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1
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6
w
&
CUTH BERT'S
EXERCISES IN ARITHMETIC
P^/?TS T. AND II.
ANS W^ERS.
AN S VV E R S
TO —
CUTH BERTS
Exercises in Arithmetic
PARTS r. AND II.
FIRST, SECOND, THIRD, FOURTH AND
FIFTH CLASSES.
BY
^V. N. CUTHBERT,
Principal, Verschoyh Public School.
TORONTO :
THE COPP, CLARK COMPANY, LIMITED,
1894
'5135
:S
PREFACE.
Much care has been taken to test the accuracy of the
Answers, and it is hoped the mistakes are few ; but in the
preparation of Answers to so man}'- pr(»l)lems, mistakes may
have crept in unnoticed, and any corrections from teachers,
using the books, will be thankfully received.
W. N. GUTHBEKT.
Vkhschoyle, May 1st, 1S94.
■#
• ansvvf:rs.
{
FIllST CLAS8
■
Exercise I.
1.
37r.4.
6. 14944.
10. 797059.
2.
141U5.
7. 44319.
11. 5390.
3.
1(55)87.
8. 61.525.
12. 1139.
4.
922.
9. 73311.
13. 785.
5.
3920.
Exercise II.
1.
894.
6. 6600.
10. 10893.
2.
59209.
7. 1209.
11. 3978.
3.
5322.
8. 12010.
12. 65152.
4.
6264.
9. 290.
13. 1909.
5.
1815.
Exercise III.
1.
115.
6. 102.
10. 666.
2.
204.
7. 108.
11. 860.
3.
617.
8. 76.
12. 377.
4.
289.
9. 1388.
13. 3066.
5.
258.
Exercise IV.
1.
84 apples.
5. 762.
9. 3 miles.
2.
325 yards ; 10
i 6. Sum =- 935S6.
10. 125.
yards farther.
' Diif. — 777326.
11. $8.80.
3.
367.
7 times.
12. 50 rats.
4.
91 cents.
8. 40 cents.
Exercise V.
13. 41 cents
1.
3279.
6. $1.75.
10. 108.
2.
3333.
7. 16 marbles.
11. 935.
3.
254727.
8. 900.
12. 229.
4.
5031.
9. 20 more.
13. $124.97.
6.
$6.75.
8
1. 9.
2. $32.
ANSWKKS.
Exercise VI.
3. 3980.
4. 999.
6 12950 pounds.
6. The sovon ten-cent pieces. Three of the five-cent pieces.
I wo of Mic one-cent piccea.
7. 27<iu;irt8. no. 444 : four hundred 12. 5H.
8. $1.75. land forty-four. 13. 530 centf
9. 14.00. 11. 72720.
1. 16.
2. 10 crows.
3. $8600.
4. 34 gallons.
5. 22 years old.
1. 99.
2. $34.
3. 3 dozen.
4. 270 sheep.
5. 200 feet.
1. 7.
2. $31.20.
3. $30.00.
4. $9.50.
5. 80.
6. $3.55.
Exercise VII.
6. $13000.
7. 159.
8. 20 cents.
9. 123 pears.
10. $35 gain.
11. $19.60.
12. 51282.
13. 0.
Exercise VIII.
6. 294 l>ushels. 10 34 cents.
7. $20. 11. 99 patches.
8. Tim, by 129 points. 12. 9.
9. 1450 hogs. 13. 252.
Exercise IX.
7. $39.
(a) 421^
(ft) ^^1
(c) 173
(d) 687^
9. 3 dozen.
8.
1312 total.
10. 36 apples.
rSiim ^ 630 ; and
11. i 630 taken 11
[ times = 6930.
12. 38 years old.
13. 10 years.
1. $6.72.
2. 23 cows and 18
calves, or 41 in
all.
3. 13 goats.
i $2,500.
Exercise X.
5. 13.
6. 2487 bushels.
7. $7.
8. 19740 cents.
9. 24609.
10. 6978.
11. 25 feet long.
12. Tom, 50,
Sam, 44.
13. 18.
i/^
ANSWKHS.
SECOND c;LASS.
OS.
Exercise I.
■'t
•>
it.
4.
5.
6.
7.
2.
:i
4.
5.
12'.M)4; 19410; 2588.^.
;5;{74 ; oOGL ; «)748.
11)008; 29412; 392 10.
24104 ; 30205.
80004 ; 10080.
34988 ; 43735.
30792; 38490.
3.
4.
o.
1.
2.
3.
4.
5.
2.
3.
4.
6.
148020.
03530.
137950.
323920.
100985.
592i>64.
129042.
470874.
239202.
444474.
212842.
501802.
90048.
207697.
496356.
3509308.
1735890.
2534272.
1008544.
3335896.
8. 34588 ; 43235.
9. 8644; 10805.
10. 28050 ; ."»5820.
11. 16550 ; 20(>95.
12. 25884 ; 32355.
13. 18512 ; 23140.
Exercise II.
6. 312930
7. 143235.
8. 60840.
9. 235695.
Bxen^ise III.
6. 520374.
7. 72984.
8. 251022.
9. 425448.
Exercise IV.
6. 292859.
7. 85148.
8. 607103.
9. 518553.
Exercise V,
6. 573584.
7. 678152.
8. 396908.
9. 103736.
10. 423845.
11. 106980.
12. 146085.
13. 4o;;50.
10. 17^026.
11. 77184.
12. 430U6.
13. 182436.
10. 279069.
11. 549353.
12. 151228.
13. 691.348.
10. 615896.
11. 691768.
12. 244864.
13. 175896.
10
ANSWERS.
1. 2222262.
2. 2151612.
3. 4258926.
4. 6415776
5. 2128239.
1. 3313917.
2. 64528:58.
a 88624M.
4. 1898172.
5. 7281576.
1. 9865317.
2. 1338678.
3. 8407432.
4. 2386824.
5. 1448678.
1. 10161372.
2. 2566488.
3. 7138272.
4. 3436608.
5. 1441152.
1. 91648.
2. 108192.
3. 11445928.
4. 6313006:5.
5. 14056:544.
1. 1268414.
2. 1286844.
;5. 16143440.
4. 4(570703.
6. 701152560.
Exercise VI.
6. 3465621.
7. 8869284.
8. 1952856.
9. 6485481.
Exercisr VIJ.
6. 3600720.
7. 7748523.
8. 7107282.
9. 4384521.
Exercise VIII.
6. 4256824.
7. 13:3867.S.
8. 5212504.
9. 2416557.
Exercise IX.
6. 59530452.
7. 25931808.
8. 692L9528.
9. 18923796.
Exercise X.
6. 11887680.
7. 33871024.
8. 11215:56.
9. 13648648.
Exercise XI.
6. 60447504.
7. 10892:376.
8. 27076554.
9. 17180020.
10. 531540
11. 737721.
12. 888444.
13. 371889.
10. 2690640
11. 8178444.
12. 2528676.
13. 6434874.
10. 3616459.
11. 6541557.
11. 238(5824.
13, 7877045.
10. :34391340.
11. 103766028.
12. 5:598523772.
13. 1156610280.
10. 19423890.
11. 2773130.
12. 4205625.
13. 652864.
10. 34449288.
11. 37982016.
12. 299391562.
13. 49369408.
ANSWKHS,
11
Quotient.
1. 9843843,
2. 542468,
3. 321845,
4. 48016,
5. 2676,
6. 36852,
7. 202623,
Quotient.
1. 4()00«),
2. 562606,
3. 319462,
4. 340618,
5. 315876,
6. 270830,
7. 14415,
8. 2039,
[14236,
9.] 32031,
[21354,
[91448,
10.-! 102879,
411517,
V
Quotient.
[5563,
1. ^ 4945,
4896,
[251093,
2. 1 167395,
[ 743'. »8,
3. 326398,
4. 103195,
p, 8364,
Exercise XII
Remainder.
1.
2.
7.
2.
56.
5.
0.
Remainde:
73.
38.
17.
63.
9.
21.
37.
41.
3.
3.
3.
37.
37.
13.
Quotient.
Remainder.
8. 4475,
8.
9. 10153,
5.
10 7749,
15.
V. 3895,
0.
12. 13792,
9.
13. 77893,
26.
XIII.
Quotient.
Remainder.
2018169,
29.
11 J 1009084,
77.
3587857,
2.
'31285,
12 22346,
(57040,
19.
46.
4.
,9776,
100.
'7684,
0.
j3 1463,
] 975,
26.
47.
1, 569,
20.
Exercise XIV.
lainder.
Quotient.
Remainder
56.
6. 529193,
.78.
45.
7. 311216,
6B.
0.
8. 3(irt940,
87.
8.
9. 6000,
0.
20.
10. 4082,
10.
2.
Jl. .3317014,
21.
50.
12. 492896,
14.
iz.
13. 551887,
33.
0.
12
ANSWEKS.
Quotient.
1. 7402,
2. 7308,
3. 25913,
4. 299761,
5. 460306,
6. 758257,
7. 717859,
Quotient.
1. 67617,
2. 65313,
3. 38860,
4. 107715,
5. 26352.
6. 76681,
7. 642857,
Quotient.
1. 39017,
2. 118022,
3. 54218,
4. 659322852,
5. 827552,
6. 50020,
7. 164400,
Quotient.
1. 6471216,
2. 75229,
3. 2365816,
4. 52852,
6. 1432085,
6. 1734859,
7. 1204464^
Exercise XV.
Remainder. Quotient.
67.
8.
403111,
31.
9.
272040,
95.
10.
87064,
103.
11.
144312,
86.
12.
87482,
1.
13.
44742,
40.
Exercise XVI.
Remainder. Quotient.
8. 3545520,
9. 16672,
10. 9421,
11. 534470,
12. 211891,
13. 75045,
23.
29.
67.
10.
58.
0.
85.
Exercise XVII.
Remainder. Quotient.
27.
6.
18.
6.
1.
12.
31.
8. 51934,
9. 53249,
10. 203290,
11. 13850,
12. 2464121,
13. 71521,
Exercise XVIII.
Remainder. Quotient.
8. 2996008,
9. 11732()8,
10. 7553932,
11. 875000,
12. 52()I83,
^3. 376228,
0.
26.
6.
52.
11.
25.
62.
Remainder.
87.
12.
31.
0.
15.
126.
Remainder.
4.
1.
126.
54.
28.
90.
Remainder.
2.
103.
21.
14.
19.
11.
Remainder.
2.
5.
2.
65.
1.
49.
■I
ANSWERS.
u
Exercise XIX.
inder.
7.
2.
1.
0.
3.
nder.
'%'
der.
ler.
Quotient.
1. 821375,
2. 210604,
3. 3852224,
4. 92841,
5. 496283,
6. 720684,
7. 64732,
Quotient.
1. 417343,
2. 1778073,
3. 1420169,
4. 037170,
5. 24691,
6. 25«)05243,
7. 32716027,
indei
Quotient.
Remainder
0.
8. 64732,
0.
0.
9. 64732,
0.
0.
10. 82641,
0.
0.
11. 246071,
0.
0.
12. 94716,
0.
0.
13. 100020,
0.
0.
Exercise XX.
ainder
Quotient.
Remainder
7.
8. 18377625,
16.
12.
9. 1585658,
24.
3.
10. 2752426,
11.
31.
11. 47166,
26.
1.
12. 2507866,
26.
8.
13. 909814,
57.
7.
Exercise XXI.
nainder
Quotient.
Remainder
11.
8. 137279,
70.
4.
9. 919502,
69.
28.
10. 61515,
100.
37.
11. 140295,
141.
4
179.
12. 120837,
161.
104.
13. 187474,
431.
461.
Quotient. I
1. 144001,
2. 400202,
3. 1272824,
4. 6515789,
6. 36365,
6. 131810,
7. 53177,
Exercise XXII.
1. 11450926081.
2. 4763, 703, and 03.
3. Prod. 679995, Quot. 28333, Rem. 3.
4. (0790095 + 079'. t950)^ 13r)«)0045.
5. 0. 8. 43;i7.S(>r.>7().
6. 30000000. 9. 34()2<)0.
7. 1. 10. 117809310.
11. 76560696.
12. 12544.
13. 53703736.
u
1. 846790.
2. 23796.
5. 6272.
6. 432.
7. 137616.
ANSWERS.
Exercise XXIII.
3. 1076.
4. Quot. 1140, and Rem. 84.
8. 166842. 11 65727.
9. 19966. 12. 1000.
1^- ^^- 13. 37016056.
i I
1. 4288.
2. .30030.
3. 243.
4. Q. 4379334,
5. 480522.
6. Q. 181,
7. Q. 1714,
Exercise XXIV.
Rem. 5.
Rem. 2.
Rem. 2.
8. 2085136.
9. 16188894.
10. 1296.
11. 116907.
12. 2823529444.
13. 250702.
1. 535210.
2. 194481.
141408.
o.
4. 60339852.
6. 29887.
Exercise XXV.
6. 0.
7. 34622368.
8. 16393.
9. 20364708.
10. 14211450.
11. 4623992.
12. 640715347.
13. 1016760240.
1. 284089,
2. 226800.
3. 608517(i840.
4. 11937747t;.
5. 64831244095.
Exercise XXVI.
6. 8532.
7. 205289217^>.
8. 29441476.
9. 426409.
10. 3390859584.
11. 92413568016.
12. 28684.
13. 20041020.
1. 19000659.
2. 5206152.
3. 3111696.
4. 5475883.
6. 93799226.
Exercise XXVII.
6. 9459328.
7. 8576.
8. 99359.
9. 1411344.
10. 726271.
11. 38432240.
12. 12777954.
13. 9698960565.
ANSWERS.
15
Exercise XXVIII.
. 84.
).
6.
1. 60625.
2. 8512357.
3. 555690.
4. 697.
5. 425663.
1. 1530816.
2. 9999.
3. 4330248.
4. 9185868.
5. 4841284.
1. 36711.
2. 34771072.
3. 2221.
4. 9999.
6. 27888901,
1. 4630206.
2. 11737752.
3. 1224492412.
4. 100761444.
6. 42150827803.
1. 725760.
2. 43545()00.
3. 341397504.
4. 783820800.
5. 381024000.
6. 0.
7. 12933043200.
6. 9370.
7. 54717954.
8. 3774.
9. 1045.
10. 86508.
11. 149.
12. 339889.
13. 6084.
Exercise XXIX.
6.
14112.
10.
28536768.
7.
52023040.
11.
1907082.
8.
1507088363550.
12.
9058.
9
2936.
13.
555'J3208.
Exercise XXX.
6. 061146642.
7. 2231481.
8. 12312559.
9. 40698996.
10. 1477.
11. 105266.
12. 1070.
13. G1550810.
Exercise XXXI.
6. 19238673250.
7. 45504.
8. 412780489.
9. 1.
10. 41242084.
11. 51380224.
12. 381048.
13. 70227.
Exercise XXXII.
8. 4004453376.
9. 100590336.
10. 90512034401280.
11. 0(J19748849150970.
12. 138:'.02928r.9120.
13. 23298085122481.
ij *
16
Q'lofcienfc.
1. 7261,
2. 300,
•^. 114389,
4. 676,
5. 132,
«• 292013213,
7. 2787,
1. 905.
2. 4474800.
3. 384120.
4. 76r)(i250000.
