver ceut. U «120. 
 
 • 1 i. i i^ — ■1^4.2 = SG = V'w of aiut. 
 
-%r^:j■^ne^. 
 
 48 
 
 HiMS AND A>iSVV£iU}. 
 
 LXXVIII. 
 
 r 
 
 ■ I 
 
 1. Weight of shilling=87 grs.". weight of silver is ^J of 
 
 3x100 
 STgrs. =3dwt. 8]^^ grs. Alloy is ^^^ of weight = — — — 
 
 per cent. =7^ per cent. 
 
 2. k- 
 
 3. Interest on S50 for 1 day = l cent .'. interest on $100 
 for 1 day = 2 cents. Interest on ^100 for 1 year is 2 cents 
 X 3G5 = '&7.0O .". rate per cent, '^er annum it 7^^ per cent. 
 
 4. Number of sq. yards of carpet equals area of fioor= 
 £5 12$ -^3s. (id. =32 sq. yards=288 sq. ft. Width of 
 room is 288-^ 18=1(> ft, Area < f 4 walls = nuniber of sq. 
 yards of paper = €17^ 4. U. =75;'; scj. yards = 080 sq. ft. 
 Length of 4 wails=G8 ft."', height = 080-=- 08=10 ft. 
 
 27 
 
 6. Number of sq. metres = 393 '7 x --v_-: =270 8q. met. 
 
 Value at 4 francs per sq. metre = 1080 francs. "Value in 
 English money = (£1080-^25.15)=£42 18s. lO-Vjcl. = 
 10300 .^.f.^d. Number of sq. feet=]03U(i.«2^d. 4-3d.= 
 34.351 ji;;. Length of cotton=3435i,";^-^4=8o8,Vt/o. 
 
 0. The use of £91 15s, for £4^ is the greater rate. 
 
 7. 3 men can do ^^Q of work in 1 day .-. 1 man can do j^^^ 
 in 1 day. 4 women can io ^}^J of work in 1 day .•. 2 women 
 can do ^^ in 1 day. 5 boys can do ^g of work in 1 day 
 .'. 3 buys tan do ^l^, in 1 day. girls can do ^.V, of v/ork 
 in 1 day .". 4 girls can do q\^ in 1 day. 1 man, 2 woiik m, 3 
 boys and 4 girls can do ,,i„ + 120 + 100 + uo i" 1 ^''y- 1 
 man, 2 women, 3 boys and 4 girls can do ^^^ in 1 day.', 
 do whole work in -?^Q=28i days. 
 
 8. Spend? ^ + '^ of money = i;j of money .'.has left ^} of 
 his money=JJ of i:3 5s. 4d. =154d. Can give away 5^d. 
 to 154d-^5^d. =28 persons. 
 
 9. Number of sq. yards in room = £G 2s. 6d.-i-5s. =24.J^ 
 sq. yards. Floor is two squares of 12 j sq. yards each" 
 Width of room is. therefore, square root of I24- = ^ yards 
 = 3. V yards. Length is 7 yards, i. e., 21 ft. Length of 
 
«if 
 
 Hints and Answeum. 
 
 41 > 
 
 rt:ills=r)3 ft. Number of yards in \vall = €l (»s. 3cl. -fT. 
 -:-'.» yd8.=o."3 sq. yards=315 8t[. ft. Hei^'ht of wail8 = 31."j 
 =5 ft. 
 
 , . 24 
 
 10. Clock goes 24„^ij hrs. in 24 hra. .-. sjoos 1 hr. m --, 
 
 24x24 
 
 1 _ 1 
 
 and iioes 24 hrs. in --^^-=2:3 hrs. SDi^^^j min., or {|{V 
 of a minute to 12 o'clock. 
 
 LXXIX- 
 
 1. Has h money left when leavin;^ first shop. Has fj of 
 ., = .'. of money left when leaving second shop. Has i of 
 \ = ,'. (if mcmey left when leaving third shop .•. i',-, of money 
 '=ls.' ./hole s>im= V' "^ ls-=:^s. '-W. 
 
 2. Wages for 30 days at 40d. per day— £5. Loss fron" 
 idleness=£5— £'3 lis. £1 9s. Loses each idle day wages 
 and forfeit— r>8d. ..loses £1 'Js. in £1 Os. ^58d.=0 days/, 
 was idle 1. days. 
 
 3. 'r^ of the voters less 85 voters— J of voter + 00 voters 
 • } of voter8=145. Whole nuuiber— 435 voters. 
 
 4. 4 hours, 48 n/nutes. 
 
 5. In 24 hrs. gains 4 min. From 6 a.m. to 7:15 p.m. 
 
 13^ x4 
 is 13i hrs. Gains in 13^ hrs. -94" "^2"* ^^^^' ^^^^^^^ 
 
 be placed back 2.;\ min., i. e., 5:57 .^^ a.m. 
 0. Rate of stream is 4 mis. per hr 
 
 ^ __2;J 
 
 ^ 8 mis. — late of stream 
 
 per hour. 
 
 7. r of A's money=B's .-. A has £2i to B's £1. B has 
 £9 to"''J's £7, or £1 to £7 .'.proportfons are 2|, 1, ;. A 
 
 haa -i- of £770=£450. Bhas ~^- of £770=r£180. 
 4fg 1 a 
 
 hau -4- of £770=:£140. 
 4ts 
 
 8 
 
 Rate.cl stream + 8 mis. 
 rate of stream is 4 miles 
 
m 
 
 
 50 
 
 Hints and Answkks. 
 
 8. Cost of 3 apples at 3 a peuny^l penny. Cost of ;] 
 of 3 apples— 2}t apples, at 4 a penny or | penny each=;7 
 
 X 3 X ] — 5d. .-.cost of 5.V ai>ples is 1^'d. /. cost of 1 apple is 
 \-^^oh=i'i, and sells IC for Gd. or i"«d.— gd. each. Gain 
 =gd.-J-^d.3.-||d.-5gd.=^gd. on each apple /. gains 1 
 
 3ix88 . .. 
 
 penny on ^^ apple, and gains 3|d. on -^ — apples— 44 
 
 apples. * 
 
 9. Interest in second oase is at i rate for ^ time .'. inter- 
 est is ^ of the former. Difference between interests f<)r 
 the two periods is $525 '.interest for time at G percent, in, 
 ^ of ^o25=$G00. Loan=$GOO- $100=8500. 
 
 10. On 1 lb. of spice at 8s. per lb. loss is 2s. On 1 lb. of 
 s))ice at 5s. gain is Is. . . 2 lbs. must be takei/ of 53. spico 
 to 1 of 8s. spice, or 40 at 5s. to 20 at 8s. 
 
 LXXX. 
 
 1. First, 21 gals. ; second, gals. ; tliird, 2 gals. 
 
 2. A in 12 days can do | of work, or in 1 day do ^^ of 
 work. B can do ^(j of work in 1 day. C can do •^\ of 
 work in 1 day. A, B and C can dv ,V, + 2'o+ iV ^f work 
 =/(-, of work in 1 day .*. can finish it in 5C' days. 
 
 3. 383, 321. 4. 15 per cenc. per annum. 
 
 5. Interest on $1280 for 1 year at 7 per cent.=|80.G0. 
 Whole interest is $220. $89. GO is interest for 1 year ; 
 
 $220 is interest for 
 
 220 
 
 89. CO 
 
 yeara=2fW years. 
 
 6. Each plank takes space 12j in wide. Number of 
 planks in 300 yards is 10800 in. -f-12^ in. =8812. V Num- 
 ber of ft. IS 881 fL X 6=5289^'.^ sq. ft. 
 
 7. $47.25. 8. $42 worth =1400 stt-mps. 
 
 9. Cubic contents of block=:24 cubic ft. Expansion of 
 water is |^q of bulk of water/. 24 cubic ft. ice=,L^ of 24 
 cubic ft. water^=21^j cubic it. 
 