5. 640720.
^- Q. 36G,
7 58112128.
ANSWERS.
Exercise XXXIII.
V'uofcienfc.
8. 4G5,
9. 27,
10. 482,
11. 2,
12. 337,
13. 441,
161.
214.
656.
602.
2879.
0.
432.
-Remainder.
481.
472.
276.
2846.
4536.
0.
Exercise XXXIV.
8- Q. 179,
10. Q. 987,
Rem. 15.
liem.
^^em. 0.
1. 4179.
2. 4179.
3. Q. 36,
4. Q. 100,
5- Q. 96,
6. Q. 846,
7. Q. 7400,
Quofcient.
1- 1858530,
2. 4978381,'
3. 405154,
4. 5267005,
6. 635747,
6. 2922355,
7. 16043480,
Rem. 480.
i3. 1769880.
f^em. 28.
Rem. 21.
Rein. 14.
Rem. 2.
Rem. 0.
Exercise XXXV.
^- Q. 7400,
9- Q. 4(;25,
11. 638.
i2. Q. 6,
i3. Q. 84,
Rem. 0.
Rem. 0.
Rem. 0.
Keni. 376.
Rem. 0.
Exercise XXXVI.
Remainder. q„,,.^J^^
«• 9423(52,
9- 3020495,
10. 1059558,'
11. 163370,
12. 285852,
1-^. 248917,
0.
7.
3.
0.
8.
4.
0.
Remainder.
2.
1.
7.
25.
0.
20.
ANSWKIIS.
17
Exercise XXXVII.
aindei*.
^J.
'2.
'6.
46.
36.
Quotient.
Remainder.
Quotient.
Remainder.
1. 48554,
27.
8. 04092,
16.
2. 185923,
20.
9. 05305,
79.
3. 10909,
47.
H). 107.548,
69.
4. 122320,
30.
11. 42580,
77.
5. 30004,
0.
12. 95043,
70.
6. 61126,
13.
13. 1010511,
11.
7. 610136,
71.
Exercise
XXXVIII.
Quotient.
Remainder.
Quotient.
Remainder
1. 6531508,
0.
8. 1300880,
0.
2. 17r41,
10.
9. 303370,
0.
3. 159256,
29.
10. 7.''203,
20.
4. 40:U4,
94.
1.1. 14932,
17.
5. 611004,
26.
12. 1473761,
29.
6. 340024,
13.
13. 43231,
0.
7. 662991,
10.
Exercise XXXIX.
1. 2895487110.
2. 4.32508380800.
3. 48750306003074.
4. 204150229823.
5. ()871030404.
6. 0070540788.
7. 6962049676.
1. 5903322073239.
2. 354745872.
3. 372990016.
4. 419007188440.
5. 28795099513879.
6. 185738003070738.
7. 33092477328.
8.
027797385540.
9.
22400151 )7(i756892
10.
41043428)910.
11.
136392592.
12.
4291(>021885924.
13.
183478853167.
Exercise XL.
9.
2952728040.
8.
893395000.
10.
1915.3891008.
11.
91132497.
12.
348753392.
13.
45080187334.
xf
18
AKSWEtlS.
Exercise XLI.
1. 20901937287.
8. 47150560.
2. 22<)i98r)88;;:i4.
9. 338814077 H;(»0
3. 3040278;i888().
10. ()025:i2480024.
4. 9131(>407(>()0370352.
11. 501278270870.
5. 201507589100.
12. 090103^708.
♦ ). 1005245i;i02944.
13. 2002480320.
7. 304027838880.
Exercise XLII.
Quotient. Remainder.
Quotient.
Remainder.
1. 2406,
69.
8. 987,
0.
2. 30079,
0.
9. 8704,
0.
3. 2083298199,
96.
10. 9989,
179.
4. 2450935884,
71.
11. 89769,
0.
5. 000403,
0.
12. 1100010667,
3916.
0. 92943, 22970.
13. 7098,
0.
7. 8794000,
0.
Exercise XLIII.
Quotient.
Remainder.
Quotient
Remainder.
1. 90366,
83060.
8. 4831,
0723.
2. 712981,
8.
9. 13076,
56.
3. 5263,
2686.
10. 4065502,
18444.
4. 479,
0.
11. 2042225,
87.
5. 977023708356
50.
12. 144108,
234.
<). 117042881,
124.
13. 79370000,
0.
7. 4590004,
0.
Exercise
XLIV.
Quotient.
Remainder.
Quotient.
Remainder.
1. 8()4795,
0.
8. 1701790,
281.
2. 9700,
0.
9. 50005,
03.
3. 2716,
0.
10. 90809,
0.
4. 594,
101.
11. 79000,
0.
5. 59835,
21339.
12. 420597,
0.
0. 36700,
1.
13. 37169,
1857.
7. 337803,
79.
ANSWERS.
19
Exercise XLV.
mainder.
0.
0.
179.
0.
3916.
0.
smainder.
G723.
55.
18444.
87.
234.
0.
Lleniainder.
281.
ea
0.
0.
0.
1857.
^
Quotient.
1. 3754394,
2. 480440,
3. 402722,
4. 367770,
5. 120074,
6. 10()6353,
7. 1103312,
Reiuaiiulcr.
16.
60.
37.
2.
5.
0.
37.
Quotient.
8. 45(i054,
9. <>1082l,
10. 210045,
11. 34706,
12. 22546,
13. 6849729,
Exercise XLVl.
1. 116581345962900.
2. Q. 4567,
3. Q. 35045035,
4. Q. 6600,
5. Q. 352000,
6. 654768.
7. 111.
Rem. 0.
Rem. 0.
Rem. 0.
Rem. 0.
8. 1854.
9. Q. 4071348,
10. 15460624.
11. 119369.
12. 37094189.
13. 24511.
Exercise XL VII.
1. Q. 435, Rem. 337.
2. 3902.
3. 105.
4. 43148322 ^product.
5. Q. 2380, Rem. 389.
6. 108.
7. 41440.
tleniain<ler.
0.
13.
30.
0.
50.
27.
Rem. 0.
Rem. 448.
8. Q. 651,
9. 402730.
10. Q. 208474,
11. Q. 2796,
12. 111.
13. Q. 10982532, Rem. 0.
Rem. 37710.
Rem. 7596.
Exercise XLVIII.
1. 2154111.
2. 24086904710898.
3. 54307264172679.
4. 66689665.
6. 27699.
6. 3141309425.
7. Q. 796124, Rem. 0.
8. 334953.
9. 285.
10. 71452731.
11. 62736602436.
12. 286286704560081.
13. 1010219670.
^5
ANSWERS.
1. 87 cents.
2. Q. 2:^2284,
3. 20730795.
4. 104.
5. 13200 steps.
6. 402 bushels
7. 851.06.
Exercise XLIX.
Rem. 2.
$281.40
8. Q. 7251, Rem. 161.
9. .'ii!2(;.:}5.
10. 110 bottles.
11. 1X)9.
12. Q. 1002430C, Rem. 94.
13. 9900 times, and 100 remains.
H
Exercise L.
1. 2052 sheep.
7. $193.69.
2. 34 lbs.
8. 98 hogs.
3. 54 sheep.
9. 100.
4. 8112 dozen.
10. 13n\its.
5. $127.26.
11. $10.
6. Product 3346085104 ; Quot
.
12. 987.
3.3885 and 00904
over.
13. 54.
Exercise
LI.
1. 204120 ; 28800 ; ]
L04037.
8. 2501100
2. Q. 786,
Rem.
993.
9. 1001.
3. $150.75.
10. 41.
4. $576 ; 24 cents a
quire.
11. 30.
5. 1280.
12. $39.26.
6. Q. 1107,
Rem
. 17850.
13. $25,000.
7. $231.
Exercise LII.
1. $072.
8.
$7.00.
2. $333.84.
9.
332 yards.
3. $180.
10.
707 doz<^n.
4. 102854.
11.
$128.04.
5. $210.
6 40997992.
12.
13.
189000000.
2015 miles.
7. 45 pair.
ANSWERS.
21
Exercise LIII.
1^ 883. 8. Sum 9r580177135.
2 (2799)2—7834401. 9. 24 do/oii and 3 peaches.
3'. $24.08. 10. 6237.
4. 100. 11- ^15-
5. 10 cents. 12. 182 lbs.
6. Q. 2ir)59971776, and 160 over. 13. 4020.
7. Sum 1904791.
Exercise LIV.
1. Q. 9810, Rem. 161. 6. C316.
2. Sum of squares = 500109. 6. Q. 1350, Rem. 128.
3. 6297 times. 7. 18400.
4. $89.10.
8. Nine hundred and ninety-eight thousand, nine hundred and
ninety-nine.
9. 230932 sum. 12. 12()0() yards.
10. Q. 3029, Rem. 0. 13. 17780.
11. $60.
Exercise LV.
1. 33029.
2. 4922 sum ; 4864 difference ; 141897 product ; 168 quotient,
and 21 remainder.
8. 5450 and 3020.
9. 45140.
10. 10500.
3. $249.60.
4. Q. 1035, Rem. 100.
5. $19.28.
0.2970478,500, Product; Q. 11. (3597 - 3488) = 109.
83720 ; Rem. 0. 12. $19.
7. 01440.
13. (a) $40.44 ; (6) Q. 43.
Exercise LVI.
1. (a) Q. 1114435, Rem. 4. 6. $90 ; $15,390.
(b) Q. 1.340, Rem. 9.
(c) Q. 19988141, Rem. 0.
2. 300 feet, or 100 yards.
:5. $839.00.
4. $202.50.
5. (a) Q. 48258, Rem. 15.
(6) P. 421790950.
(c) Q. 9700, Rem. 58.
7. 18309 ; 4882613.
8. 70004 X 5005 =^-. 353373020.
9. $86.25,
10. (13364 X 1049) ^ 14018836.
11. $1540,
12. 80 days.
13. $54.19.
22
ANSWKRS.
Exercise LVII
1. ^10.03.
2. Q. 4070W,
Q. G135451,
I. .Sr>2()l.
5. $1:101.
Rem. 0.
3. Q. G135451, R.-m. 0.
6. (a) 182418(5, (o) 79228058, (c) 94()0»;5750 :.^
7. 10(>(> dnys. li. 1428574.
8. 40 dozen. 12. 250 pigs.
9. 19 cents. 13. 072.30.
10. Q. 3902.
1027117994, sum.
1. ^.60.
2. 97 hiUs.
3. 81.
4. 62787.
6. 1642.
Exercise LVIII
6. 3225(JOO.
7. $1.00.
8. 576 pennies.
9. 203.
10. 11 times.
11. $71.33.
12. $9().32.
13. 180 yards.
1. 1860.
2. $34.30.
3. $13.50.
4. Q. 408445,
6. $184.86.
6. $67.23.
7. Q. 2776626,
Exercise LTX.
8. 27.
9. 2061.
10. 734.
Rem. 0. 11. $19.
12. (a) Q 4703,
(b) Q. 1078,
Rem. 6. 13. 16 seconds.
Rem. 11.
Rem. 201.
Exercise LX.
1. (96493 X 94119)^^:8987705067 ; and 8987705607 -^ 138 Quotient
66128301, Remainder 129.
2. 20 times. 8. $20 a b-ad.
3. 41 pair. 9. Q. 023, Rem. 1235.
4. 1547 lbs.; and $495.04. 10. $0.00.
6. $96. 11. 5023009.
6. Q. 53550, Rem. 0. 12. Cannot add these. AVhy ?
7. 611. 13. 99 fish.
ri)l>4, sum.
a.
d,s.
ANSWKRS.
Exercise LXI.
23
1. 3r.l20.
2. $504.
.-{. |328S.(;().
4. <)87(M)t»04()86.
6. 2220.
0. l«ir)r)772(» and 30 over.
7. 60 lambs.
8. No ditfoiKiifo. (Identities ;
each 174;i(K)).
0. «r..'J0240.
10. 281044.
11. 'M dresHOH ; 1 yard more.
12. $30 a head.
13. $66.
Exercise LXII.
1. $288. 4. 19.
2. (a) 198 ; (h) 5053212. 6. $394.
3. $2.75.
fi. Twenty millions twenty th«.usand and twenty ; and 7707.
7. 13075. 11- iV.Jdays.
8. 2602480320. 12. $3(>26.
9. $960. 13. $24 gain.
10. 436306.
Lein. 11.
em. 201.
Quotient
5.
kVhy ?
24
ANSWK^S.
THIRD CLASS.
ilif^
1.
2.
3.
4.
5,
6.
7.
8.
9.
10.
11.
12.
13.
Exercise I.
2082973* feet.
423294 inches.
1 acre, 92 aq. rods, 15 sq. yards.
370242
inches
29334
•I-
feet.
1805170185 sq. feet.
25 sq. rods, 7 sq. yds., 4 sq. ft., 108 sq. inches.
19 acres, 157 sq. rods, 8 sq. yds., 4 sq. ft., 108 sq. mcnes.
7 ac. 2 sq. rods, 18 sq. yds., 2 sq. feet.
207 rods, 2 yds., 1 ft., 10 inches.
142704 inches.
$0760.
33 miles, 726 yards.
Exercise II.
1. 7 miles 300 rods, 1 foot.
2. 7 miles, 144 rods, 2 yards.
3. 3 miles, 115 rods. I f()i>t, <> inches.
4. 2 acres, 6 sq. rods, 9 sq. yds., 4 sq. ft., 72 sq. inches.
5. 51 lbs., lOdwts.
6. 3 tons, 9 cwt., 3 qrs., 6 lbs., or 3 tons 981 Iba.
7. 22 miles, 124 rods. 4 yds., 2 ft., 9 inches.
8. 41296.
9. 15 miles, 188 rods, 1 ft., 5 inches.
10. 13 miles, 30 rods, 2 yds.
11. 3 miles, 2(*>2 rods, 5 yds.
12. 4. miles, 90 rods, 3 yds, 2 ft., ,3 inches.
13. 16 miles, 194 rods, 3 yds, 1 foot.
Exercise III.
1. 201 rods, 1 yd., 1 ft, (i inclios.
2. 12 sq rods, 1 sq. yard, 7 sq. ft., ()4 sq. inches.
3. 14 acres, 32 si[. rods, i;> sq. yds.
4. 103 sq. rods, U sq. yds,, 30 sq. inches.
ANSWERS.
26
5. 2 acres, 42 sq. rods, 18 sq. yds., 4 sq. ft., 72 sq. inches.
6. 10 acres. 158 sq. reds, 9 s(|. yds., 1 sq. ft., 28 sq. inches.
7. 18 sq, rods, 28 sq. yds., 1 s(]. ft., 77 sq. inches.
8. 53 sq. rods, 28 sq. yds., 32 sq. inches.
9. 1 mile, 5 fur., 4 yds.
10. 1 fur,. 35 per., 4 yds., 1 ft. inches.
11. 30 miles, 247 rods, 2 yds., 1 ft., inches.
12. 642] feet.
13. 258 acres, 82 sq. per., 29 sq, yds., 4 sq. ft., 72 sq. inches.
Exercise IV.
1. 16 tons, 450 lbs.
2. 44 lbs., 10 ozs., 15 dvvts.. Ill, grs.
3. 15 acres, 105 sq. rods, 4 sq. yds., 3 sq. ft., 95 in.
4. 89 miles, 135 rods, 4 yds., 1 ft., 6 in.
5. 22 a ■'■ '^, 145 sq. rods.
6. CiO tons, ;">>!5 lbs., 8 ozs.
7. 27 tons, l;)38 lbs.» 12 ozs.
8. 23; '> cubic yds., 3 cubic ft., 214 cubic in.
9. £30.
10. 1 acre, 40 sq. rods, 2 sq. yds., 4 sq. ft., 45 sq. inches.
11. $138.60.
12. ^385.44.
13. 5 miles, 2(>9 r.^ds, 15 feet.
Exercise "V.
8. 16638241.
9. fl4.(i0.
1. (32230)^
2. 31527.
3. Q. 2/21,
4. 5687136.
5. 454381.
6. 280 apples.
7. 71368296.
1. 1468271.
2. 1328 feet.
3. $24.
4. $54.00.
5. $969
1038772900.
Rem. 0.
10. P'ourteen thousand and three.
11. 973.
12. $64.40.
13. 17 tons, 708 lbs., 2 ounces.
Exercise VI.
6. $14.20.
7. $(>2.60.
8. $286.80.
9. 75.20.
10. 7 tons, 1000 lbs.
11. $6251.
12. 6840 lbs.
13. $3129.28.
I
II
Sl\f
ANSWKKS.
Exercise VII.
1. ^22. 68.
8. $4.50.
2. 1 ton, 580 lbs.
9. 17 tons, 1000 lbs.
a 587 rods, 8 ft.,
3 inches. 10. $1.70.
4. $7.70. .
11. $34.05.
5. 15. a9.
12. $78.75.
6. $221.70.
13. $275.30.
7. $137.40.
Exercise VIII.
1. $12.76L
8. 14 tons, 800 lbs.
2. $14.(12^.
9. $285.20.
3. $37. 50.
10. 8 cents.
4. $1K).00
11. $1120.
5. $5f).12.
12. $70.62/<j.
6. 3800 men.
13. $900.00.
7. 3 pints.
Exercise IX.
1. $33.95.
6.
$3015.68. 10. $720.00.
2. $165.12.
7.
62 cents. n. $1357. 3(;
3. $7.87i^.
4b
8.
17 cu t., 40 lbs. 12. 400 yds.
^Olhs. 13. ^450
4. $701). 83.
9.
5. $199.07.
Exercise X.
1. $79.21.
8. 3672.
2. $25.01^.
9. 6941 lbs.
3. $77,625.
10. 2514 lbs.
4. 270 bush., hemp
seed. 11. ^^ of a cent.
5. $136.00.
12. $94.71.
6. 1980 lbs.
13. 18.36.
7. $20.79.
Exercise XI.
1. 85 cents.
2. $21.28.
8. (a) $450 ; {h) .$676.
^. 5 cents.
3. $9.31.
10. $27.64.
4. $20.00.
11. $47.08.
5. $46.26.
12. .$91.05.
6. $975.12.
13. 76 cents.
7. $3,500,000.00.
m
Hkflai
ANSWERS.
Exercise XII.
1. 15 cents.
6. $975.12.
10. $46.54f.
2. $16.06.
7. $22.50.
11. $450.31.
:i 20 yards.
8. $191.50.
12. $3693.27.
4. |38.31||.
9. $67.65.
13. $862.53.
5. $161.50.
Exercise
XIII.
1. $64.61.
6. $38.87.
10. $25.21.
2. $50.28.
7. $22.48.
11. $67.32.
3. $18.51.
8. $30.08.
12. $82.85.
4. $25.53.
9. $65.00.
13. $654.50.
5. $22.29.
Exercise XIV.
1. $91.83.
6. $32.94.
10. $103.93.
2. 145 pairs.
7. $55.16.
11. $3.15.
3. $544.32.
8. 269 tons,
1000 lbs
12. 3087 apples,
4. $481.70.
9. $374.40.
13. $110.20.
5. $51.12.
Exercise
XV.
1. $5.86.
6. $6.55.
10. $46.48.
2. 392.
7. $73.45.
11. $73.18.
3. $117.75.
8. $26.63.
12. $24.68.
4. $74.10.
9. ^.25.
13. $254.76.
5. $35.78.
Exercise XVI.
1. $28.96.
6. 109 sheep.
10. $69.81.
2. $23.49.
7. $196.55.
11. $98.47.
3. $768.58.
8. $9.80.
12. $4.80.
4. $3.73.
9. $19.67.
13. $10.08.
5. $6.40.
Exercise
XVI]
■•
1. $70.02.
6. $273.
10. $30.00.
2. 324d()ZGn.
7. $41.36.
11. $10.50.
3. $100.46.
8. $26.96.
12. $97.20.
4. $56.37.
9. $208.40,
13. $5.63.
6. $56.01,
%7
28
A.VSWKRS.
1. $20.89.
2. ?!3r..8G.
3. 36 5-cent i)iece3.
4. $27.45.
5. $26.25.
Exercise XVIII.
6. 53 yds.
7. i?78.00.
8. SIO.OO.
9. 208 llxs., 8 ozs.
10. $87.30.
11. S4.48.
12. $49..~)3.
13. .«637.
1. $231.44.
2. $8.00.
3. $48.97.
4. $53.04.
5. $60.00.
Exercise XIX.
6. $80.68.
7. $88.64.
8. $6.00.
9. $52.04.
10. $13.3.06.
11. $r;.44.
12. $76.(»9.
13. 48 cunts.
1. $123.55.
2. $207.45.
3. $113.12.
4. .:37.38.
5. $35.45.
Exercise XX.
6. $64.2.5.
7. 17988.69.
8. 55 cents a lb.
9. $7.07.
10. $16.20.
11. $13!».43.
12. $13.20.
13. 5^2.
Exercise XXI.
1. $163.88.
6. .S584.06.
10.
72 cents.
2. $155.79.
7. 27 hats.
11.
65 dozen.
3. $1(50.00.
8, 3 coiihs.
12.
$14.19.
4. $94.59.
9. 65 lbs.
13.
$39.32.
5. $1226.67.
1. $120.
2. $1005.
3. 250 iniles.
4. $58.32.
5. $20.
Exercise XXII.
6. $583. ()8.
7. 3738406.
8. $82.
9. $3.90.
10. 510 ponies.
1 1 . 35 cords.
12. $2706. 87 i
13. 3 hrs. , 20 minutes.
ANSWKRS.
29
Exercise XXIII.
1. The boys by $1
2. 1375023660.
3. 7706307420. •
4. 12764.
6. .1^55.44.
6. 16 tons, 1600 lbs.
7. (a) $12.20; (h) $17.08
(c) $58.56.
8.
i^mx
9.
(a) Q. 83448,
Rom. 95.
{b) Q. 206,
llein. 0.
('0 Q. ^^^.
Rem. 0.
10.
1.
11.
.«2lM>. 16.
/
11.
*!^;50.72.
12. Q. 14112(52013333, Rem. 125.
1. 36 and 6.
2. 136.36.
3. 48 cents.
4. ;}.".75 tons.
5. 6V)0880('.0080.
Exercise XXIV.
6. 11177.".
7. 75 ctMii.s.
8. 0.
9. S:;71.
10. Th(H)ry.
11. 336.
12. 00 yjirda.
13. 780.
Exercise XXV
1. $42.
2. $40.
3. $15.32.
4. $720.
5. $14, first.
$20, secoiKl.
81), third.
6. 1208460 L. CM.
8.
9.
10.
11.
12.
13.
$237.60.
1352 yards.
,SS004.00.
$25000.00.
828.20.
576 yards.
.$140.
Exercise XXVI.
$640.
2. 601) days.
3. $608.25.
4. (a) Di gluing post-holes ;
(b) $20.12.
6. $101.00.
6. $;i253.75
7. $66.00.
8. $15.00.
9. $.46 gain.
10. 126 doz. and 8 apples.
11. A $105 ; B $72.
12. First $1.85 ; second $1.66 ;
third $1.50.
13. $12000.00.
30
ANSWERS.
■I
1. $360.
2. $225.00.
3. $100.
4. $42'3.50.
5. 99 acres, 20 sq. rods.
6. 2061.
7. (^) $76.66; (6)12 lbs., 8 ozs
8. $70.66.
Exercise XXVII.
9. $15000.00.
10. 58^.
7li.
11. $3r{3.36.
12. 156.25.
13. (a) 2100.00; (6) 12 8h.,l(l.
Exercise XXVIII.
6. $33.30.
7. $5426.
8- $486.78.
9. 6.
1. $126.63.
2. 3 miles per hour.
3. $70 gain,
4. $225.
5. 78 mUes, 232 rods.
u'6'Ji''?^'^'^'^^^l^><^^^2^><3- 2-^.33x7x11
11. 26 gallons, 1 quart ; 20 barrels. x 7 x 11.
12. 25 cents per lb.
13. A $3.00; B $9.60; $12.50.
1. 2052.
2. 1260.
3. 0930.
4. 30240.
6. 29.
Exercise XXIX.
6. 131.
7. 1221.
8. 454.
9- 11 ; |.
10. f;
11- I ;
13. U ;
s
7-
23
Z5-
12. ft; ,■/,
4(JT.
5.5
ST'
Exercise XXX.
1. 18.
6. (a) 5 ; (6) iq^ . (c) i.
7. 3.
8- 5776.
». 20.
10. 13.
11. 1.
12. 453492
I3ii;iar.
•'5415
ANSWERS.
n
Exercise XXXI.
0; (b) 12 8h.,ld.
1. 69088 oiiricos.
2. 1 mile, 94 rods, 3 yds.
3. $4.77.
4. 46 acres, 142 sq. rods.
5. By ste;uu})o;it, hy 104 rods.
6. 11 g;ill()UH, 2 quarts.
7. 61 acres, 40 sq. rods.
8. 18 gallons, 2 quarts.
0. 21 miles, 165 rods, 4 yards,
2 feet, 6 inclies.
10. 23 bush., 2 i>ks., 1 gal, 2 qts.
11. 1028 parcels.
12. 12 days.
13. 121 posts.
2'x33x7xll.
Exercise XXXII.
1. Q. 216, Rem. 0.
2. 2' ;22x3* ; 22x3^x7; 22x5x43; 3^x112 ; 22x.32x5x7.
3. 672 ounces. 9. $2.16.
4. 79020 inches. 10. 2249775.
5. $330.00. li. $700 gain.
6. .$24,750. 12. $371.10.
7. $2.25. 13. $15.00 a ton.
8. $17.50.
s
23
6.5
Exercise XXXIII.
1. 20 acres, 97 sq. rods, 15 sq. yards, 3 sq. feet, 3 sq. inches.
2. 2193 lbs., 12ozs.
3. $400.00.
4. 61 bushels, 34* lbs.
5. f of a ton, or 166()j lbs.
0. 22680.
7. 13.
8. $39.12.
9. 20 barrels.
10. $4080.00.
11. 45 pairs.
12. A $16 ; B $16.
13. 37 tons, 1025 lbs.
Exercise XXXIV.
1. 1.
2. $70.
3. ^.
4. $.20.
5. 38 acres.
6. 1440.
7 $121.
8.
$29.20.
9.
30 hours
10.
$2.50.
11.
36.
12.
h
i:;.
A $350 ;
B $420
C $560.
3^
ANSWERS.
Exercise XXXV.
1- $752.
•5- ^^i.o2gam. ^ *^''' '^O^q. i„ches
4- ^57«j0. 9. i;a3,S400;)-«oi .•
5. .$147. 10. SCtons. •^^^'*^"^'^-
«• $21.65. 11- $117.
?'. 14.23. 12. $515.75.
S- 20 cords '^- il«5 bushels, 3o lbs.
1. $7.93.
2. 3fi65 lbs.
3. 13.
^- $94.53.
5^- 871.
Exercise XXXVI.
^' («) $i885.68 • r^^ «irro .,^
9. $205. ^^ »a72.
^Coal, $210.00/ C'oal by .$19.60.
12. $1747.20.
13. 60 cents.
Exercise XXXjttt
1. $2160. ^^XVII
2. $52.50.
3. $4.93.
4. $60.13.
^- 60 tons, 1585 lbs «
6. 1760. ^"^'^-'^o;...
7. 9376 bags.
'^ $27.50.
9. $5.00.
^^- $8.40.
M. 150.
12. 4 bu.slu,|,s 5 ots
13. $4.06. ^ •
1- 96 cords.
2. $864.
3. $451.
^- 2401b,s.,l0ozs.
^' 1.493,284.
6. $46.80.
7. $403.20
Exercise XXXVllj.
^. $311.04
9. $2u.
12. $747.05.
13. $hl7.87.
.-i. --=-■■ ■•5i,--i2.. -ft-.j..^...
'^""^"f ^^ f^ mm^m mmma
ANSWKR8.
83
es.
?i times.
oO lbs.
'^»al by .$19.60.
>ds.
yds.
1.
2.
3.
4.
6.
1.
2.
.S.
4.
5.
6,
7.
1.
o
3.
5.
,«;(;006.25.
$30.72.
1() (lays.
$25.20 gain.
240 dozen.
Exercise XXXIX.
6. $1512. 10. 28 dozen.
7. 98G0.
8. 421 lbs., 1 ounce.
9. $52.10.
Exercise XL.
11. $4.80.
12. $:U5.
13. ^0.13.
$35.28.
$587.00.
$500.00.
13 hrs., 42'f iiiinufces.
$1314.
$434.24.
2898 acres, 127 rods, 15 yds.,
1 foot, 18 inches.
8. ;»1 couts.
1). $5.25.
10. 8()(; yds., I foot, 4 inches.
11. 14322420 inclius.
12. 720 fathoms.
13. (a) 80 rods ; (b) 177120.
IfiOO rods.
400 turkeys.
$159.46.
$518 gain.
$8.25.
Exercise XLI-
6. $764.73. 10. $44,000.00.
7. 7684 and 978. M. $11,088.00.
8. 24511. 12. $29.70.
9. 13 busliels, 32 ll)s. 13. $210.68.
I.
2.
3.
4.
5.
6.
1.
2.
8.
4.
o.
0.
$67.50.
$1710.50.
142704 inches.
Exercise XLII-
7 . 3 days , 23 hours, 30 minutes.
8. 480.
9. $260.19.
(a) 116200 ; (b) 1 mile, 26G 10. Q. 4032.
rods, 4 yds. , 2 ft. , 4 inches. 11. $26.50.
1500 fathoms. 12. 13 days.
806 yds., 1 foot, 4 inches. 13. Q. 23872, Rem. 73.
Exercise XLIII.
14,322,708 sq. inches. 7. ~o% time.
11 acres, 123 rods, 17 yds., 8. 18 hrs, 20 minutes, 24 sec.
5 feet, 7:' i:!'tlies. 9. $r09,800.00.
$40.00 gain. 10. 40 chains.
$18.72. 11. $550.00.
$14.67. 12. £60 Srcr.)
54 lbs. 13. 923 bushels.
34
An'SWEkS.
Exercise XLIV.
1. 188 times.
2. 1280 lbs.
3. 2n(l (l<-iy ; 8 cents more.
4. ,*?17.70.
5. $1512.00.
6. Sceiits; $1.20.
7. $1'.).1)8.