 J>'^;«^«^*c..- 
 
 Hints and Answers, 
 
 61 
 
 10. Cost of flour without makiiifj is $5.62i per bbl. when 
 wheat is $1.25 .'.when wheat is 90c. it should cost /^*5 tf 
 f5.02|=r$4.05. Cost, including making=$4. 422 per bbl. 
 
 LXXXI. 
 
 1. Length of A's step:=32 in. Length of BV. step:= 
 22 in. 
 
 2. First consider A and B. A goes 4 miles to B's 5 .•. 
 A will have gone 4 times when B has gone 5 times round 
 the island, but A reciuires lOh days to go round the island 
 .'. A and B are together p'c the end of 42 days. Next 
 consider A and C. A goes 2 miles to C's 3, or twice round 
 to C's three times .'. A and C are together at the end of 21 
 days. A, B and C are together at the end of 42 days. 
 
 3. Man's wages=$00. Number bushels=:75 ;. price per 
 bushel=80 cents. 
 
 4. Cost of a horse = $90. 90. Gain on each = $120— 
 
 $90. 90=$29. 10 .-. number of horses = 
 
 ^349.20 
 
 = 12. 
 
 $29.10 
 
 5. $64. 
 
 6. Bought 1298 quarts for $51.92, or 4 c^nts a quart. 
 Sold 404 quarts for $20.20, o.- 5 cents a quart . • . his gain 
 is 1 cent a quart, or 32 cents a bushel. 
 
 7. $6400. a 16x10x9 = 1440. 
 
 9. For *'lb." in ^his question read "bbl." $1568- 
 $224-=$1344=cost of | remainder .'. remainder cost 
 $1680 . • . 20 bbls. cost $120. or $6 per bbl. .'. number of 
 bbls. is 300. 
 
 10. $78.21. 
 
 LXXXIL 
 
 1. Consider 24 miles (a multiple of 8 and 3) ; this would 
 take him 3 hours going and 8 hours coming back, or 11 
 hours altogether ; but as 5^ hours is all the time he has, 
 he can go 12 miles only. 
 
 I 
 
52 
 
 Hints axd Answers, 
 
 I 
 
 2. If 2 ho'is and .'} ducks cost 81.15 then 8 hens and 
 J2 ducks cost ^4.00, but 8 hens and 5 ducks cost 8-^85 /. 
 7 ducks cost ^1.75, and 1 duck cost 2oc. .-. 1 hen cost 20c. 
 
 3. $19.20. 
 
 4. The buor^ry cost 5 of his monoy, the harness ^t. jind 
 had i^. or $1.5 left ..his money = $225 ; buggy cost $150, 
 and harness $()0 . rec^uired answer is $90. 
 
 5. Interest for the re(juired time = $45.00 : interest for 
 a year = $20.04 .-.the required time=$45.0!) 4-$20.04 = 2!' 
 y( ars nearly, 
 
 0. A does ? in 4 d;iys. and therefore the whole work in 
 10 days. A works 5.7 days, thus doing ^Jj, leaving J;] for 
 B, .vhich he does in If days /. B can do the work in 3k\ 
 days. 
 
 7. Half an acre = 80 rods ;. width of lot = 5 rods/, 
 distance round the lot is 2ol yards = length M inner edge 
 of path ; lemrth of outer edge of path -=247 y;>rcls.-. avel*- 
 age length of path = half the sum of these=2;}!) y.trds • 
 area of path = 230 x 2 = 478. 
 
 8. 1 per cent, on $.'500 for 2 years=$(j, leaving $1.W as 
 the interest on both surnsat the lower rate ; at 1 ptM'ceiit. 
 the interest on these will be $20 ■. the required rate is $1.'^0 
 -f-$20 = 0i, and the higher rate, 7^ per cent. 
 
 0. Withdrawing }j the mixture does not change the ratio 
 of wine to w.iter, so that the wine is still ] '! of the wliole, 
 or the water is ,''^ of the wine. After 8 Lfals. water are 
 added the water is h the wine, so that the water added 
 increases the w iter from /'„ to ,';, „f the wine, and must, 
 therefore, be=,-„()f the wine.. ,H^ wine:^8 gals., or the 
 wine = 40g.ils .. wine at first = 00 gals., and water = 18 gals. 
 10. 100 ft. wide and 435' fr. or 204 rods long make an 
 
 400 i 
 
 — 15 185 nearly. 
 
 acre .'. number of acres 
 
 2()4 
 LXXXIII. 
 
 1. One-twelfth to A for management leaves S.3300 to 
 be divided as $15,000 is t.. $18,000, or $1500 to A and 
 $1800 t(» B . . A's complete .share is $1800. 
 
 
 
Hints and Answers. 
 
 53 
 
 2. 3 hours lost in tiine=00 miles lost in distance ; then 
 if 10 miles iiie lost in goinjr 20 miles, 90 miles will be lost 
 in going 180 miles. 
 
 3. In 72 days A and B can do the work 12 times ; B 
 and C, 9 times, and C and A, 8 times .-. the three will d(j 
 the work 29 times in 144 days, or once Ar,"^, days. 
 
 4. B's share is SlOO more than A's, and C's {?210 moie 
 than A's, so that if $100 and .^210 be both taken from 8700, 
 what is left v/ill be three times A's share .-. A's share is 
 8130, B's, 821)0, and C's, 8340. 
 
 5. Cost of house = |i of whole cost = £616 14s. 7d = 
 £6162ij=8i;| of 616^^ = 83001.41. 
 
 6. Number of steps, 21 ; 17 in. of carpet for each step ; 
 cost = 86. 20 nearly. ^ 
 
 7. Length of carpet = 357 inches /.number of surface 
 
 357 X ^^2 
 
 ^""^'=-36xiir=^y^^-'7^"'- 
 
 8. The 16 in. =5x3 in. + 4 x | in ; the 22.V in. = 7 x 3 in. 
 + 6 X ] in. ; the 23 ft =85 x 3 in. +84 x ] in. .-. number of 
 cubes = 85 X 7 x 5 = 2975. 
 
 9. Every 3j in. in length gives 35 cubes., the number 
 of such lengths=^' !»'-;"=200, and 200 x 3j -()50 .-. required 
 length = 650 -I =54 ft. 1^ in. 
 
 10. 39 -37079 x 4 x 10000000 - 1574831600 in. =24855 '296 
 miles. 
 
 LXXXIV. 
 
 1. 1 egg = 3oz. beef; 4 doz. eggs = 9 lbs. beef; but 4 
 doz. eggs cost 80 cents, and 9 lbs. beef cost 9C cents. 
 
 2. Each tree has 16 sq. yards of ground .. the number of 
 10 X 4840 
 
 trees = 
 
 16 
 
 =3025. Cost = 8399. 30. 
 
 3. Average cost per basket = 60 cents ; commission on 
 
 $12 
 
 60 cents=l^ cents. Number of baskets = - — = 800 
 
 l^c. 
 
i^ 
 
 54 
 
 II 
 
 I 
 
 5. 
 
 Hints and Answeks. 
 
 81' 15' 
 
 63° 36' 
 
 15)17^39' 
 
 "rTO' 36"=1 hr. 10 min. 36 sec. 
 10,000x128x1728x55 
 
 50x36 
 
 = 67,584,000 boxes. 
 
 ^ 1847 X 00 
 
 6. ~^Q^ xl3=$144.06|. 
 
 , 360 X 60 X 10 
 
 '• 60x24 =1^0 days. 
 
 8- f of tVoV of $6000=$1500. 
 
 1260 
 a 3gg-x$5.25=$33.75=value of the flour, and tK. 
 
 note will amount to $31.20 . . wagon cost $64.95. 
 
 10. Each shingle covers 18 sq.'in., or 8 shingles will 
 cover a foot, and there are 1080 sq. ft. to cover .' nu.iiber 
 of shingles = 8, 040 .-. cost = $19. 44. 
 
 LXXXV. 
 
 f\ ^" wu^'^^^y, ^^ ^"'^- ^^^ '^ *a^'e» because ^' and ^ 
 of It are both whole numbers) there are 15 wheat, io oats' 
 9 peas, and the cost of these is $24.50 /.number of bush' 
 $73.50 
 
 $24.50 
 
 X 40=120. 
 