8. $70.80.
9. $450.00.
10. 12 bushels, .'JO lbs.
11. $1.50.
12. 1() miles.
13. 05 bushels.
Exercise XLV.
1. 01 acres, 00 rods, 20 yds., feet, 108 inclies.
2.
3.
1485.
$8 a head.
8. $34.7'.)^.
9. 784 loaves.
4.
$5 H head.
10. $8.00.
5.
127 biirrels.
11. $1.92.
6.
10,500 times.
12. ^ a bale (20 pieces).
7.
A, $7.00 : H,
C, $12.00.
$5
00;
13. $111.92.
Exercise XIjVI.
1.
23 cents.
8.
$3,939,190.80.
2.
$259.20.
9.
$9(;.843.
3.
$327.00.
10.
71 minutes, 174 rods, 6 yds.,
4.
$3150.00.
1 foot, 2 inches.
5.
$000 ; $50.
11.
1 shilling, lOd.
(>.
105 acres.
12.
10 days longer.
7.
125 acres,
05
sq.
rods, 7 yds.
13.
030.
4 feet.
108 inches.
Exercise XLVII.
1.
$45.00 gain.
8. $131.53.
2.
819074 8(1.
feet.
9. 1 cent.
3.
817,947.
•
10. Q. 2,042,225,
4.
0330 times
11. 32.
5.
400 head.
12. 20.01.
G.
$92.64.
13. $4500.00.
7.
320 cords ;
$2.50 left.
Rem. 87-
ANRWKHS.
35
bs.
>3).
rods, 6 yds., I
i.
em. 87-
Exercise XL VI II.
1. (a) 2\ 3, 5 ; (ft) 2, ;r-, 5- ; {<•) 2-, 5-, 7'^
2. (") 24.",;j(); (/>) 1070()514.
;;. :i, r,. 7, '•>, 1 1, i:5, ir,, 17, li), 21, 2;i, 25, 2.7, 20, 31, 33, 35, 37,
3<>, 41, 43. 45.
4. S, 10, 12, J 4, H), IH, 20, 22, 24, 20, 28, 3(», 32, 34, 3(), 38, 40,
42, 44, 4(J, 48, 50, 52, 54, 5('), 58, (K), (;2, 04, m, m, 70, 72, 74, 76,
78, 80.
5. Composit.'s 21, 31), 40, 03, 81, 84, 99: Primes 7, 13, 19, 29, 41,
53, 79.
1x24"^ nx54^
. , . ,2xl2l .,.rix27 ) . ., 2x27
<•■ (")i3x8 r (^)|3x9 I ' ('^-|3xl8r-
|3x8 I
14x0 j
7. 0300L.C.M
13 X
f0435
5005
f40t)5
9
8. L.C.M. 45045: Quotients '..'''fy: Smn 24148.
3oo;5
1,214;:
9. 13 l)iisliols, 1 trillion.
10. 28, li.C.F.
11. («') ]U(i>) t> ('•) V}'
12. 81 liHif.s ; 5 niarhh's.
f 7ji 432 \
144 504 1
13. 72 ; { 210 570
288 048
1300
Exercise XLIX.
1. 7500 L.C.M.
2. 5040 L.C.M.
3. 03750 L.C.M.
4. 6 H.C.F.
5. 74 H.C.F.
0. 81 H.C.F.
7. (L.C.M.) 18018 -^-(C.C.M.)
99 = 182 times.
8. 3^.
9. 5.
10. 2025.
11. 0.
12. $5553.84.
33. (a)l; (b) g; (c) ,%',.
■H
"^ ■*:"*"-'*- -.at "r:
<d
PART II.
FOURTH AND FIFTH CLASSES.
i i
FOUKTJ-J CLASS.
Exercise I,
1.
,190 ; B .1r()00 ;
J^o(JO.
8.
^185,000,' 00.
2.
15 minutes.
9.
70 dozen.
41
o.
61 days.
10.
$()3.
4.
r*;!.'. per cent.
11.
^i^ of an < aince,
5.
31 lbs.
12.
19
C.
mo.
13.
450 times.
7.
$155«52.
Exercise II.
1. $<>7r)0.
2. Prudnt't r)18 acres, Mi rods. I) ft. ,48 inches. Quotient 57
acres, 90 rods, 20 yds.. 1 ft., 1 25 J. iuches --301095020^ inches.
3. (a) 50 miles ; (/>) :vl()HU(H) inches.
4. 207 rods, 2 yards, 1 t. 10 inches.
5. ^385-'. 10. ,1:80.
6. 2 inches. 11. JS^708.
7. $1 .05. 12. $29. (JO.
8. 13. ((() $13.75 ; (^)99 times.
9 25 [)er cent.
Exercise III.
1. 660 yds.
2. 6 years.
3. $•■20.
-'. 38 bushels 24 lbs.
5. $666 gain.
6. ((0l8j^, ; (h) 9.,V
7. $6300,
8. $.72 a cwt.
9. 5 s d;i.ys.
10. $2.92.
11. 31 miles, 219 rods, 4 yds., 1 ft , 3 inches.
12. 27i"5 min. past Yl.
13. (a) $6480 loss; {b) \\^ }[;^- I '^^X ; (.) $J89.61.
[39]
40
ANSWKUS.
I I
1. 1 mile.
2. 80 lods.
3. $9.r,0.
4. $05.00 '^idn,
6. 49 (lays.
6. 25 ;4alloiis.
7. $5.84.
Exercise IV.
8. li.C.F. 3 inclios ; L.C.M.
KJ5000.
9. 25 per cent.
10. $01200.
11. r)20.
12. 105 feet.
13. 7^ per cent
1. 4 lbs.
2. 330 yds.
3. 7^4 cents.
Exercise V.
4. 45 gallons.
5. 41 per cent.
0. $102.
7. (a) 1^552 cub. feet, 1088 cul>. inches ; (/>) 1120 sq. feet, 06
sq. inches.
8. 50 per cent.
9. A's $400 ; Bs $700 ; C's $:i50.
10. 40 tons, 500 lbs,
11. 112 days.
12. 225c..n]s.
13. (a) $240 ; (6) $902.40 ; (c) $95. 10.
Exercise VI.
1. 2Mj\ luin. past 5 o'clock.
2. 11. 24 o'clock, or 24 min. past 11 o'clock.
3. 10 /j inin.
4. (d) 21^ min. past 7 o'clock; (b) 2\^\ nnn. to 8 o'clock;
(c) bl\ min. to 8 o'clock.
6. 9y4y min. to 12 o'ch»ck.
6. 48 min. past 11 o'clock, or 12 min. to 12 o'clock.
7. 4.43j^^, o'clock i).m.
8. 5(\ min. to 11 o'clock.
9. 24 min.
10. 43/^ min. after III.
11. iS-l'^Q nnn. past 4 'clock.
12. 4 min.
13 (a) In mill. 12 seconds ; (b) in 16/y nn'n. ; (c) in 24 min.;
(d) in :'<2^\ min.; (c.) 49ji| min,; (/) in 1 hour (at oue o'clock);
Ig) ill 55i^ff minutes.
ANSWERS.
41
L.C.M.
feet, 96
'clock ;
mm.;
ock) •
1. $10.
2. (a) $4.80 ; (o) |1.00
3. $i)40.
4.
5.
6. 8 bushels.
7. 3 acres. 106 sq. rods, 22 sq.
yds., 7 sq. ft., 72 sq. inches.
Exercise VII.
8. 79.
4 75
US'
9. 14 days.
10. gdlTvgdxv.
11. 1000.
12. $40.
13. (a) $823.44 ; (b) $40.30.
2.
3.
-^. '^li
G.
7.
8.
9.
1.
2.
3.
4.
5.
6.
7.
Exercise VIIL
£2, 13 sh., 4d.
12 minutes to 10 o'clock, or 48 minutes past 9 o'clock.
5750 pieces. 10. $2294..
(a) 22 feet, 6 inches ; (6) 112. 11. 100 per cent. g;iin.
12. 4320 times.
13. (a) $85 ; (b) $1 ;
f 1050 first.
(c) j 1008 second.
1 1200 third.
385 tons.
180 bushels.
$2.92, per day.
$800.
320 loads.
45 bushels pease.
$500.
$4.00.
$3t'C-0.
Exercise IX.
8. $73.50.
9. $1.75.
10. $100.
11. 35 per cent.
12. i.
13. 12| per cent.
1.
2.
3.
4.
5.
A T^a:*, B $240, G $300.
$25,520.
Exercise X.
22x5x17; 2*x5-x7 ; 2-x5x3x7''5.
2^x3-^x5; 2^x3x7x71 ; 22x3-x5^
2* X 3 X 5- X 7 ; 2* x 239 ; 22 x 3 x 5x23.
2* X 52 x 11 ; 2S X 3-i ; 2-3 x 3-^ x 5^.
2^x3x5; 27 X 5 , 2 x 3'J x 11 x 13.
2"^ x 3 X 5 ; 23 x 3'* x 5^ ; 2^ x 5*.
3- \ r» / 7x11x13; 2 X 3 X 7 X 11 x 19 ; 2« x 5- x ^ x 11,
y X 5 i 2^ X 32 X 62 ; 2- X 3* X 5-.
42
ANSWKRS.
I
9. 22 X 3 X .5-2 X 1 1 ; 2-= X 53 X ] 3 ; 22 x 3 x o- x 13.
10. 2-« X 3« X 5- ; 2' x 5^ x 13 ; 2^ x 3 x o'.
11. 2 X 52 X 23 ; 2"^ X 3 X 5 x 47 ; 2- x 5 x 7 x 13.
12. 2- X 5- X 3 X 7 ; 2-^ x 3 x 5- x 21> ; 2- x 5« x 7.
13. 2- X 5 X 07 ; 2 X 34 X 5- ; 7 x 2!)-.
Exercise XL
I ('
1.
iir><)2.
^>
74;;()429
• >
720720.
4.
r,72.
i").
IHO.
i).
.004.
7. 1530.
1. 5l(C.lO.
2. 5040.
3. 2;)20.
4. S400.
5. 2520.
C. 501O5SU575.
7. 277200.
8. 5(M0.
9. 181K)0.
10. 1(3731 •»i;525.
11. 2162 [<;(>.
12. 3255840.
13. 5(;50«H)20.
Exercio.j XII.
8. 28728.
0. 3300.
10. :*.7'Sooo.
11. 804.
12. 1511040.
13. {a) 3517800; (b) 400.
Exercise XIII.
1. 477.
G. 89.
2. 788.
7. 13.
3. 192.
8. 3.
4. 47.
9. 3224
5. 1 (I*rinn' ti) (•.icli
10. 39.
11. 2G7.
12. 43.
13. 837.
utl
lUl",
Exercise XIV.
1. 225.
0. 7.
2. 207.
7. 41.
3. 29.
8. 180
4. 131.
9. 37.
6. 4.
10. 492.
11. 21.
12. 97.
13. 99.
ANSVVIiUS.
43
Exercise XV.
1. 028320.
2. 32:340^ 1()17= 20.
3. 1(580- ir.8-r= 10.
4. 55)!>7<>0fl47 :=-4080.
5.
G.
7.
720720^1001^720.
2227()80-^4()41 =-- 480.
128 X 2304 = 294012.
4«
57<
/').
8. 232702561.
9. 00-^
10. 184i.
11. ll
12. 9.
13. (a) }', (b) G.O.M. 3; L.C.M.
12 ; (c) (50 cents.
Exercise XVI.
13
2U-
1.
2. 8,^2.
8. (
I 1 7
JllK
I
it!7
9. 7i",'.. iuid4.''
1 1
4.
5.
6.
14
8
Ul
•.i 4 7
17(T0*
10. (^0 5.^ . (/,) 4
11. (a) C,; (/>)2
I no 9
II Tii'
Si-
12. 3.
LO.
7. (a)3f;(6)2f^ (c) 2^]
('
r,*>i m s
i».»
i <i .") 9 '
(6) 23 sq. yds. 5
sq. ft. 30 sq. inches.
Exercise XVII.
1. (a) 115^ ; (b) 100.
2. 1^.
8. (a) 16 ; (6) I
1 7 'ff'
9.
;in(
1 ti
3 it •
o
0.
7.
1.
2.
3.
4.
I.
2.
3.
4.
18.
16j
85.
I 5 '
{a) 19^ ; (b) 31/,
10. {it) 8,
11. 5 ; 144 ; 1
12. |.
13. ((() 3i : (6)
Exercise XVTII.
(h) 1
1 ()(!7
I8«i0*
Il-
ea-
1^.
9>
(iO*
6. 6.
6. 2.
7. 1.
8. 1.
9. i.
10. 5i
11. |.
12. 2.
13.
4;{7
Exercise XIX.
6''!
32 vests.
32.
93^ yds.
»s.
10
OZH.
5. $31
6.
7.
55.
4aai_J5..g7.
IODh
J1.4.A
lours.
8. 7],", uui'es.
9. 13 & lbs., or 13 II
10.
11.
12. Ih.Msc, $2100. Lot, .-:;300.
13. {<() 1089.
(6) 2 quarts, 1 pint.
ED-
1 T -J H •
1
44
1. 21
2. Sum = 1^11; Quotient 7
3 + 4
3. i, , find |.
ANSWKR^..
Exercise XX.
16
5j
4 + 5
4. (tt)L.O.IM.38210D;(6) Jil^f,.
3
5. --X,
5i
f
13 1^''^^'^' (c)^'
1 .■■) (T >
^*ofl
K 3108.
10. (ct) ^ ; (b) 1480.
11. 1.
12. M-
^A D B=one whole
E B rectangle.
A C F E=t5 of the
whole.
(J C F H=^ of I of
the whole ; =f or
.\ of the whole
rectanifJe, etc.
H h
D
F
{d) 7^^ ac.:=19 sq. rods, 6 sq. yds,, <)4.8 sq. inches ; (e) 1
Exercise XXL
1. 28(»r)6 ounces.
2. 13| dozen.
3. 12 acres, 85 stj. rods.
4. .$1.55.
r A 12 days.
\ B 6 days,
6. 3 feet.
7. 15 miles,
8. 5880(i00 sq. inches.
9. .^4791.12.
10, 142992 cubic inches.
11. 25 per cent.
12. ^.
13. G240,
Exercise XXII.
I
1. $900.
2. $1540.
3. $3430.
4. $5.
5. $34.28$.
6. $1000.
7. $8100.
8. $311.11 >.
9. $00.
10. $2.50; 3.\,lcent3.
11. 9000 sq. feet.
12. 1800.
13. (a) $49; {b) II, I
= $072. OQ.
i^x$noo.oo
■M
A"t^SVVl5RS.
45
Exercise XXIII.
1. lOf days.
2. fff'o,
3. $116.34.
4. -637.
5. SIO.
6. $1057.50.
7. The latter, by $10.
8. 1987.
9. 21 ^^r minutes.
10. $19.78.
11. 350 bushels.
12. 1 ton, 1125 lbs.
13. (a) $80.(*.4 ; (6) 3 d.ya.
Exercise XXIV.
2. A $120, B :?105.
:i $4000, and 12^ per cent. loss.
4. $222.
5. A 16 years, B 24 years.
6. A $60, B $80, C $90, D 205,
and E $180.
7. 10 miles.
8. 6^ gallons.
9. 54 men.
10. 76400 chains.
11. 27 cub. feet.
12. 4 lbs. green and 10 lbs.
black.
13. 587 lbs., 8 OZ3.
Exercise XXV.
1. $900.
2. 120 hats.
3. $87.50.
4. 40 per cent.
5. A $22.50 ; B $15.00 ; C 10.00.
6. (a) ^ ; (h) ^.
7. $12.00.
8. $99.00.
9. $200.
1.0. $397.50.
11. 40 per cent.
12. $8.00.
13. $96.86^1 an acre.
Exercise XXVI.
1. (a) 5 hours ; (b) 5 miles.
2. 200 yards.
3. yV-
4. 140 lbs.
5. $60.
6. 2m).
7. 105 acres, 128 sq, rods.
8. 15 gallons.
9. $42 safe, $147 contents.
10. 12 feet.
11. $150, $200 and $250 for A, B
and C, respectively.
12. $750.
13. 35.
¥
4C
AJJSVVKRS.
? iii
. i>
Vj,
Exercise XXVII-
1. 8. I3G o'clock, or 24 iiiiiiui''« to 9 o'clock.
2. 10 rods.
3. J2S() acres.
4. 22^(1. per 11).
5. .'18 larrels, 127 ll)s. ; .iiul 25 lbs. in ;i bag.
6. .^152.90.
7. $6.
8. 1 acre, 38 scj. rods, 29 scj. yds., 5 s({. feet, 90 sfj. inches.
9. $112.
10. 9.4L/j o'clock.
11. 8 days.
12. 143]]^ per cent.
13. (a) 87318 bushels ; (h) .'551 times ; (c) $12(3.'
1. 8210.03.
2. .S2.50.
3. 82252.25.
4. 602 carats.
5. $14000.
6. 5 dnx-on.
7. 10(X) |)apers.
1. 280 sheep.
2. §000.
3. S7.. 30 an acre.
4. .84 a cwt.
5. 1400 five-cent pieces: 874
«. Tlio first, l)y 763 lbs.
Exercise XXVIiI.
8. 1036 acres, 127 sq. rods, 30
sq. yds., 2 sq. feet, 36 sq. in.
9, 4 dozen.
11. 12 o'clock, noon.
12. 405, ;}<)() and 324, respectively.
13. 82,.".95,800, an acre.
Exercise XXIX.
8. 27.'>90foet.
9. 109 feet.
10 (o) J ; (h) 2|.
11. $37800.
12. !S428.'J4.00.
13. 1 foot, 6 inches.
7. 871.28.
Exercise XXX.
1. 171.36 tunes.
2. (a) (2x2x3x3x.5), (2x3x3x5x7), (2x3x5x5x7x7).
{h) I. (x. C. M, — (2 x.'ix5) the (ffViOi'st selection of ct)Uinion factors
of these numbers -- 30. 11. L. 0. M. =^ (2'-^ x 3^ x 5'- x 7-) the
smidle.sb selection of factors, including the factors of each given
number = 44100.
ANSWERS.
4?
'tively.
x7).
cfcors
) tbe
jiven
a (a) (.'ixS X 7 X 13) and (2 x 5 x 5 x 7 x i:{). (/>) (i.) (i. C M. \h
(■(|ual to [7)x7 X V,i) = 45'* ; (u ) L. C. M. is iMnial to (2 x 5 x 5 x 7 x
i;{x3) ■= 13050. ((0 (i.) From (/>) (r.) and (ii.) we have G. C. M. x
L. C. M. = (5 X 7 X 13) X (2 X 5 X 5 X 7 X 1 3 x 3) -^ (3 x 5 x 7 x 13 x
2 X 5 X 5 X 7 X 13) all the facrors of 13()r) and 4550 ; (ii.) from (c) (r.)
we see that G. C. M. is C(»m[)o,scd of the factor.s of 13(j5 and 4550
rejected by L. C. M. and vice versa ; (iii. ) G. C. M. and L. C. M. are
made up of all the factors of 1305 and 4550 [c (i.)]; therefore G. CM.
X L. C. M. — product <»f the two numl)ers (because (i.C.M. and
h.C.M.^^ oil the fiidors of the given nund)ers) ; (iv.) since G.C.M.
X L. C. M. of the two numbers = |)roduct of numbers ; therefore
their product -r one of the numl»ers — the other innnber, and
rirc cersa ; (v.) since product of the two luunbers =:^ G. C. M. X
L. 0. M. ; therefore their product -^ G. C. M. — L. C. M. and
vice versd.
4. 180.
5. (Theory).
6. 740.
7. The smallest number we coidd have for one is 240 ; there-
f(»re, 240 and 2880, or 720 (third multiple) and OOO, etc. (N.B. all
the nmltiples of 240 will not do, however).
8. L. C. M. 40 ; Quol.., 525.
9. H. C. F.,5 ; L. C. M , 30.
10. (a)H. C. F., ,,',^ ; L. C. M.,
ively.
11. 24.3, 70«i, 050.
12. L. C. M., 1)0, and H. 0. F., ^i,^.
13. 272.
Exercise XXXI.
1. 312 bushels.
2. 4.
3. 50 of each.
4. (a) The latter kind by 5^^ of a cent, per inch, (h) 40 sticks of
the 7-inch khid.
5. 410 and 015.
0. 4840 times.
7. 21 lbs., 01 ounces, (21, |^ Ib.s).
8. 050 l])s. at 4, ami 8 cents. res[>ectively, and 15{;() lbs. at 15
it'Uts.
9- ^m- 12. .1:;240.
10. Sl)0.24. 13. (a) 514 bushels, 10 lbs. ;
Jl. r^Ocost. (6) 9000; (c) ^18.00.
.3 .
■i '
(/>) 1 and 81 times, respect-
48
ANSWERS.
*l|-
Exercise XXXII.
8. 7 cents.
9. 5 duys.
1. Hi cents.
2. 3| ozs.
3. A $78.32. B $121.04. 10. $1()13.20.
4. 3 : 13.
5. §4,150,000.
6. 416 sq. ft., 96 sq. indies. 13. (a) 50 cents, (b) L.C.M.,90
7.
11. £10, Sterling.
12. WM-.
$240.
v.>
times.
Exercise XXXIII.
and 136, the
200.
J!?5,700.
20 per cerxt.
1 25
210.
22.
567, L.O.M.
1. A 84.50. B $2.00. C$1.80. 9. 357, the greater ;
less.
10. 1(50 Ihs. of the dearer, and
120 of the cheaper.
11. 70 cents.
12. 2^ per cent.
13 (a) $7000 cost, $8000 askinj;
. price, $7500 selling price ;
(6) $32.60.
Exercise XXXIV.
7. 200 bnshels.
8. 4 per cent.
9. 66 ':| per cent.
10. $6875. ■
11. (a)67j^; (6)351.
12. 9 years.
13. (a) 16 feet ; (6) 36 years.
1.
$2.
2.
November 19th, 1888.
3.
40 per cent.
4.
$200.
5.
First cost, $4 ; second
cost, $2.
6.
$131.25.
^'*,l
Exercise XXXV.
8. $4800.
1. '^h ytiars.
2. 4 per cent.
3. $1800.
4. 112 J)arrels, and 560 Ixixes
5. 20, 80 and 160.
6. 510 Cords, 60 cubic feet.
7. 516(5 acres, 119 sq. ro(is, «Ss(|. 13. (a) 336 ; (6) $2.35.
yds., 2 sq. ft., 36 sq in
9. $54.
10. $504.
11. 4 times.
12. G:B: ;2:3 (or 120 Ibs. green
and 180 lbs. black).
A NSW Kits.
49
r ; JXTid 136, the
Exercise XXXVI.
1. $(;()7.50 amount (principal 8. 5585 miles, 1050 yards.
o
3.
4.
6.
0.
7.
;ui»l interest).
5 per cent.
12i
years.
The Litter by $5440.
I
$4.50.
$33.75.
9. 10 t-oiis, 18(;0]hs.
10. 13 acres, 157 sq. rods, 139
sq. yds., 5 aq. feet.
11. .$10.20.
12. $-90.
13. 3170 miles, 80 rods.
Exercise XXXVII.
1. 4 per cent.
2. 25 per cent.
o
• >.
3000
men.
4. ,$57.00.
5. 2040 times.
0. 40
cents.
i ■
8.
,ny (lays.
$1750.
1.
Es
$1880.
•>
$327.00.
• >.
9H da.y.s.
4.
3 min. per hi air.
5,
OO gallons.
0.
31,536,000 seconds.
i •
$180.00.
s.
4 months.
9. 20 lbs. at 40, 50 and 75 cents,
resi)ectively, and 9 lbs. at 80
cents.
10. 38« per cent.
11. $133331.
12. .$02.
13. 104 yds. at .$1.80 ~ .$187.20
(l)ractically); 25%.
XXXVIII
9. (a) Side iiicasuremout, 32 sq.
ft. to a cord, (h) Fn tiers
lengthwise of the pile.
10. $271.25.
11. 8 lbs. at 50 cunts, 5 lbs. at
70 cents.
12. 18 gallons.
13. (a) $10 ; (h) .30 cents.
i ■
Exercise XXXIX.
1. 4 hrs., 35 min.
2. 1 50 per cent.
3. 20.
4. 420 sq. inches.
o. 02 j\ per cent.
6. $24.80.
7. i
8. 0732 ; 1070, sum.
9. $8.
10. $4.20.
11. $75.
12. $22.50.
13. (a) 70 tons ; (b) $384.
50
ANaWKllS.
Exercise XL,
m
4;
■(
1. '^2Ml.
2. First, 70 ; second, 140
third, 60.
3. 17136.
4. IOha<;s.
f). lH75buslu>ls.
(•). .S41.
7. 50 lbs.
8. A, ^!l.0() ; B, ii?4.3() ; C, $2.90;
D, $V2.m.
9. 90 fives ; 80 tens.
10. !$1432.32.
11. $36.50.
12. 113.
13. (a) 16 cents; (6) A, $350 ; B,
$50 ; C, $250.
Exercise XLI.
1. $7000.
2. 00 i; ^6) ::?;(.0 |.
.3. $1(»75.20.
4. 9 miles.
5. $175.50.
0. I of ;ia inch to the mile.
7. 90 cents.
8. ,^,.
9. 4 per rent,
10. 107 cart-lo.ula.
11. 5200.
12. 80 per cunt.
13. 6 p.m.
r
Exercise XLII.
1. («) 10 minntes ; (6) 3 miles. 8. 33| per cent.
2. 432 days. 9. $2250.
3. $33.3. 10. $216.
4. 12 days. 11. 10 days.
5. .$1440. 12. 1| per cent, f^ain.
0. 24762 tons, 1078 lbs., 2 ozs. 13. 6 per cent.
7. 2 games.
Exercise XLIII.
h <Q
1. (a) 80 cents ; (h) 3^ per cent.
2. 2(X)0 gallons.
3. 48 tons.
4. $156.06.
5. 5 per cent.
6. $27.50.
7. A, $40 ; B, $120 ; C, $180.
8. 2 lbs. 8 ozs.
9. 12 per cent.
10. 15 cents a doz. , before ; 12
cents a doz., after.
11. $244.48.
12. 20.
13. $84.
ANSWKKS.
61
Exercise XLIV.
1. $1.4G. 8. .f(;.I2.
2. ^f,. 9. $1880.
3. 7 yoar-H. 10. 85.S.82.
4. A, .^81 ; B, $90 ; 0, $108. 11. NovomUer 19t,]i, 1888.
5. 49 buys.
6. 420.
12. 8 1i()uns.
13. $4.00 loss.
Exercise XLV.
8. 24 miles.
9. $41.()0.
10. $517.11.
11. $2200.00.
5. 20 days, 12 hrs., 48 minutes. 12. 24 miles an hour.
6. 50 per cent. 13. 1089.00.
7. 2254 casks, and 2f pints left.
1. $737.10.
2. $436.4a
3. 20.
4. $40.30.
1. 435.
2. 1120.
3. 40 cents.
4. 2105.
Exercise XLVI.
5. $1530. 9. $125 and $280.
6. 150. 10. f ;^' of a sq. inch.
7. 32. 11. $81)88.80.
8. 112. 12. 7.5.
13. (a) 6 turkeys, 3 ducks, 2 geese and 2 chickens ; (6) £10
14sh. lid.
Exercise XLVII.
2. Yea ; because it is the measure of a ((iiautity.
3. Due Dec. 13th, 1891, but must l)e paid <m the 10th Dec. (3
days' grace) ; $654 will redeem it.
4. $1.55.
5. 6.
6. A, $560.00 ; B, $784.00 ; C, $1 120.00.
7. $180.00.
8. 132.
9. 42.
10. $1287.45.
11. $420.
12. 25 per cent.
13. (a) 840 ; (/>) 1 ft. 4 in.
52
ANSWfeUs).
« i
t
' 5
8 ■!
A
4. A
Exercise XLVIII.
$14()0(K).00. 7. «uiu .S8(X).00 ;
A S^U.W ; B .^70.00; TA's §500.00.
$28.(K). Shares JB's ^(lO.OO.
13 sq. feet, 153 sq. inches l^'s $240 00.
) 8. 4.
er.j 9. 33.33.^ less.
r20^Y4 .i^alhnis of wine.
\ *^/4 4 gJilh)ns of water
of l)j'*:^*:f gaUons of wine. I 10 73 Jr cents
(lOj'Yi gallons of water, j n.
5. 7r>o.
6. ^30.00.
$122.88.
115 yards.
12 liorses ; 108 .sheej*.
1.
2.
3.
4. 100 i^alions.
5. 8 j)or cent.
0. 700.
7 9 A
18 11 )s., 12 ozs.
12. g?00.
13. («) 504 riuls ; {b) 515 yils.
Exercise XLIX.
H. 81.
0. 0(5 trees.
10. 13,'{ / <,'ain.
11, 135 ounces.
12 (lOO times.
13.
I 20 ll)s. at «iU rents.
V. '^^
rr-
t:;o
ro
Exercise L.
1. $11,000.00.
]2(1
>z (lo/.eTi.
80.
3.
4.
6.
C.
7,115,505.
|!183.
A. $118.80
H. $1<;08.00
$115.71.
{
)
r(»tal, $172(5. 8<>.
1!.
10.
11.
12
• >i
1 \)vr cent.
X U07 ; 2- X
2^x5-.
.)* X b
na
oo.
I (4i mill,
132
7. H^ per cent,
) 1 14
I II
13. $21(5.31
Exercise LI
1.
2.
3.
4
6.
6.
7.
A, $3r» ; Ti, 848 ; C, $40. <>. H-.th (a) an.l (h) Theory ; (c)
*1(). (I.) ir:i ; (H.) r,2; ((/) (i.)
0001; (II.) (51 ac. 0(5 rods,
2fS y.ls., (5 ft. 108 lU.
-!1li
Clay, (50 feet; sand, 12 feet;
rock, 18 feet.
13 (1;
28.
5040.
lys.
.io. $103,000
11. >^.2.
12. \, *(1I5; li,
1.'). 10 cents.
25.
8. 6 (lays.
It
ANSWERS.
53
1. 560 acres.
2. 60 per cent.
Q '>
4. 5 lbs.