 54 X 40 X 56 
 ~277-274"''«=^"^'^^^- 
 
 3. Each plant has 3|xU = 5i sq. ft of ground ..the 
 
 , r 1 . 4840x9 
 number of plants= 
 
 4. The Canadian oil lasts | as long as the American, but 
 does not cost | as much, and is therefore cheaper. 
 
Hints axd Axrwrrs. 
 
 55 
 
 5. 2 miles by rail will retjuire 4i minutes, and 1 mile 
 by sta«e, 10 minutes .-. 3 miles so travelled will take 141 
 2 hrs. 42 min. 
 
 minutes .'. — ;-— - 
 
 141 min. 
 
 x3 = required 'rftunce:^ 45 miles. 
 
 <;. 82.80 nearly. 
 
 7 Each load of gravel makes 13| ft. of road .. 6 loads 
 make 81 ft., at a cost of 82.25, or 4uf! cents a rod. 
 
 ^ „^ 120 100 ^, ^ , 
 
 '- «^^ loo ^1)0=^^-^^- 
 
 9. 4840 X 9 X i X f = number of cubic ft. = 18150 • weif'ht 
 = 5081 tons. ■ " 
 
 10. The son does r as much as the father, and therefore 
 earns 50 cents a day or $3 a week. 
 
 LXXXVI. 
 
 1. Expenses = ^ + ji. + ,1, + ^V = U :. profit = J» = $03 i 
 on every $100 worth sold. 
 
 2. Area of two sides ^^ 2 x 60 x 18--2in0 ; average height 
 of end = i (30+18! = 24.. area of ends = 2 x 32 x 24-^1530. 
 From eave to ridge of roof = 20 ft. /.area of whole r(K.f=i 
 2 X GO X 20=2400': and floor=2 x 60 x 32=3840. The sum 
 of these results = n03(). the numberof feet lumbe*- icquired. 
 
 3. Cost=$2.25x 24 = 854. 2 lbs. =11520 grs. • sold for 
 $115. 20 .-.gain is 861.20 on 854, or 113J per cent. 
 
 4. Find the number which multiplied by itself will aive 
 1296 Answer, 36. ^ 
 
 5. The street being 66 ft. or 4 rods wide occupies | of 
 the field, leaving 8| acres— "^ = 70 lots. Each lot contains 
 605 sq. yards and is 77 yards deep, and therefore has a 
 frontage of 7? yards. 
 
 6. Taking 1 bush, of each, we have 62 cents nearly. 
 
 7. L. C. M. of 34, 48, 60, 56=28560 lbs. =840 bush, 
 oats, or = 595 bush, barky, or 476 bush, peas, or 510 bush. 
 
5(5 
 
 HixTS AXD Answers 
 
 lii 
 
 Sr.- .^-,.^"'^ "*"*" ^"-'^ ''^•'^^■^' : ^^^ ^"^J^- l^arlcy cost 
 in - ; :^'.:'?^'■J'^''''' ^*^"* ''^'^•"»' ' ^"'JO ^'»«1^- rye cost $357, 
 niak^n. 2421 buah. at a cost .,f m'28, or nearly 59 cents a 
 
 nv\ cV/'w ^ ;?^'c.i^o-'^^^ P^^'"' "^ ^y^' ^« ^^'^^th 1] cents, 
 MI 1 cwt^ worth |1.2o ; but toll leaves 'JO lbs. at a'cust of 
 ^i.Z,\ or nearly $1.39 per cwt. 
 
 is iVcen'ts^'''^' '^^ ^'''"'' ''"^ ^^'^^ ^0.50 /.cost per hour 
 10. S(i.50x6x2Q = S33.43. 
 
 LXXXVII. 
 
 1. Return fare = 5 cents a mile.-. $1.80^5c.=3G miles. 
 hA ^^ ''^•t.^-^''!?' ^V^Pf Pe^ will make 540 leaves, each G in 
 A^tertLI^r'^ ''' '^ ''''^' ^^-^"- - "-h- 
 3. «4.8(1^=£1. $1095=£225,andi (500-225)=137A 
 
 .-. amount =- §40. 03 L. ^ *'*^"'^- " «'^- ^'^i 
 
 <). The 75 lbs. are worth $45 • thp 40 1K=. „« ^i 
 
 S22.40..35 1b.s. are worth $22:00; whLhtL'^lc^n^sTf^^ . 
 
 7. In 10 min. the machine goes 440 yards and ^ acre = 
 605 sq. yards .-.required width is ^^ yards = 4nt. 
 
 8. The sides are 220, 132, and 124, and H. C F of 
 these IS 4 .-. boards are 4 varda lonu- ...j , \ 7" ^ 
 once round is 119. ^ ^' ''""^ """^^^' *« go 
 
 9. 5francs = 92icents.-.lfranc=18^cents. £1==R8GJ 
 
 18^ 
 
 111 
 
 1 shilling=24J cents .-. 1 franc= —-- sh - "^ 
 
Hints and Answers. 5^^ 
 
 LXXXYITI. 
 
 1. The mnn earns 82. 50 a day Thp hov' m 10^ 
 does what would rake the man 3 d^ys .• heearns"as nfu'h 
 as the man, or 82.50 in 4 days, „r SIO in IG iays'/' '""'^ 
 
 2. It t;cks 3 times in 2 seconds, or 720 times in 480 
 seconds=8 m.nutes. In 8 nnnutes the Ste hand 
 makes ,-^ of the circuit, or goes 4 inches. 
 
 3. miO-f-3k. =0(50 = number yards round the field • 
 one side is iGo yards ..area is 105 x 105^4840=5^ acre^^^ 
 
 88U£niorSr'^^"=^ watch .-.850 = ^ watch ; 
 
 ;n^ht 3d:r 8?;rcer\i ^;r:^i^^ 
 
 1 per cent. =$1!): 85 per cent. = ^015^ ^^ '^^^' 
 
 areJI^d^ ^' '""''^' aG5.-.cloth is worth SCO. •. there 
 7. 315. 
 
 8. -370 = •3790. 
 farm = 01 ^(J acres . 
 
 •3700 
 
 farin = lIXS acres 
 
 •0000= '3100= 171 171 
 •>'>o- r. -,(T 
 
 of 
 
 9. He earns $140 a month; he spends $08 a month • he 
 saves ^'i2 a month, or §504 a year. '"""cn , ne 
 
 10. Inte.est on S14(;0 is $140 per annum, or 40 cents a 
 day.-, number davs = >^lO-40.. — ha • ' "^ ^" ^^"ts a 
 13lh August. ^ " • • ~^^ • • '"^"^y was paid 
 
 LXXXIX. 
 
 1- H-s = ij=70 acres . • . farm = 240 acres. 
 bu!hel~""''" ''^'^'''' = ^^-'- "'atssold f.»r $03, or 37^c. a 
 
 3. Ji boys = I class . • . boys = ? class . • . airla = ? d-ms • 
 »u-6 Class. . 00=;.; class = number boys. 
 
 II 
 
58 
 
 Hints and Answers. 
 
 4. He had at first 120 acres, then 175 acres,', bought 
 55 acres. 
 
 5. $57. 20 X I ? = $52 = cost of what was sold . • . $72— 
 $52 = cost of 25 yards, or 80 cents a yard. 
 
 6. 84x12x14=14112 cubic in.=84 cubic ft. in 1 sec. 
 =352,800 cubic ft. in 12 hours. 
 
 7. Divide the previous result by 15x20x30, and we 
 have 391 times. 
 
 8. 4840 x 9 X 144 x 2^=number of cubic in. of ice ; this 
 multiplied by |Y will <iive the number of cubic in. of water 
 or cubic ft. of steam ; then divide by 27 to get the cubic 
 yards of steam. The result is 528,000. 
 