Exercise LII.
8. 027045.
9. $100.
10. 2880 times.
11. Lose, J?1400.
5. -$(K). (PTe is $()0 in debt.) J 2. 25 ft. 6 in. long ; 17 ft. in.
6. (a) 71 ; (b) 1,244,880. wide.
7. A, 60 days ; B, 380 days. 13. {a) $91.26 ; (6) 28 cents.
Exercise LIII.
1. $1 25.
2. $200.
3. $649.97JJ,^.
4. $6864.
5. 5.\ cents.
6. $677.60.
7. $28.75.
8. ^44.00.
9. $764.00.
10. $.32.
11. 242.
12. $497.61.
13. 114.
1. $80 per annum.
2. $8,500.00.
4. 17 days,
o. 40 days.
6. $192.
7. A, $480 ; B, $3()0.
Exercise LIV.
8. ^«j.
Q 'Jit
10. $170-5.~»a264.
11. 40 i)arrels.
13. (a) $189.00; (6) $75.60.
Exercise LV%
1. A. $242.10; B, $121.05.
2 The ninth =^ 9 X 450= 4050.
3. 7?5 ])or cent,
4. 28000.
5. 1048 yds.
6. $560.
7. $4(J0, tirst ; $350, second.
8. 225 bushels.
9. 2 tons, 913 ji 11 )s.
10. L.C.M. 40320; ll.r.F. 133.
11. $15.48.
12. 456 bushels,
13. (a) $12.75; {!>) 15 acres.
VHHI
54
ANSWERS.
Exercise LVL
1. 18 times.
2. 43 tons, 4(H) lbs.
3. 704 busliuls.
4. ^2ir)4.27.
5. ^^2 tons.
6. 154.45.
7. A : B : : 45 : 32.
8. $4:J75.
9. ^1.05.
10. 5.
11. s:^;!0.0'!|.
12. $121.21^.
13. $;7.00-.im.
Exercise LVII.
1. 45 slioyp.
2. ^320.00.
3. 4 per cent.
4. $15()3.90.
5. $192.50.
6. l^r-
7. $81.60.
8. iJS.OO.
9. 23 li.C.K.- iui.l 211 L.C.M.
10. $19.80 + ^3:;.75 ^--: .i<r,3.o5.
11. l^^iy of cost.
12. .i!?9405.
13. (d) 34.5() ; (h) US.
Exercise LVIII,
1. |.
2. $20.00.
3. («) Vi ; (/>) .^1 ; (c) 1.
4. 28|%.
5. 117,612 tons.
6. 2 ton.s, 56 lbs.
7. $84.00.
8. $4.80 (SO cents each).
9. $31,500.00.
10 •"'>
11. 3^.
12. 20 miles.
13. $1(X)0.
Exercise LIX.
1. $30.00.
1
8. $30,000.
2. The foriaer ; $0.00 saved.
9. $5:{2. ((,)uintal = lowt.)
r 3. 2^ li.C.M.
10. $13.80.
4. 35 .lays.
11. $350.00.
5. $21.07.
12. 3 days.
0. 10 yt-ai-s ; per cent.
13. 60.
7. 4 per cent.
ANSWKRS,
55
Exercise LiX.
(4
1. $17.04.
rFirst, i7() bushels,
2. \ Second, 17C
iThird, 348
3. lf(j.
4. $U>0.
5. 107 A-
6. A, 800 ; B, 300.
7. 2*rj of a ton.
8. 6ay«,080,008,41H, 003,412,800.
9. A, ii?32.00 ; B, ^30.00.
10. 870 bbls.
11. 4 acres,
12. 1583.
13. $280.
't
Exercise LXI.
1. $34.40.
2. ^\ ; $2400.00.
3. 32 days.
4. A, 450 ; B, 400.
5. $125.
6. 1 ton, 625 lbs.
7. $38.70.
8. $240.
9. $1400.
10. f .
11. $40.
12. 80 dojcon.
13. (a) Gains 10 per ctub.;
(6) 27 times.
Exercise LXII.
1. $270,000.00.
2. A, $480 ; B, $160 ; 0,
W. $24.00.
4. $73.60.
5. 243.
6. $15" t-O.
7. $27,376.
8. 408 yards.
640. 0. 8%.
10. B, $1.02 ; G, $2.04.
11. 45 gallons.
12. $87.50.
13. 1, 4, 3 and 2 lbs. resp., (or 1
lb. of each, for anofchwr set.)
1. 13^.
2. 81 tons.
3. $1300.
4. 20 per cent.
5. $0 a head.
6. liO miles.
7. $360.
Exercise LXIII.
8. 1 day.
9. 117,628.
10. $1364.
11. 8.
12. 5.20 p.m.
13. {a) llOsq. inches ; (6) 1005f
sq. inches ; (c) 2354 sq.inchoa.
^■'*l-
56
ANSWERS.
! 5
i
« n II
Exercise LXIV.
1. 154 sq. inches.
2. 10 font, (■> inches.
3. 56 yards,
4. 188(i sq. yards, 4 sq. feet, 7*2 sq. inches.
5. 8 acres, 23 rods, 8 yards, 2 feet, 30 inches.
('). r(80- - (i()2) sq. inches — 3} (140 x 20) sq. inches = 6 sq. yds.,
7 sq. feet, l«i sq. inches.
7. 1078 cubic inches.
8. 1121-12 + .. . sq. inches.
9. 81)1 cubic inches.
10. 20 inches.
11. 42 rods.
12. 20 inclies.
13. (a) 9 feet, 4 inches ; (6) 44 sq. rods, 6 sq. yards, 6 sq. feet,
72 sq. inches.
Exercise LXV.
1.
2. $1261.40.
3. $165.12.
4. 8 : 5 respectively.
5. 1230.
6. (a) of, first ; -^, second ;
X , third ; (b) SiVff-
7. («) ni'^, (b) IH, (c) ^.
8. 50Jg days.
9. 303 dozen and 4, chairs.
10. He wouhl neither gain nor
lose.
11. $120.
10:j48 87 75. 15
■^'^- .Ttioj 3()0> Add » ^I8«
13. 10 years.
r
i
I' '
Exercise LXVI.
1. (a) 9h ; (6) 9^. 8. $2707.20.
2. $6.00. 9. $133.20.
3. Eitlier duecUij North or 10. 1st, 205 ; 2nd, 328 ; 3rd, 4th,
South. 5th, 123 ench.
4. $121.70. 11. $160.70.
5. 7800 miles. 12. $390.
6. 9 acres, 52 rods, 24 yards, 13. (a) 8^ ; (ft) 48 cents, tea ; 40
3 feet 21 jl inches. cents, collee.
7. 21,315 lbs.
ANSWERS.
67
Exercise LXVII.
1. 1.
2. $1.20.
3. O^V Ihs.
4. 45 sheep.
5. 733 yds., 1 ft.
6. 4,^ hours.
7. 1 pint.
8. At, A's corner ; once. (But A
will liavo reached liis corner
the second time).
9. Tldise, 8240 ; carriage, ^400.
10. i=^nr)0.
11. <i:;o.
IL'. 20 per cent.
];». 7 inches.
Exercise LXVIII.
1. (a) Book-work; 3341520 ; (6) 17 ; 3id, 4th, 5th, fith, 7th,
8th, and Dth.
2. (r() P>ook-work ; (?)) $14.37i ; ('•) 25 percent
3. (a) Book-work ; {!>) 150 barrels.
4. 75 cents.
5. July 13th, 1890. <
6. 2 days.
7. 7.
8. Book-work: 375-70440355.
9. (a) i<'\2 ; (6) 104 days.
10. ^40.71.
11. 11 dozen.
12. 07.
13. ^00, A's share ; $50, B's share and $30, C's share.
Exercise LXIX.
1. 5 days.
2. 4hrs., 22 ram., 30 sec.
3. $4.50.
4. 13 miles.
5. 4 lbs.
6. 20?;. i)er cent.
7. i of an acre.
8. 13 lbs., 8 ozs.
9. $43,200.
10. ((0 2,505,0()0sec's.j
(/>)7 times.
11. A. $70 : B, $80.
12. 004 lbs.
13. |1(J,044.
•s^ "i^
- 4 it
1 -'I
■■ 4 ' «?
n
58
ANSWKRS.
Exercise LXX.
1. 80 yards.
2. 45 acres.
3. 03 cents.
4. $:>A00
5. 63942.
6. {5><;0.
9. 1st., $(500 ; 2iul, ai200 ; Srd,
$;)(>(» : -Jill, SL'700.
10. ^i')2.8:.:'.
11. 147 sq. rods, sq. yds., 8 sq.
ft., 90 sq. in.
12. 70 times.
7. A, $100 ; B, $150; 0, $250. 13. $8U.09.
8. $13500.
Exercise LXXI.
1. 28 per cent.
2. 50 lbs. and 37i lbs.
3. $221.
4. $902.40.
5. 300.
6. 80 per cent.
7. $40.30 ^ain.
8. 244 acri^s, 88 nxls, 24 s(|. yards,
2 sq. feet, 72 sq. iriches.
9. A $4 to ; B S87.50, and $202.50.
10. (a) $10 ; (6) £3, 3.s, 3d.
11. $18.90.
12. 37.
13. (a) 28512 ; (6) (i.) By the ' local vdlue^ of a digit is meant its
value awordiwj to the posliioit it occupies in our scale (decimal scale)
of NOTATION, (ii.) First its real or intrinsic value as the nun)l)er 7
(7 times the unit) ; and second, its ' bjcal vahte ' in the tkns' pla(;e
(7 tens, or 70 timks the unit), (ill.) CXLlCLXXXlCMXXIV.
.. »
Exercise LXXII.
1. (a) Book-work ; (/>) 247 : (c) •ili:.-;57.
2. (a) Finite: Pure llepetend : Mixed Repetend. (If the de-
nominator of a fraction contains no otJier factors than 2 or 5, the
decimal is finite ; if the denominator c<jntains neitlur of the factors
2 or 5 it is a p\u-e repetend ; but if it contains either uf the. factors 2
or 5 it is a mixed repetend.) {b) (i.) ,",7„ ; (ii.) ^[\ ; (iii.) j^^f.
3. i
4. $010.
6. $10.
6. 078125.
7» $075.
5. H.C.F., 41 ; L.C.M., 34,440.
9. I.IXCCXXIV.
10. $384.
11. $41.25.
12. lOl barrels.
13. 1036 acres, 128 sq. rods.
ANSWERS.
59
Exercise LXXIII.
1200 ; '3rd,
I.
72 jrals.
7. .1?4.07.
'00.
O < 2 /o •
8 $240.57.
3.
The ^rfi/cr, by $1 on $100.
9. g.
yds., 8 sq.
4.
$17.81.
10. 3 sh. St'g
5.
10 Ins., 48 mill., a.m.
11. 2 niilos.
6.
Length, 27 ft. ; bread Ui,
12. 7 ft.
18 ft.; height, 13 ft.
13. $100.
Exercise LXXIV.
■^'I- yards,
-•lies,
I $202.50.
d.
iieant its
lal scale)
iuni})er 7
fs' PLACE
UY.
the de-
r o, the
'■ factors
''actors 2
7S
S)ff-
ods.
1. $72.
2. Total, 14215.
3. 2 ozs., 13 dwts., 4 grs.
4. $1313.
5. 60%.
8. A, $1.0; B, $8; C, $22; $2
a day.
9. 15 045.
10. 71 ac, 08 s(i. rods, 29 sq. yds.,
3 sq. ft., 100 sq. in.
C. (a)3r>36; (?>) Sl.OT-r/Hrackets) H. .^^.
7. A, 54 ; B, 3(); C, GO sheep; 12. $22.16.
$5 per head. 13. $5.10.
Exercise LXXV.
1. $604.80.
2. A, 123 lbs., 6 ozs. ; B, 164 lbs., 8 ozs.
3. 54 yards ; $2 left.
4. $23.04.
5. $2646.
6. $19.08 gain.
7. 28 hours.
8. 27 acres, 20 sq. rods, 16 sq. yards.
9. 54 minutes.
10. 15 miles.
11. 42 acres, 108 rods, 7 yards, 81 iiiclies.
4i+(i of ^^)+aof ^v
12. \ \ ^^.
''J
83J
13. 236250.
I^lf
i
hi
h i
60
ANSWERS.
Exercise LXXVI.
1. 21 G yds., 2 ft.
2. 5 (lays.
3. GO [icv cent.
4. 240 11.8.
5. 5 per cent.
G. ll> cents.
7. .^4:i.20.
1. 25 cunts.
2. S!«72.
8. 24 diiys.
9. 9 cents.
10. 30 lbs.
11. ??9(i7.50.
12. 4(i§%.
13.
o ce
nts.
Exercise LXXVII.
7. I7r» liours,
8. 45 niinntes.
3. 32 l>l)ls. Ht 14.50 ; 113 hbls. 9. A, .^ISO ; li, $^100 ; 0, |280.
at 85.00.
10. IG'q' ])cr cent.
4. A, $90 ; B, 870 ; C, $<i40. 11. Tom, $5.91 ; .-ind Bob, ^liA-i.
5. 99.
6. 3 dirk
1. $43.20.
2. 9-4137^ p.m.
3. Eacli ni;u) 815 ; e;ic1i A\ oman 9 850.
12. $55.12 gain.
13. 41 acres, 120 rods, 19 yards.
Exercise LXXVIII.
7. 33.
8. 8:;go.
85 ; each child 81.
4. 881.
5. 895.
6. 23 lbs.
1. 828.
2. 848.(54.
3. 20.
4. 1522 yards.
5. 8«;00().
G. l."> miles.
13. (a) 89210 ;
(/>) (1), ll.C.F. 8'
10. A must ]y.yy B 80.50.
11. 48<; lbs. IO5 ounces.
12. G7.
13. 4!>2 bu.sliels
' 11'
Exercise LXXIX.
7. 30 eent.s.
8. 5 per cent.
9. 87.20.
10. Note (J'ace valve), 8584,
Jl. 8112.
12. 8
(O.
f
1G128 18
10128 2304 288 IS
i'-i)
i8153() 91 . 8153G 11048 1456 91
^ -f^ ^ 18
(3) - X — X — ^ —
>tS^ 9) H 91
Answkus.
61
Exercise LXXX.
i. 2 (luarts, 1 pint.
2. The mnUiplicr = 1
3, of a 11). troy.
> >
li X $560 = i?()72, the amount.
7o;w
4. 20 per cent.
5. 40.
6. .18 tons.
7. $700.
8. 10 do-A.