 9. Number lines =27 x 9 x 12=2916 ; and f of 8c. is the 
 profit on each line ; hence the total profit is $139. 96|. 
 
 10. 303 X f X I X is X 57G0-f ^ of f j of 412i=320. 
 
 XC. 
 
 1. $9000x]§;^xV\j=priceasked=$12,500. 
 
 2. A 10 acre field contains 1000 rods, and since this 
 field is square, each side will be 40 rods, making 320 rods 
 of fence at S4.50, or $1440 for the fence. 
 
 3. 22x18x7 X 1728 = number of cubic inches ; this 
 result divided by 277 "2 will fjive the number of gals., and 
 10 times that the number of lbs., or 172,800. 
 
 4. The farm consists of 12 square 10-acre lots, 3 in 
 width and 4 in length, and as the side of a square 10-acre 
 lot is 40 rods or 220 yards, the length of the field must be 
 220x4^8S0 yards. 
 
 5. 90 half-inches, or 1] yards. 
 
 6. 208,920 = distance in ft., and in 1 minute they march 
 
 290 ft. . *. — - = number of minutes — 12 hrs., ^5 min. 
 
 7. 2218'192 cubic in. in a bush. .'. 221819-2 cubic in. 
 in 100 bush. The bin contains 210000 cubic in., and 
 therefore does not contain 100 bush, by 5819*2 cubic in. 
 
Hints and Answers. 
 
 69 
 
 8. TTf(ny«f |of$10,000=$15. 
 
 9. 00 articles would cost 81 cents and would sell for 81. 
 u gain of 10 cents on 81 cents, or 23'|( percent. He gaii.s 
 10 cents on 7 5 dozen . • . $19 on 750 dozen. 
 
 10. Goods which cost manufacturer 100% are sold to 
 merchant at 150%, but only 1121% is received for them . ' . 
 there is a ^ain of 12i%. 
 
 XCI. 
 
 1. 1 cwt., 3 qrs., 17 lbs. avoirdupois. 
 
 2. Amount of water in well at 6 a.m. Tuesday =300 
 gals. Number of hours from 6 a.m. Tuesday to time well 
 is emptied=l!>8 hours. Amtmnt tiows in — 30 gals, x 108 
 =5040 gals. Amount emptied by pump=:5940 gals. +3G0 
 gals. =()300 gals. l\nup works 10 hours a day for 5 days 
 and 4 hours = 54 hours. Number of gals, emptied per 
 hour=G300-^^54 = ll(>j gals. 
 
 3. 14.30 feet. 
 
 4. Water expands in freezing ^jj of bulk ". 1 cubic ft. 
 water maKes 1^'^ cubic ft. ice.', waters {"^ of 143 cubic ft. 
 = 130 cubic ft. Weight = 130 x 02^=8125 lbs. 
 
 5. 8250. 
 
 6. A makes I of sales .'. cost is i of sales. Gain is i on 
 f~^ of cost. iJitlerence in protit=4 of cost — i of cost=- 
 .}q of cost .". .]q of cost=Oc. Cost=81.20 per yard. 
 
 7. Selling price per false yard is f of 81.08=.S2.10 per 
 
 910 X 3fi 
 Sells34/i in. for82.10 " "'" " " 
 
 yard. 
 
 sells 30 in. for -— — — = 
 
 $2. 20. Gain on $1.08 is 52c. . ' . gain per cent, is 
 
 34 ^ 
 
 52 X 100 
 ~~1G8 
 
 =30^7 per cent. 
 
 8. As yV ^^ ^^^^ ^^ matching, we have but ^^jleft.'. 
 refjuire \^ of 00 yards = ()(y4 yards. Again | overlaps, 
 leaving but 'J of width available . * . J of amount is required 
 =^l of GO J yards=77i yards. 
 
60 
 
 Hints aM) Answeks. 
 
 I 
 
 0. The hands will be 5 miimte-spiices apart in 1 hour 
 /. I'., one will be 5 niiiiute-spaccs ahead of the other in 1 
 lionr. •. GO niiiii'to- luces ahead in 12 hours. They will 
 be together a<,'ain in 12 hours. One will have gained in 
 12 hours o.l nan. x 12=40 niin. Time is, therefoi 12 40' 
 o'clock. 
 
 10. Receives as 1 yard \J. of yard. Sells \;\ (.f yard as 1 
 yard.' . \l of yard as }l, of i-l=i.V yard. Receives f«)r 1 
 yard ^ of cost of yard .-. receives for , t yard }I of ^ of 
 cost oif y ird = -iji of cost = 13G per cent, of cost . • . t,'ain is 
 30 per cent. 
 
 XCII. 
 
 1. Length of held, 80 rods ; width, 20 rods. 9 rounds 
 will cut a strip 5^ X 9=4!)^ ft. wide along each side and 
 each end . ". length of part still standing = 80 rods— 09 ft. 
 Width, 20 rods -00 ft. Length is 74 rods; width, 14 
 rods. Number of acres=0|;J acres. 
 
 2. ^f;,, of inmates in 1883- 140. •. inmates =2800- 
 Increase and decrease are ] and ^^^ ; average increase =^'g 
 . • . proportions are 15 miles to 20 females. \^ of l*800=s 
 1200 males, jj;^ of 2800= 1<)00 females. 
 
 3. By laying out the rectangle, it will be seen that the 
 diiZerence between areas of .lide walks is eijuJ to 8 corners 
 each in form of a sc^uare. 100 ft. of lumber cover 8 
 squares, but 100 ft. 1] in. lumber cover only 128 sq. ft., 
 therefore each square is 10 sq. ft. , and side is 4 ft. , which 
 is width of walk. 
 
 4. Received for 175 yards @ $1. 50=$2G2. 50. Value of 
 175 yards @ 81.20=8210. S210 + loss = cost price. Add 
 to this twice the loss and 810.50, we have selling price= 
 82(52. 5U. •. ditfo?'ence=.t<r'2. 50 = three times the loss and 
 810.50, that is, three times loss is 842. Loss is 814. 
 (iain by selling for 82G2.50 is 838 5(». •. cost is $202.50- 
 838.50=8224. Cost per yard is 81-28. 
 
 5. It is evident there is more clay than sand. A digs 
 in 17 days 51 rods of clay. B digs 09 rods in 17 days= 
 4jV rods per day. B digs 5 of sand or 2 of clay per day 
 
IliNTH AND Answers. 
 
 61 
 
 . • . 69 rods must be divided in proportions 16 of clay to 35 
 of sand. Amount of clay in G9 rod8=^5 of 69= 21 U rods 
 .-.clay is 51 + 21}}= 721 f rods. Sand = 120 - 72}^ f ^47 A 
 rods. 
 
 6. If gain be 20%, cost is S2.08J per gal. Proportions 
 are 8^ to 91 5=1 to 11.'. 110 gals, of $2 wine will be 
 required. 
 
 7. In CO min. stream would carry him | mile. In 64 
 min. stream would carry him ^ of ^ mile = y«.- mile. In 
 going down, he rows a certain distance and stream carries 
 him ^ mile. In coming back, he rows the same distance, 
 the ^ mile the stream carried him down and the -|\ mile 
 the stream retarded him, in all ^ + t\ miles mere than 
 going down. Rows in 4 min. ^1 miles . • . rows in 1 hour 
 15| miles. Length of course is 15^ + ^=16 miles. 
 
 8. If B had borrowed no seed he would have drawn 
 away 150 bush. ^ of crop is 150 bush . • . crop is 225 bush. 
 A is entitled to ^ of 225 bush. =75 bush, and to the 30 
 bush, lent, in all 105 bush. 
 
 9. 5 men and 3 boys complete ^^ of work in 1 day. 12 
 men and 6 boys complete ^ of work in 1 day. Multiply 
 1st by 12 and 2nd by 5 . ' . 60 men and 36 boys complete 
 |§ of work in 1 day. 60 men and 30 boys complete f of 
 work in 1 day. Subtract, and 6 boys do it-|=g\y in 1 
 day . • . the boys are a hindrance. 
 