9. (rt) The L.O.M. (»f ^(rr)?)»f»?7)«r.s- consists of tlic,s»nr7/f'.s'i.sc^v-hV)n
of fiu'toi-o ivhicli cnidaiuti the factor.s of each given nuiuher ; an<l the
H.O.F. of tivo numhn-s consists of the yredfed selecfloti of fartors
common to both numbers. The H.C.F. is comi)oso(l of <dl the fartors
rejort(>d})y the L.C.M. and rirr. rorsa ; therefore, the factors of tlie
TI.O.F. and L.C.M. comprise "// llic for tors of the tiro nnmhrrs ;
and consecpiently, the H.C.F. nniltiplied l>y the L.C.M. is e(pial to
the proiliict of the tojo numbers, aj. ; - Question 9 {b). H.C.F. and
li.<^^^. of 2.'^»40 and 2.520, which rcs»lcrd into their prime factors —
J2:;4().^2x2x:{x:ix5xi:i j ^r^^ the m-mfes^. selection of
{ 2520 --- 2 X 2 X 2 X .S X :5 X 5 X 7. j ' '^
fortirrs, comm,on to these numbers, is 2x2x3x3x5 = 180, the
irrC.F. ; and the .-oiKilli'^l srlrrfio)i <f f«'t<o-s wliicli contains the
factors <')f each of the ^iven numbers, is (2 x2x3x.3x5x 1.3) x (2 x 7)
-:527(JO, the L.C.M. ; 1>ut these are all the factors of these two
umnbers : therefore the H.C.F. x L.C.M. of amj ti'-o uumbers is the
H.C.F. X L.C.M. of idui two No's,
piuduct of the tiuo numbers ; .'.
81 X 28520
= the otlier No. (c) -= 1 240.
713
10. L.C.M. ^1582.30800 ; H.C.F, -^
;')5ir>2400.
One of the No's.
387()0
-^ 120.
(d)
323
1582;i08()0 X 5 =
11. (I.) $.5.. 30; (11.) .^4.80.
12. A, $90 ; B, $(•>() ; C, $50.
13. (a) A, $100; B, $150; C, $180. (h) A, $.30; B, .$20; 0,
$16.
Exercise LXX.XI.
1. 7200.
2. If) days ; ^ of the work.
3. 10 [)er cent.
4. 3 cents a pint.
5. 10 ]) T cent.
0. 70x56 rods.
i^J
62
ANSWKRS.
i n
7. In bntckets = -( 4^ (| of |e) J- + ^ (f of ^)-^2f\ }- - ^ i x
7 |of|-^ 2,«^ ^\ 7
8. 20 at $3.1)0; 13 at $0.50.
9. 60 tons.
10. Length, (54 ft. ; breadth, 48 ft. ; height, 5 ft. 4 in.
n. 12 (lays.
12. 60 gallons.
13. $10.50.
Exercise LXXXII.
1. A, 20 clays ; B, 27^ days.
2. 30.
3. 25 times.
4. $80.
5. 4 por cent, loss,
6. $1.20.
7. A, $180 ; B, $240.
8. $3024.
9. 15 days.
10. $429.
11. $9000.
12. 373.0(3 not.
13. f of an inch.
Exercise LXXXIII.
1. Of all the farters of the two numbers ; hence L.C.M. X H.C.F.
=Prodnct of the t wo uuiiiIum-s : 170,(390.
2. In the simple rules the unit is uniform ; in the compound
., f Product, ]
rules it varies ; \ ?\irT- — T = smaller numl - =-= (J.OBl ; and
I Quotient J ' '
V (Product X Quotient) - large number =^ 1,806,867 ; 1 lb., 2 ozs.,
12 dwts., 10 gra.
3. Same difference as between simple and compoKvd rules; in
decimal fractions the tmit is uniform {dvcimol scale), and in vulgar
fractions the unit varies; 2; 13'00069615.
4. (6 stri[>s :v2 double rolls) $245.
5. $1425.
6. $22.50.
7. $5000.
8. 250 gallons.
9. A, $80; B, $90; 0, $100.
10. 16 ozs.
11. 2.
12. 3 h()rses=2 oxen.
13. $18.
ANSWRUS.
63
Exercise LXXXIV.
1. l[.
2. $42.
3. i
5 14 ll)s. toa ; Mfi lbs. o«.fi'ee.
H. $03.75.
7. £66.
8. 637500.
9. A, $40 ; B, $00 ; C, 90.
10. 33.
11. $1.50.
12. $504.
13. 13064.
Exercise LXXXV.
1. €24 6s. 2d. 7. $122.20.
2. Wheat, 40 bushels ; barley, 8. 6 ft.
00 bushels. 9. $50.40.
3. $100. 1<>- tIs-
4. 30 rods. H- $45.
5. 09 cents. 12. $7488.
0. A, $00 ; B, $75 ; 0, $90. 13. $310.10.
Exercise LXXXVI.
1. 10 days.
2. $531.
W. 8 days.
4. ^8.89.
5. 8 mil OS, 80 rods.
0. 6.
7. $79.
8.
9. Each equals— 64 sq.rods, 9 sq.
yds., 5sq. ft.
10. 9 hours.
11. 300.
12. ofj"^^.
13. $329.
Exercise LXXXVIL
1. 6 days. 7. 750.
2. 25 cents per hour. 8. 11.30 o'clock p.m. (every 10 J
3. A,$*)27;B,$2020andC,$3443 hrs.^
4. 3J per cent. gain. 9. 31.
5. 693bbls.,19gals.,41bs.,9^ 10. 9.
ozs. 11. $140.
6. Rye, 70c. per bush.; barley, 12. $U.40.
56c. per bush. 13. A, $81 ; B, $90 ; 0, $108.
\i'
f ».
64 ANHWKHS.
Exercise LXXXVIII.
1. lOduys. 4. $1.76.
2. 7. 5. 8:{S.4().
X A, 8:V2.L>() ; B, Slfi.lO ; C, (>, .-JOO foet.
S4«.:j(>.
(•();its, .S;5<"<l.«<' \
'(. { Wlu'it, ^'.lilO.iMJ. .^ICtd.OO.
|Biirley,.Sl.".>;;.:{O.J
8. l.S,<,r;ill,,iis, 2(iuarts. 12. \.
1). ,^17.50. i:}. A, !?350: B, $420 ; 0,
1(1. 24l)nshels, 27 lbs. $5()().
II. i:;si4(in
Exercise LXXXIX.
J. 3 yi-ar.s.
2. 8701.10 not.
.'{. \V7 hushcl.s, 24 U.S.
4. 41 cu't., MS ll)s.
5. 14 acn'S, 15 i-dd.s, S yai-ds,
2 ft., .'{('» inclii'H.
<). A, $27 ; 15, ^.'ifi; C. si.->.
7. .S7.00.
S. .S1.">1(>.0<).
'.». i;;i,:!s4.()o',>,^';T;'j.
10. »i.
11. ;> (flits.
12. 8 per cunt.
l.*{. Siini i)f ijMdtionts, 4.S7.
Exercise XC.
i
r i,
•■ r
t
t ■
*i'!
1. 28!).
2. (a) ('.,4 1-^.108; (/>) KSa
3. 80 jxMiiids.
4. |5270.0().
5. $945.00.
6. 55 cents.
7. 8 per cent.
8. .^.S2().()0.
1). 3J) auiinals,
10. $7r,(;().
11. Fir.st, .^21.<;0; .second, $18;
tliinl, S15; fourth, $12.50.
12. $17.00 ;tn<l $8.20.
l.'>. 84 inches.
Exercise XCI.
1. £95, 10 sh., 8d.
2. 3(1 cents.
3. $290.00.
4. 8 dozen and (> e<4gs.
5. 100 acres.
(). 18.
7. A, $4.-.0.00 ; B, $400.00 ;
0, $:}.j0.oo.
8. 10 per cent.
9. 45 K(juare yards, 1 .square
foot, 72 s(piare inches.
10. 90 times.
11. 3.55 o'clock, p.m. (or it lacks 5 minutes of G o'clock, p.m.)
answkrs.
65
12.
. 7;-,(;() 2 X 2 X 2 X H X ;5 X -^ X 5 x 7.
) ss-!() 2 X 2 X :{ X .") X f) X 7 X 7.
( 44 100 2 X 2 X :•. X :i X 5 X 5 X 7 X 7.
N,.w tlH. sn.nllr.t selocti.m ..f factors which contains the
factors of each j^'iveii iiiim!>cr is : t .^ tut
[■{ (2x2x2x3x:jxaxr)x7)x7 'r x^'.l=^ 2(;4.<;('0 L.(..M.
\,ul the ,im,hsl seh;ctiou of factors .•onimou bo thesu
numl.ersis:2x2x3x3x5>c7-lli«iOll.C.K
13. (a) 21 years ; (6) $745.
Exercise XCII-
L. ^ of a ton.
2. iOOroda.
:;. 1440.
4. U)8'.).
5. {a) <;<)48: (/>) 112:;2().
(■». .■)() mih>s.
7. 6 miles, 240 roils.
«. ^4^y^a tn 4032 times.
9. $r>7*.>.43.
10. 5() gallons.
11. I5C..25.
12. -tOj^.,--" — 1200 limes.
13. Hr.r>.
Exercise XCIII.
1 . 2<i40 dozen.
:i. .fUi,000.00
4. '^\ cents.
5. iO liarvels.
id, $18; ■
1, $12.50. 1
6. 15 tores.
7. $748.80.
8. .lames, $145 ; Andrew, $132;
Robert, $119.
9. $20.t>O.
10. $42.00. {gi^F" Ceiling three
times oidinary height.)
11. $2(U.00.
12. $17.00.
13. $15.00.
1. iSP.=iC.P.
i^
l()c.zr:rJ. . ,f $9.00.
2. 7101 sum.
3. 00 days.
4. $54.40.
5. £B1G, Ish
6. 240 rods.
:::;2998.11
ExerciFo XCIV.
of SO yds. 7. 11, $550; L, $440.
8. $1950.
9. $27.00.
10. $20.59.
11. $182.
12. 11,948,1(;0.
13. (a) 8289 ; (6) 25%.
G6
ANSWKRS.
■- <-<
BxercisH XCV.
1. ,^405. 00.
2. 84.
d>. (a) lvc.]i!('t> il\ein to fraofcicns li;i\ ing it, junuiion .ItMioiuiiijitoi-.
4 4,7.'5."),(«OvS.
5. 47 times.
(3. 5 per C'jiit.
7. 8 yoiirs.
8. $1<).(>0.
IK 48 weeks, 3 days.
I'K 87 i ocnta.
11. r,(C424,2(H.
12. 11 8. (K).
1.1. ((/;.f 20.75; (?/)«|?9,441 + - • •
Exercise XOYl.
1. |1(> » ; KM) .Inz.Mis. 8. 4.
»> 1 r, (1 -• r> 7 50
^- ffs- •'• .'v .;' ... <i}f«
3. 2 miles, 2<i;; .o.U, 1 yd., 2ft., 10 14.
r. inches. 2I!I8>;»
4. 824.00. 11. '—
5. 12.'', [HV cent. 2(51:5
(i. 11? pei' ceiiO. 12. 11a Ihs.
;. $iO;io. 13. ((I) 25 percent. (6) 12ll>s.
.i
I , ■
H r
Exercise XCVII.
1. 2 mile.s, 1)0 rods, 2 yni-ds, feet, iiichos.
2. S7I20 times.
3. ^.'1:^57.
4. A, $1014 ; B, 2535 ; C, $:\bV.).
;>. S(>.().).
G. (.() 12. u res, 80 reds; (M $3250.00.
7. ii?c>r)24.oo.
8. *;io.4().
'J. 7 |)er cent.
10. 12S,755.
11. 4i! miles .m hour.
12. $i3.05.
13. A, ;t5(;.12 ; B, :§5.10 ; C, .«!2.04.
W
. .s
i4«i^i
ANSWERS.
«7
iioiiiinator
Exercise XvOVIII.
'.i.
4.
5.
(5.
t •
8.
.John So(J7 ; Robert $42.
!?4(),n2.
31300.
5.
y. 411 mik-s. 2()G rds, .3 yds, 2 ft,
10. .s«;<>.
L.(J.M. ==840
11. ^56.
12. 44li>.
13. %5 147.00.
15
Exorcise XCIX.
1.
6.
8.
3 days.
2.
JB85.
9.
2 .'UTt'S.
:}.
$8.
10.
S., ^I2i); T., 3yeara
4.
L.C.M., lOi;
G.n.M.,
I
11.
r- 1 1 ^ J
1 ., ilays.
;>.
12 s(|. rods.
1"
( l'a|Hrin- ^:t;^7<i \
<».
2i) |»(>i' cunt.
1 I'.nnti.iL', SL>2.«3| "
A, .i;?l08i 15, $\U ; C, !5!28H. l.). .s:>!.01.
Exercise C
1. (a) 13(11. (\ F.); (/.)7I7<;(I>. ('. M.)
2. .* 17.00.
3. I'nxhicf, (i0,r»I0,O8(j ; sixly-iiinc millions, six iiundnid and ton
tliousiiml and ciulily six.
4. 37)0 tens ; 47") twenties.
E
(i2r).
10 gallons.
$«23..37A.
(") .s2r);(;oo.oo ; (/>) .>^2i.40.
13,r,80,
('0 I of A of 1 ; (/>) A ootnponnd fraction ;
TT F
(c,
.\
B
G
C
D
Finish out, dirii/i),>f
tlu' whole Fii;. K
< JI)|"\ So MS f«)SJlo\V
it as coiii[»os»m1 of
-j t'iijhfhs, then, A r
D li is thirv ont of
th(> vljlilli, eii^hths,
•»!■ i of whole Fii'
K(JDF.
12. A, PIO- I?, ii?(J0; (!, $20.
13. $120.00.
I
Id
68
ANSWFJt?^.
i i
Exercise CI-
H' I'r
*!if*M't
si
IT'
1. ^v;47.50.
2. 27 v.u\vs : ."^nn each.
4. '.>-44+ ....
i-<. si so. 00.
0. Sl'7(J.(M).
1(». 25 rents.
I 1. \H) rruts.
5. .•\,i?4.0(), r.,8.'{.00, C, r«2.()(). 12. A 8«:o.()(», I5.S72.00.
(j. r» [KT ct'iit. 1|{. K)(>]R'r cc'it.
7. ('0 I><>Ml<-\v()rk. (6) A, 8 (lays,
B, 15 days.
Exercise CIL
1. 24 cents.
2. G.O.M. - 329; L.C.M. = 2i)!;i0.
3. 20 (•..u-s.
4. ;»;;.
5. :;i a.T.'s. 1 30 r.Mls. 27 yU., I ft.. 72 in.
0. 83. Tift
7. Mi'll''i>'i'iifi(>n: Kx. 42 •■ 73 73 takci '/ / I !,in'f< ns tni (itJ(Ji>nil
.'{0<i<i. Miili iplicil ian is a slmrf /<•///(. of Ad'liliuu.
.S. .^22. 40.
9. 4:>,"j laiiiutes past 12 o'eloi-k.
10. Kl.
11. 7 (l<>/.on-r3 + 2-30 mai-Mcs.
12. 30 (lavs.
13. S42r..()0.
Exercise CIII.
3. (>2rt 1 CM I IS.
4. £121)1, lOsh.
1. !?3,S0.
2. 9.', j)or cenb.
5. 103:>() .2 X 3^x5^x23.
1 1 ;:i )22 - 2 X 3' X 7 X 1 3 X 2."..
I)i'.t;.3:;.-3^x7x 13x23.
.-. L.('.>r -2x3-x5' x23x3x7x 13 x3 = 8,47<i.r..'>0:aii.l(; O.M.
((.!• II.C.F.) -3' X 23 -207.
(1.(1) .\, .^70.20; r». SliruO; i:' \, SS(;7.S0: IJ, .^3.7. 50;
(.">) 'riu> first iu'hU- is tho huttor oik; fm ly ><2.40.