 10. B gains on A 5 miles per hour . • . gains 1 round in 
 y hours. C gains on B 5 miles per hour . • . gains 1 round 
 in V hours. A, B and C will be together every ^ hours 
 = 14;| hours. Will be together at point of starting in L. 
 C. M. of V, It and ^^73 hours. 
 
 XCIII. 
 
 1. ^ of cask is wine, | is water, difference ^ . * . 4f gals, 
 is difference in 431 gals. Amount of wine drawn off is | 
 of 43.^ gals. =24 gals . • . aroount of wine still in 120 - 24=» 
 96 gals. 
 
 2. 3| minute-spacei, 
 
62 
 
 Hints and Answers. 
 
 A runs 1700 
 of 
 
 8 A runs 8 yards while B runs 7 yards 
 yards while B runs 1540 yards. A can give B a start 
 1700 yards— 44 yards— 1540 yards=176 yards. 
 
 4. Interest for 6 months at jj per cent, is ^^jj of ^5 of 
 sum = <^of sum. Interest on sum for 4| months at 7 i 
 
 per ceni. is JS of ,'oV ^f 8"»»=.^Vo, ",( «""'• ^?'?fr"''^ = 
 5j^_ ^^•5 = ^1^„ of sum . • . sum is ^{'{^ x V =^1112i\. 
 
 5 A can do ,2^ of work in 1 day. B can do ^V "» 1 ^^V 
 . ■ . both can do j% of work in 1 day. In 1^ days can do 
 4 of ^%=^% of work. 
 
 6. 110. 
 
 7. Interest on ^80 for 8 months is 3/j per cent. . • . 
 interest for 1 year is ij~ of 3^ per cent. =5 per cent. 
 
 8 Cost of wheat is $1.08 x 240 = $259. 20. Receives for 
 80 bush, at $1.12^ $90 ; for 00 bush, at $1.20, §115.20. 
 Receives for remamder, 04 bush., §2.J9.20 + ai2.80-($90 
 + $llo.20)=$0e.8o.-. receives for 1 bu.sh., $1.04§. 
 
 9. 1 man can 
 16x13* 
 
 do 2 J^ of work in 1 day .'. " 
 
 in 13| days=^ig of work. The 4 
 
 of work. They can do ^l^ in 
 
 men do 
 
 men 
 
 do 
 
 1 day . 
 
 240 
 
 remainder ^"/^ 
 
 they do ^j\ in 6 days. 
 
 10. Worked 6 hrs. 15 min. =375min. Made 5 articles 
 in 12 min. .-.made ,5^ of 375 articles = 156^ articles. 
 Receives for them \^c. each. {^ of 156i=$1.30/^. 
 
 XCIV. 
 
 1. 2 sq. yards. 122 sq. in. 
 
 2. In 70 ft. driving wheels make 5 revolutions and front 
 wheels 7 revolutions . • . front wheels make 2 revolutions 
 more in 70 ft. ; 88 ft. more in 3080 ft. Train goes 3080 
 ft. per rain. =35 miles per hour. 
 
 3. Costof land, $75xl50 = $11250. Sold for $12250. 
 Race ves for 2 acres, 3 roods, 20 poles, at ^80 per acre, 
 
^^^^.^ .^^f#: 
 
 
 Hints and Answers. 
 
 63 
 
 $230, and for lot 25 by 20, $250. Receives for remaining 
 144 acres, $12250- (^230 + ^250) = $11770 ; for 1 acre, 
 $81.7311. 
 
 4. "Walks 16 miles at 3i miles per iiour, t. e., in 4j hours. 
 Walks 16 miles at 4^ miles per hour, i. e., in 3| hours . '. 
 walks whole distance in 8J^^ hours ; is therefore ^"^ hours 
 late. 
 
 5. Earned in 5 months ^"^ of $215 and ^% of watoh = 
 $80/0 and -{^ of watch. Receives watch and $75 . ' . /.. of 
 watch is worth $89,"^ - $75 = $14 ^^^^ . • . watch is worth $25. 
 
 6. Cubic contents of earth of cellar is 30 x 20 x 6 = 3600 
 cubic ft. Depth on field is 3G00-;-y'y acre=[5 ft. 
 
 7. Cost of suorar=$125. Sells it for $167tV Sellp ^ 
 of 2000 lbs. =666:^ lbs. at 11 lbs. for$l, which gives $60:'; ij 
 .'. receives for remaining 1333A lbs., $1065;?, = 8c. per lb. 
 . • . gives 12^ lbs. for $1, 
 
 8. Dick has 75 ; Harry, 100. 
 
 9. Length of sides and enud of box = 10ft. 10 in. +10 ft. 
 10 in. 4 18 in. +18 in. =24:-; ft. Cubic contents = 24 j x f 
 x^— 6,V "ubic ft. Cubic contents of bottom is 10;? ft. x 
 ff xJi = 3..jV Number of cubic ft. in box is 6^ + 3,"-' — 
 9|^t cubic ft. 
 
 10. 6 sq. in. in surface of each block. *. number of sq. 
 
 1728 X 6 
 rards = — — — g- =8 sq. yards. Number of edges in each 
 
 12 X 1728 
 is 12 . • . number of yards is , „ „ =576 yards. 
 
 12 X 3 "^ 
 
 XCV. 
 
 1. 10 suits ; 72 '5 yards. 
 
 2. 227272 miles, 5 fur., 32 per., 4 yds. 
 
 18 years, 47 
 days, 8/1^ hf its. 
 
 3. Value of each kind is $12.50.- . there are 25 half- 
 dollar coins, 50 quarter-dollar coins, 125 ten -cent coins, 
 arid 250 live-cent coins ; in all, 450 coins. 
 
u 
 
 Hints and Answers. 
 
 I ' 
 
 250 grs. X 200000000 r-^nnnnnooo 
 4 Wei-ht of gold= ^ ^ =uOOOOOOOOO 
 
 5000000000_ 
 grs. Number of t<>n^=7oo6^2000~'^'''' ""' 
 
 5. Proportions are 3, 2, 1. Value of wheat | of $2280 
 = ^1140 Number of b-.'.sh.=S]140-^05c.=1200 bush. 
 Va"lue of barley=| rf 82280=^700. Number of bush = 
 S700-00c.=12G0H bush. Value of oats=i of $.2280- 
 ^380. Number of bush.=$o80^40c.=9o0 bush. 
 
 C. 5sq. ft., 29s(i. in. 
 
 7. 30 lbs. flour are worth 37Ac. y2;i=$1.00. 190 lbs. 
 
 100 lbs. beef are 
 
 flour are worth -o^— x 100=^0.53^ 
 
 oU 05 (JO 
 
 worth ? of .^0.531 =$5. GO, and 775 lbs. are worth ^^^^X 
 
 775 = 843.40. 
 
 .5000000 X 2^ 01 01 «o..a T Pr -yth 
 
 Q "NTn.^i^or nf pfl.rs = =- = 312^ cars. Jjengia 
 
 8. Number ot cars- 2000x20 
 
 of train 
 
 ^ 625^x30 ^ ^3^5 f t j^ umber of engir es required 
 2 
 
 . 312.Vx20 ^,, . oo 
 to draw it= ^oo =^^J' '• ^•' ^^' 
 
 9. 'i of whole 4- 8250 + f of whole - 8500 + j^ ^f whole- 
 81.50 -4 whole property. ^ of whole - ^400=-hole . ' . ^5 
 of whole property is 8400. Whole investmenU is 87000. 
 Cash, 82250. Stock, 83700. Notes, 8IO0O. 
 
 10 Lencrth of side of square field is 40 rod8=m yards. 
 l.en<rth of"streets=220 -H 220 + 180 + 180 = 800 yards. Area 
 =8'.)0x 20 = 10000 fe(i. yards. Cost at 7oc. per yard= 
 812000. Area of whole piece=10 acre8=48400 sq. yards. 
 
 Area of 9 squares^48400 «q- y^^^' ' ^*^T.nf?-- ^m 
 32400 square yards. A ea of 1 square=32400^ 9=3600 
 so yards.-, lencrth of side=60 yards. Length ot tour 
 
 2*0x<tf' 
 Bides=240 yards. Cost of fencing 9 squares=- ^1 ^ 
 
 
Hints ani> Answers. 
 
 65 
 
 ?=8ir.7.00TL. 
 
 Value of each 8quare=-|*!,2j ^ 1*^ -' = 
 
 XCVI. 
 
 
 i. He receives only 14 oz. in the ib ; is therefore 
 cheated out of 2 oz. in 10, l. c, ^ of goc»di ^ of money 
 =^1jV. in the 12^ or 12^%. 
 
 2. Proportions are G, 4, 2. Men get GO, whilo \\ )men 
 get 48 and children o;et 40. Each man ^^ets y','^~ of $740 
 —830; each woman, y*^ of $740= '^'.20; each child, jf^ 
 of $740=$10. 
 
 3. Solid contents of pile is f of 43500 xG cubic ft. = 
 17'-:240 cubic ft. Numbor of cord3=:174240-^128=13Cli 
 cords. 
 
 4. 585540 min. 
 
 5. 3 r. , 39 po. , 29 sq. yds. , 6 sq. ft. , 108 sq. in. 
 
 6. Weic/ht of butter=:f ^ of 12 lbs. =11 j lbs. Received 
 for it value of tea=.«!l.o0 + 30c.=r..$1.80. Value of butter 
 per lb.=$1.80-r ll^=10c. per lb. 
 
 7. Cost of 10 lbs. tea=cost of 10 lbs. coffee and $4 .* . 
 cost of 22 lbs. of cotlee=$8. 40 - $4=$4. 40. Coat of coffee 
 perlb.=20c. ; tea=:G0c. 
 
 8. Lengt' ofsidesof box=6 + 6 + 4| + 4|=2Uft. Area 
 of sides=2H x 42-= 90^ sq. ft. Area of bottom and top:= 
 X ^^•' X ^=57 aq. ft. Total surface=1534 so. ft. Cost= 
 153|xV'=$1.705. 
 
 9. i lb. avoirdupois=3r)00 grs. =3500-^480 ozs. Troy. 
 Value" is ^^^ of i:3 17s. 9d.=£28 Os. 11 J d. 
 
 10. Interest on $100 for 1 year at 5 per cent, is 85. 
 Interest on $100 for ;i year or 438 days is $0. Interest 
 on $2400 Tor § year at 5 per cent, is $144. 
 
 XCVII. 
 
 1. 4 men do as much as 8 wo nen ; 10 boyb do as much 
 vs 5 women .' . 4 men, 6 womea and 10 boys do as much 
 

 z-lfxr. 
 
 06 
 
 Hints and Answers. 
 
 as 19 women. 10 men do as much as 20 women. 22 
 women can do the work in 4 days .*. 19 women do it in f f of 
 4^11 days=:4|| days. 
 
 2. Area of leaf =36 x 24=864 sq. in. Thickness is 1 -4- 
 864=^1^ in. 
 
 3. Makes 4 cuts to cut log into 5 pieces ; 9 cuts to cut 
 into 10 pieces . • . should receive f of 40 x 2 x J;0=$2. 
 
 4. Number of ft. required=660 x 5*^3030 ft. Value 
 at 87.50 per 1000 f t. =?5^^=|27. 22^. 
 
 5. Profit=^ of cost . • . cost=f of 5c. =4^c. per oz.=50e. 
 per lb., apothecaries weight. 
 
 6. Loss on sugar=-^jj of $75^=$5.62|. Gain on tea^ 
 j% of $144=$23.04. • . gain is 823.04 - 85.62^=$17.4U. 
 
 7. Number of bbls. sold=8216-i-6|=32 bbls. Cost of 
 theses ijf of 8216=8240 .'. cost per bbl.=8240-f32= 
 87.50. Total number of bbls. =8690-^ $7. 50=92 bbls. 
 Receives for it, 8690 + ^'^'^^ 8740. Must receive for 
 remaining 60 bbls., 8740— 8216=1524 .-. receives for 1 
 bbl., 8524 + 60=88.731. 
 
 8. Number of cubic ft. in cistern=5 x 4 x 6=120 cubic 
 ft. 
 
 ^T , . , 120x1000 
 Number of gals.= — — 
 
 =750 gals. 150 gals. 
 
 16x10 
 =1500 lbs.=24000 ozs.=24 cubic ft. .-. depth=24+20= 
 
 Gain is ^^j 
 
 1 ft. 2§ in. 
 
 9. Cost of mixture=82.80 + 81.80=84.60. 
 of 84.60=20c . • . sell 7 lbs. for 84.80, or 1 lb. for 68fc. 
 
 10. 6250. 
 
 XCVIII. 
 
 1. See toxt-book. 
 
 2. (a) 15 weeks. (b) 9491724 sq. ft. 
 8. 434463 ft. 
 
Hints and Answers. 
 
 67 
 
 4 (a) 177 bags : 8 lbs. 12 oz. remaining. (6) GO bags : 
 1 bush. 7 gals, remaining. 
 
 5. Cost of 14| yards silk at $2. 40 = $35. 40. Cost of fur 
 cloak, $70. Groceries, 114.00. Total cost= $120. 
 
 G. Mrs. F. L. Woodcamp, bought of Messrs. Anderson 
 &Co: — 
 
 Sept. 
 
 
 Oct. 
 
 19 
 
 M 
 
 3 
 
 To 3 lbs. 2 oz. tea @ G4c.. 
 " 5 lbs, 4 oz. lard @ W.c. 
 
 " 3 qts. syrup @ COc. per gal 
 
 " 25 lbs. rice @ $4.50 per 100.. . . 
 
 " 18 herrings (^ 25c. per doz 
 
 " 5^ lbs. sugar @ 11 lbs. per $1. . 
 
 $2 00 
 G4 
 45 
 12^ 
 37i 
 50 
 
 $5 09~ 
 
 ^ TWT 1 r , . 4xG8x7 
 
 7. Number of cords is — ^g— =14§ cords. 9 cords (^ 
 
 U. 50 = $40. 50. 5§ Cords @ $4. 40 = $25. 85. Total value, 
 $6G.35. 
 
 8. If carpet be placed across room, 3H-f2|^ = 14 strips 
 are needed, each 13 ft. 4 in. long. Number of yards = 
 
 14 X 13^ 
 g-^-G22 yards. Cost = 622 times 85c =$52.88f. 
 
 If carpet be placed the other way, 6 strips will be needed. 
 
 9. $71.42^. 
 
 XCIX. 
 
 1. See text-book. 2. 2. 3. 1600. 
 
 4. Breadth of room is 493^^31^ = 15 ft. 9^% in. 
 
 5. Increase in two years to || of [| = .^f^ of population 
 /.|5.'i of 34500 = population of two years ago— -30375. 
 fopulatiun one year hence will be || of 34560=30804.'. 
 ditiereuce is 0489. 
 
 0. Length -4840x50^220 = 1100 yards. '.perimeter is 
 2640 yards = 1| .niles. Walk 4 miles per hour .'.walk lA 
 miles in § hour = 22^ niin. 
 
Hints and Answers. 
 
 200 while B runs 197. ".A runs 108 while B runs 
 
 7. C runs 200 yards while A runs 1!)8 yards, h rinia 
 
 197x198 
 
 = 195,;|jy. C can run 200 whih- H runs 19r),;^,^.'.0 can 
 give B 'i^*J(^ yards start. 
 
 20 X 72 
 
 8. 48 boy8=20 men.\72 boys= -30 men. If 30 
 
 48 
 
 men ran do ^ work in 24 days, the 72 boys could finish it 
 in 48 days. 
 
 9. Gain = .,V.-..^,\ of cost = $133. Cost is 20 of l?133. 
 To gain 25 per cent., should be sold for •* of HV of $133 = 
 
 $158^. -' "^ 
 
 10. 1 003.^3 V 
 
 11. C, for collecting, rec ives 1| percent. =^V, of $ri{\HO 
 =$71. Remainder is $5()09. A receives ,•;,";, oF .i!?r>ii09 = 
 $1903.15. B receives /-.."-.y of $!5()09 = $1570.52. C receives 
 iVo of 5^5009 = $2075. 33, or in all, $2075.3J + «71 = 
 $2140.33. 
 
 12. Ist pipe tills ^ of vessel per minute, 2nd fills 1, 3rd 
 empties j\^ of it.'.3 pipes fill Hi-T- <>»' it i" 1 minute== 
 i^'f in 1 minute, or whole vessel in 4i minutes. 
 
 I 
 
 0. 
 
 1. 128357. 2. $312.18 + . 
 
 4. A gets ^ of $540 = $108. 
 C gets yV ot $540 = $144. 
 
 3. 37 miles per hour. 
 Bgets ,V of $540 = $288. 
 
 5. Gain =$360 -$270 = $90. Gain per bbl. is 7oc 
 Number of bbls. = $90 -j- 75c. =120 bbls. Cost per bbl - 
 $270-=-120=$2.25. * 
 
 (o. I-^ngth of walls = 24 + 24 + 20 + 2:1 ft. =88 ft. Area 
 =88 X i sq ft. = 1232 sq. fc. Area of floor- 24 x 20 = 
 480 r ft. Cost of painting = 5^c. x 480 $20.40. 
 
 7. See Arithmetic. L. C. M. of $5, $27, $105=$945. 
 
X 
 
 Hints and Answrus. 59 
 
 •u.L^ri'-''''" '^^^•^'^^^''J^Hl-lL'O .t(?r,. U,H.oivcd f,.r ;{(> 
 «TM at «;.., por aero, ^22M. R«coiv»Ml for * reu.aindor 
 
 $.m) + ^.m l?SI()0.-.,vcv.prs for flu, 4r, ac vs still ', 
 hand must >,. 8SI(K) S4-,()() «S'«<:m c • 
 ao^o==,^;U;()(»-^4^,^S0. ^' tolling pnco per 
 
 OT. 
 
 1. Sfo AritliMiotie. 2 4(;j ^ y.mls. 
 
 •^- ■ ton, i;{cwt., L>qr8., 10 iUs. -iUi lbs. :=33 boxes. 
 
 4. 108 yards. D. $!>(;0(). <;. .-{^^ ,<„,; 
 
 w,iVtlf^l'->o"'l()'T "r"'' '^-'--^ '^'''^''''' or 3 ducks are 
 l,\ V""- .^^ ''"^ ':" '•'■ '^ -'^'^'^^ •"•« worth JO of $1 20 
 
 8 Paid for each horso v;il„o of 2 wa-ons * !«'>10 is vilno 
 
 of i) wai,'(ms. 1 wa<n)n is worth «5i-> • 1 1.' ■ A 
 
 <5<^^ '^ '«».,»'n 18 worm J5»4- ; 1 liurso is worth 
 
 ^10.^ A and B do U - of work^J of work/.C does ^ of 
 
 CIT. 
 
 DFcKMnEii, 1881. 
 1. 35i:O0030.2 + . 2. 252. 3. 8350.80,V. 
 
 flioe^i D'Hereuce, £1270 Is. -£U7 m.^ 
 
 |2.72.~ •• *^''" ■^' '""'^ ''^'^ f^*" «1.00 + n.l2= 
 
70 
 
 Hints and Answers. 
 
 7. Cubic contents of plate = ()()x;}(;x J cubic in. ; 
 thickness of sheet is {6Q x 3C x |)-r(54 x 72) in. = },l in. 
 
 8. Cubic contents of brick = | x ^ x ^ = j-'^ cubic ft. 
 Cubic contents of wall = GO x 17 x 4 cubic ft. " Number of 
 bricks = jS (60 x 17 x 4) -^ (.^ ) =-- 409C0. 
 
 9. -f of cost = 81.*. cost = 81 1 c , or cost per lb.^8.\c. 
 Selling price = i^'^ = ll?,c. per lb. Gain=lli-8^c. =25c. 
 Gain per cent. =(2| -^8^) x 100 = 33 ^ per cent. 
 
 June, 1882. 
 
 1. G. C. M. is 1. 
 
 2. Gain = 9c. per 100 ft. /.gain is ^^^^,^^^^ =$71.06^ 
 
 100 
 
 3_3 
 
 T8%- 
 
 4. 54G2 -9911235. 120020 ounces. 
 
 5. In 3| minutes goes G072 ft.. '.goes 1584 ft. per 
 minute, or 1584x60=95040 ft. per hour=18 miles per 
 hour. 
 
 6. Cubic contents of pile of brick is 432 x 198 x 174 
 
 ^. . . ,. , , f u • 1 432x198x174 
 cubic m.. .cubic contents of one brick = 
 
 cubic in. =121^ cubic in. Thickness = 121i-=-(9x4^) = 
 3 in. 
 
 7. £1 = 24 francs, and 6 francs=$l 14.'.£l=81.14x4 
 = $4. 56. £250 10s. = $4. 56 x 250* = $1 142 .28. 
 
 8. ^ of inch represents a mile.'.^ inch represents 5 
 miles. Township contains 25 sq. miles=640 ac. x25 = 
 16000 acres. 
 
 9. 4 men can do work in 8 days.'.l man can do ^^ in 1 
 day, and 8 men can do yf^ or l of work in 1 day. 1 boy 
 can do jV '^^ 1 day .'.4 boys can do ^V of work in 1 day. 
 8 men and 4 boys can do :| + ^V = ^ of work in 1 day, or 
 whole work in 3 days. 
 
 10. A's votes were || of number polled, and B's fy.'.^V 
 or 2"f of votes polled = 100 votes. Number polled = 2400 
 votes. Number who did not vote=300. 
 
fyg^^ 
 
 1. 
 2. 
 
 Hints and Answers. 
 Decemrkk, 1882. 
 
 ;U) lbs. 8 oz. beef @ 10c. . .i?5.84 
 10 " 10 " imitt(.n (.'^ J4c.. 2.:{2| 
 
 pork (" 12 1)3 
 
 turkey ("> 18c... 2. 70 J 
 
 71 
 
 
 
 15 
 
 4 
 
 
 12 " 
 
 " 
 10 " suet C<i^ 10c. 
 
 3. 40800 ; 1. 4. 1. 
 
 $12.(;0i 
 
 5. 
 
 •0025 of 112 lbs. =7 lbs. .-.cost =7 times 0703125 of 
 10s. =7s. 10\d. 
 
 6. 7 acres, 1 rood, polos, 21 sq. yds., 7 sq. ft., 20 
 sq. in. 
 
 7. Number of cubic ft. in cistern = 3750 x 10-^1000 = 00 
 cubic ft. Depth = 00-T-(7^ x 3i) = 2j*| ft. 
 
 8. A would have run 1700 yards while B ran 1700-22 
 = 1738 yards.'. while B runs 1738, A runs ^ of 17«;0-1320 
 yards. Rates are as 1320 : 1738, that is, as 000 : 800. 
 
 9. A does f of work in hours, or ^ of it in 1 hour. B 
 does I of ^ =] of work in 2 hours, or J in 1 hour. C does 
 remainder ^V of work in 30 min., or ^ in 1 hour. A, H 
 and C can doi + ^4-i=f| of work in' 1 hour/.do whole 
 work in 2^;^ hours. 
 
 10. 90c. per lb. 
 
 June, 1883. 
 
 1. Quotient, 5783. Remainder, 3080. 
 
 2. Weight = 1031 tons, 5 cwt. Value, $3,300,000. 
 
 3. $28784.50^. 4. $319.37^. 5. ^i^^. ^^i,., 
 
 6. rf*^ of orunpowder is charcoal. '.weight of powder is ^.o 
 of 20 = 133^ cwt. Weight of nitre is Ij^ of 133^ cwt = 
 100 cwt. Sulphur is t;-,, <'f 1331 cwt. =13^ cwt. 
 
 7. Cost of wine-=S2. 00x300 = 8030. Carriage -$17. 20 
 Duties = $80. 50.'. total cost = $1039. 70. Selling price = 
 $1089.70^300 = $3.39 + . 
 
72 
 
 Hints and Answers. 
 
 8. $5.25. 
 
 0. 1 inetre=70 yards -f- 04 = 30 -375 in. .•.cliflfercnce = 
 :V.> 375 in. -31) 37071>= 00421 in. 
 
 10 The minute-hatid moves 12 minute-spaces while the 
 h.u.r -hand m..ve3 1 minute-space. -.i.i 12 nnnutes the 
 minute-hand will yain 11 mijiute-spaces on hour-hand. 
 At 4 o'clock the minute-hand is 20 minute-spaces behind. 
 
 1 2x20 
 Will Kain 11 spaces in 12 minutes, or 20 spaces m — jj— 
 
 = 21y\ minutes after 4. {2) In 5 ,\ minutes after 4 o'clock. 
 
 De(;emceh, 1883. 
 
 1. Quotient, 72G300 ; remainder, 1281. 
 
 2. 11 boxes = 2040 oranges, which cost $24.20, and sold 
 for $58. 08. 
 
 40x25 
 
 100 
 
 = 6|^number acres, and $300xGl=$1875 ; 
 
 $1.50 X 130 = $105=cost of fence. 
 
 4. A = 2C, B = 2C-70..A-fB-|-C = 5C-70.-.C=254, 
 
 A=508, B=438. 
 
 6. 15. 6. 00141)07. 
 
 28^-10^^ 25=n4.56. 
 *' 2000 
 
 8. B should have a start of 1 minute=^ of a mile = 2035 
 yards. 
 
 0. When the first man stops, i^ of the work remains to 
 be done, and this is done by the other tw(j men in o days, 
 hence they would do it all in 13;'. days ; hence m the 10 
 days that they w.jrk they do ^- the work ; hence the hrst 
 man must have done the other I before he quit. 
 
 10. $275. 80 X ..,^5 X rS-o=iB4. 81. 
 
 June, 1884. 
 1. For 'Hwenty-three" read " forty three. " Answer, 
 7070. 
 
^:;^^^::^^..w- 
 
 mm 
 
 Hints ani> Aksweus. 
 
 7;i 
 
 •) (a) Sirikc o,.t 11, 7, 27, 81, and divide by 2, 2, 3, 7, 
 i. Answer, 140(;»8. (6) 110. 
 •'. 4 min. -=-23 hrs. 50 min. =^lg= '^^^^TSo. 
 
 4. (1) 7H;. (2) I. 
 
 r> Wci.rht of ba-s=:li^ X 04-112 lbs. .-. weight of oats = 
 
 . 3504 
 ^-m lbs. ; -ain on 1 bush. =8^c. .-.whole gain=-- x«. 
 
 -^8.70. 
 
 lis. Od 
 
 1 • lis, od. r,rii Number cubic in. 
 
 0. Number sq. in. = „i^j — --•.»• ^^""'"«^ ^ 
 
 ^,.1 X 1-^?;-. Weight = ^6' X 1 72S oz. =17im oz. 
 
 7 A r> and C can do 4 times the work in 48 hours ; 
 ^ -uid B can do 3 times the work in 481iours ; hence C 
 i; do the ;ork once in 48 hours, A in 28| hours, B in 
 :\(i hours. 
 
 8. After the first engagement there were j«^ ^f^lJ^'^ 
 after the second vjl of j% or ^^V ..army =^^ of 3J0U- 
 ,')0()0 men. 
 
 0. {\*^^ of 0000 times l§c. -8110.88. 
 
 10 (l) S'M04 (2) 83r2-^.J07.20 = H.80 = interestfor 
 it.^' in'teret; for 1 ;ear = 8l9.20;.interest for 3^ years 
 L^7.20.^p^ulcipal = i;07.20-807.20^$24a^ 1^^^^^^^^^^ 
 on 8240 for 1 year is 810. 20 /.interest on 8100 for 1 year 
 is 88 .'. the rate is 8 pei- cent. 
 
 December, 1884. 
 
 1. 8907x8007 = 80407089. 
 
 2. 11007-17 = 11050, and 35002-21=35581. G. C- 
 IVl'of 11050 and 35581 is 221. 
 
 3. 8120.81 nearly. 
 
 A (n\ 91 • ll=*x7J^-7o • ?-^^^=ie ; 5* + i? + 16= 
 
 2211^ {h) H of ii = ii ; 2! 501)00 X Ih^^VMU- 
 
 -i 
 
74 
 
 Hints and Answers. 
 
 822 50 
 5. '-^- — = 25 yds. or 75 ft. of carpet. This will make 
 
 .") strips the length of the room .". width of room — 27 in. x 
 o-Ujft. 
 
 (>. Boy can do 3 times the work in 14 days and the man 
 7 times, or both together 10 times.*. they can do 5 times 
 tfie work in 7 days. 
 
 $4^j<92^ 
 
 8. The lime is 423 days ; ^275.00x^5 ^To(y=^19- 15. 
 
 9. First when the minute-hand has gained 18 minute- 
 spaces on the hour hand, or }j of 18 minutes past 4 
 o'clock. Next \ hen it has gained 22 minute-spaces, or 
 \^ of 22 minutes past 4 o'clock. 
 
 June, 1885. 
 
 1. Seventeen millions eighty-nine thousand six hundred 
 and tifty-three and five thousand nine hundred and four 
 millionths. Seven hundred and five dollars, sixty-three 
 cents and seven mills. One thousand eight hundred and 
 eighty-five. 
 
 2. ^r(3i + 91f)=2;T*3of 
 
 £15 10s. 2d. 
 
 _ 4 
 
 16s. 2d. 
 
 T*J of i^fl ; 
 
 3. 
 
 17 -654 = 17 -65454545 
 4-835= 'i -83583583 
 6-408= 6-40888888 
 
 Sum = 27. 89927017 
 
 4. $93.39i. 
 
 5. $7. 50 -h 10 per cent. =$8.25=8|c. a lb. 
 
 6. $167x3|XTj;o = $37.99i. 
 
 7. i'^a=i6^ years. 
 
Hints and Answers. 
 
 7r) 
 
 8. A gets HS26(5ii. B -ets 7=$033J. 
 
 9. (1) When the hands are on opposite sides of the 
 figure III. The minute-hand will have t^ono 12 times as 
 far from the tigure XII as the hour-hand has from figure 
 III, and is still as fn,r from reaching figure III as the hour- 
 hand is beyond it, or ,^3 of the distance from XII to HI. 
 The minute-hand has, therefore, gone ]H of that distance 
 
 .-.the time is {5 of 15 minutes past 53 o'clock. (2) When 
 the minute-hand has caught up to the hour-hand or gained 
 16 minute-spaces . . the time is |t of 15 minutes past 3 
 o'clock. 
 
 10. Receiving back once as much as he spent would 
 bring his money up to $720 .'. the other G^ times must 
 
 increase it from $720 to $1305, that is by $i58o .-. = 
 
 $90=amount spent. ^ 
 
 December, 1885. 
 
 1. 2, 3, 5, 7, 11. 
 
 2. (a) U' (P) ^^- M. =28152. 
 
 3. Amoimt left at end of one year=| ; amount left at 
 end of next year=f of 5, which = $900 ; hence the whole 
 fortune = 11890. 
 
 4 The remainder after dividing 159| by 12 1, which is 
 
 5|. 
 
 5. 3-74976-f60^24-^7= 000372. 
 
 6. $27.50X111 = 6323.12^. 
 
 7. The unit of length is the yard ; of time, the mean 
 solar day ; of sterling money, the sovereign or pound 
 sterling. 
 
 8. $132. 
 
 9. In ()0 hours (L. C. M. of 10, 12, 15) the first could 
 fill it G times ; the second, 5 times ; the third, 4 times .-. 
 all together would fill it 15 times in GO hours, or once in 
 4 hours.