7. 2 cwt.. 24 11 )s.
8. .Hi40 (Im;/.,-!,s.
9. 1 ,s(). I'imI, Hi S.J. yards, 8 sq. fci't, 54 sq. iiu;ho8.
JO. („) a ; and (/>) ,',-V.
11. 21 coiifs.
12! T"^ .*t.SO; r//) Id-^ U.S. f..r a dollar.
13. {>() 17 ; (A; 4!>.
ii.. -.J
ANSWKRS.
69
Exercise CIV.
1. 810 doz.
2. 6 tons, 1950 lbs.
3. (a) lutoL^ral. Prime, Odd, Al)straci. (h) Fru.-tional, Vulgar,
F'roper, Simplu (r('])rt\s<Miting 4 fract.iouai units whose prime unit i.s
one inch). DciiuMiiiiatc.
4. 7 hours, 15 minutes.
5. $56.51 ; Receipt :
Burnside, May 13th, l.S'.Hi.
Received from John A. liruce, the sum of fifty-six dolhirs and
tifty-one cents (^aOiVo) ''i ^"1' l>'i'ymtMit of account.
A. B. Burns & Co.
6. 24 sq. rods, 'J scp yanls, 2 sq. feet, 24 sq. inches.
7. i-l5, 15s. Sterling.
8- $90.
9. $30.25.
10. $198.76.
11. $1.50 an acre ; 128 acres.
12. 40 cents.
13. $4(1«)0.50.
Exercise CV.
1. A,$10.(K); B, $2.40; C, $2.U0.
2. 54 tons.
4. $2()''>.70.
5. $19. ('.5.
6. 240 trees.
7. 13.
8. 17323.
9. A, ;> mihis ; T5, 4 mihss ; C, 4i miles ; D, 5 miles.
10. («) riu! muhiplicand. (/>) Tliu multi[tlier. («•) Wiicn hoih
, ; * f // |3x4-4 + 4 + 4-=12 I . -y^A^A^'l
nuuilicr.s are aoi'C/uct. {(l) ' i ^ •» . •( i •< i** j."-_^ 12 "' •'^^*~*'^«^'
{>') r, X 7.
11. r.Kso
12. 240 barrels IM.U's. ; 420 l)arrels N.S's.
13. •0138. '
1^
^1
inmimg^mmmm
70
> 1
1
1
2
3
4
.1
i
1
5
6.
< •
j
i
8.
1
9.
" l»
»i
JO.
ANSWERS.
Exercise CVI.
Q..'SH084, Rom. 78; I>. 'A7,o:>0,342'M2.
Q 2r;i, Rom ;;8().
A, $L>L'r,0; H, J?24.0(»; 0, .s'4(;.r,0.
A, a'JL'OO; B, sum; G, ,^5040.
105 lbs, :', ozs.
< )r;iiigo.s, ;{() cents ; lemons, 28 confs.
11. ♦'O (lozon,
H) I)ii,sliel8. 22 3'
7 chains, 7 feot. 13' $.49,
04 cents.
„■ !
r 1) I
.. It • I
^i
,^l
ANSWERS.
71
FirrH CLASS.
Exercise I.
1. 54 and 6.
8. 192 men.
2. ^y.)AO.
9. $1000.00.
3. 4.
10. 24 miles an hour.
4. 45 pairs.
11. 00 cents.
5. 17187 tons, 1000 lbs. 12. l.C.\r.,45; II.C.F., ^.
6. 93 cents a lb.
13. 84 times.
7. $45.
Exercise IL
1. 54 miles.
2. 88 cubic feet.
3. $104.00.
4. A, $70 ; B, $42 ;
C, $30.
5. 144 niilos.
6. 70 bushels at 90 cents ; 130 btishels at 85 cents.
7. (a) 7h days ; (h)
15 days ; (c) $17.25.
8. 12 lailes.
9. A, $40 ; B, $20
; C, $40 ; 1), $280.
10. 13 J days.
11. 45 bushels @(iO
cents ; 75 bushels (<2j 80 cents.
12. 32 jjer cent.
13. 1987.
Exercise III.
1. $373.06 net
9. $72.(K).
2. 45 bushels.
107110(44 L.C.M.
3. $17.00.
1A _. r,(».>()0 fiiniH
Xv. .. ■ ..^ U.'.ir.'.J l/illlt-'ti
4. $7.00.
1807 H.C.F.
5. 7 biodiiis.
11. $(;4.0(K
6. 42 ualliins.
1493:582 L.C.M.
7. 30 hours.
12. — ^ 1122 and
345'. »82 L.C.M.
13'. I FLC.F.
8. ^-
=182 times. ' (1122) '^—1258884.
1901 H.O.F.
13. 6 tons.
15
r '
» 9 '»*
72 AN'SWKRS.
Exercit^e IV.
1. 21 lbs. chicory ; 7 lbs. cotl'ee.
2. $4052.00.
3. $988.
4. £300.
5. 90 X 90 = 8100 product.
6. 2-^"^ X 34 X 7 X 11- X 13- X 17 x 19 x 23.
7. {«) $2.88 ; (6) O0pev.:oiit.
8. 2'-^ x 3"^ X 5 X 72 X 11 X 13 X 17 X 19.
9. 10«) feet, 4 inches.
10. Green, IG lbs ; Black, 44 Iba.
11. 9 lbs.
12. 6 per cent.
13. 2 feet, 9 inchea.
Exercise V.
V
i 1 '
'i
1. $75.00.
2. $1875.00.
3. $1639.30.
4. $1752.00.
5. 28 slieep.
6. $100.00.
7. $1120.00.
8. (a) 515 ; (/>) 5 quarts.
9. (a) 225 ; (/-) 3:}0.
10. (a) 12 apples ; (6) 8 piars,
11. S409.40. •
12. i542.00.
13. (51-44 lbs.
Exercise VI.
1. 1st time, 9t^y minutes past IX o'clock ; 2nd time, 22j? minutes
past IX o'clock.
2. With the Romans, the symbols used maintaijied their relative
values, no matter in what order they wt're written ; thus, IX stood
for 11, and was read di'ven, just as XI ; and XL stood for 60, and
w:i,s read si.yty, just as LX, etc. Thoir system of notation was by
mdts, fines, fens', fifties, hniu I rcda, etc., insttvid of mUts, tens, Inm-
drccU, etc., as in our system, tl»e symbols l)einfj written in that
order, and each one repeated in a(H'or<lance with tlieir system of
notation — I and X might be repeated, /'(xu- times, but V or D would
not be required to be repeated as two V's == X, and two D's = M,
ANSWKh'S.
7:]
t'tc, etc. In writing? Ilicui down, place lik- syiuhoj.s uikUt ouch
(.ther, i.r., units under units, fives under fives, ti'ii.s under tens, etc.
(a) Dec LX
CO xxxx
(6) MM
L Willi
DCCC
MDCC XXV
XX Vim
(c)
XXXX ri
cccxxxxniidifr.
ni.
LXXXXV
(<f)
XX V^ .\i i )CCC XX V(LXXIll quot.
M.xl'
(HJCC
CUi'C
CCCC
CC
XX
XX
XX
XX
X
.M ,M M DCCOCLXXXX yn-nd.
M CCL
D
C(.
LXXV
CCC XXV
CCL
LXXV
XXV
I? minutes
;i. .S7000.00.
i. '-> iiiilus, (10 rods.
5. .^r>(i7().()0.
<i. s4!Hi. 10.
7. s;5;;.75.
<^. 1<> liuurs.
XXV
XXV
XXV
1.
i<'2{).
o
$40.
3.
$45.
4.
$00.
^
.'».
$7.
• ».
S d(i/,(Ml.
7.
0.'} gallons,
0. s:.(HJ.20.
10. Losu .SL50.
11. lVO sheep.
12. 117.
13. 23-{.l i)er cent.
Bxercia? VII.
8. .^77.
9. 12 per cent.
10 :n.
11. A, $4S : 15, !i?72.
12. SI if).
13. 54 cents.
.■'ir
ANSWERS.
Exercise VIII.
a'{
1 I t
.'i. '^1 '^•^
4.
5.
(i.
Kirruls.
lUJirts.
A, 5?L'0().00 ; B, $125,00. 11. S2.00.
15(1 { b.'irruls.
8. SI. 00.
9. Priii<ii)a], ^.'i.W.OO, time 5 yrs.
10. (a) .ii5l.20 ; ib) $2.00.
;w 1
Kii'i'els, 18.'
lUo
Lrauons.
12. rriiicipul, $72."), timo, 7 yrs.
13. A, $27.00 : B, $30.00 ; C,
$108.
$82;"). 00.
$45.00.
Exercise IX.
2. $500.00; $;'>00.00
3.
4.
5.
6.
7.
$24 : $40.
$9.75.
1444.
4141.
30 cunts.
8. tiO per cent.
9. t)0.
10. i.
11. $2.00.
12. {a) 15. (h) The 7tli.
13. 49 yards, 2 ft. , 5 inches.
Exercise X.
1. $180.00.
2. $1.80 an lionr.
3. $501.00.
4. 21.
o.
(1.
L.C.INI. 250208595; Ouotients, 0043, .3285, 4095 ; Sum, 14023.
r>, $90.30, or 7i"i cents alb.
10. A, $7400.00; 1?, $8400.00.
A, $250.50, (.1- 8' cents a 11.. ; li, $90.30,
7. 24 .lays
S
$514.50. (Sue I'.S. arith., 11. 15 iiiilus.
p. 8.S).
9. .V, $500.00 ; B, $370.00.
12. 20 .lays.
13. 6455743577.
I .
^i
Exercise XI.
1. L.C.M. -289, 092, 179, !>00, (>. $18.00.
050, 2(M>, 943, 335, 120. 7. $448.(K).
(Ti'st .|uu.sti(<ii.)
2. L.C.IM. 783,029,520.
8. $420.00.
9. 4 pur ctMit.
4.
5.
$892.08.
10.
() years.
(u) 8641 ; (//) 2801 ; (c) 9S(C9; 11. $73.00.
(d)707; (e)004I; (/)2841; 12. l;; years.
(c/) 8056.
(a) 500 ; (/>) 287 ; (.;) 4547
(d) 4070.
13. A, $1690.00: B, $1820.00
C, $1950.00.
'^^v
A\S\VKKS.
75
Exercise XII.
1. $84.
2. (a) $777 ; (/>) $'•)•>().
3. $:3()4.
4. A, $81.75 ; B, )?24r>.25 ; C, !?()5i.OO.
5. 5.
(■). t. The iiunil)(!r of e([n;il parts (fractional parts) of the prime
unit, 1 lb. II. The' uuiiil)i.U' of fractional T)arts (nnits) in fcho
fraction. III. 'i'liiit flu; j»riinu nnit, 1 D). is divided into Jirc etputl
parts ; the nann- of cacli i»art . the wei-^ht 'in this instance) of each
part or fractional unit. TV. 1. lb. V. 1 of a lb., 5 of a lb., i| of a
11.., i of a lb., (g of a ib.) VI. The tkkms of the fraction. ' VII.
Vt;s : l)ccause it is the tmasure of a qaantUy.
7. 5 "4 inches.
s. .i«;i8,;3()0.oo.
y. 15th.
10. ffV
1 1. 2() ; 27fch.
12. 18 lbs.
13. (a) (1) Write out in succession, the ivrULTii'LES of these nuni-
l>ers : —
24 :— 24, 48, 72, 0<;, 120, 144, 108, 102, 216, 240, 2(54, 288, :iV2,
336, 3<)0, 384, 408, 4:52, 450, 480, 5vU, 528, 552, 576, 600,
(524, ()48. {>72, 696, 720, 744, 7(v8, etc.
42 :--42, 84, 126, 168, 210, 252, 204, 336, 378, 420, 4()2, 504,
346, os.s, ♦;:{0, 672, 714, etc.
N'ow we see, by ins|)oction, the cnmvKni midfipJes of th(jsc nnni-
heis, and of these iiiidUpli-s 1(58 is the least ; therefore it is the L.C.M.
2. Write out all the prime factora of these numbers : —
24 2x2x2x3.
42=2 X 3 X 7.
Now Hie li. C. M consists of the smallest (htist) selection of
f'icfors that, contains the factors of each given nuni])er; therefore the
L. C. M. is 2 X 2 X 2 X 3 X 7 - i«>8.
(3). 2) 24, 42
3) 12, 21
4, 7 L. C. M. = 2 X 3 X 4 X 7 == 168.
76
ANSWERS.
I
♦ I
(h) (1) AH the inoiiauros of
(Facff)rs). (Co-fiictors).
96==1, 2, ::, 4, 0, 8. 12, UI, 24. 32, 48, 0«.
240 -1,2A4,5,(;,8,1(), 12,15. l(5.20,24,;iO,4(>,4H,(iO,S!),12(>,24n.
Xm\v the roiinii 1 1 II iin'iisnii s ;i\\\: 1 ,'J,.'{,4,r»,8, 12,l!),24.4S, hiuI 4'**\fl'i'
;//■/ 'f /-t'.s^ of these, niiita ills. ill t lir < itlui iiic.'i.sures; ht'iico it i.s thoG.O.M
(2) Writo out ('// fu'niii- f((ctoi'n of thcau uunibers:
96 =2 X 2 X 2 X 2 X 2 X 3.
240 -^2 X 2 X 2 X 2 X 3 X 5.
Now (he i,'ro;ito3t .soU^ctioii of nic'irtiiros (fuctors) cuiiiiiiun to tliu.st-
miMihcrs is : 2 x 2 x 2 x 2 x 3:^48, the (i.C.M.
(3) 0())24()(2
102
48/.m;(2
90
-.48 is the <i.C.lVI.
" V 'I
Exercise XIII.
1. 960 men. 6. .*!ir>000.
2. 32 per cent. 6. {a) 20 lioiirs. (h) At starting
3. 5 (Iwls., IS|; ^aviins. point, (r) A, 4 ; P., 7 : C, 12
4. 33 (lays, IS Inmrs. times r(nni(i the island.
7. Rt'dnt'o to ilfoinials of same oi-dcr, tli.ii divide as in !onf
division, striking "ut a tiL,nne in divisor vxvvy division, instead
of adding to the dixidisnd hy bringing down additional li-nires :
378-7878 . . . . )3i()(>o-(;<;i;{;(;i; . . . .(83-(; Ans.
3030;; o:;o;:o .
1 3(531 i3«):!ti . .
113(i3{;:;(i3 ....
22727272 ....
2«>7'>r'>7s>
8. 271828 ... n. m p,>r .vnt
'», 60 yds., and $1.r>0 p.-r yd.. 12. 80^.
10 2100 ft. by KWO ft. i;;. {„) r> it.. " in.; (6) F., $1200 J
Exercise XIV.
1
1 ^:^^i^)^\\). 7. ^sr,.:25 gam.
r „ !"J. L'H rods.
of all tiz. !-. -
,, oOOl.iraH. >:'>■ nWO Hctuare yards.
Exercise XV-
1. o'clock i».iu.
2. 5i\ ntiniitos to 7 <)'cli)ck p.m.
;5. o'clock p.m.
(5. 2'.)i':^, seconds after '•> o'clock.
7- r)<>,":!;:i seconds after 1 o'clock.
S. 5lii:ii: sec.mds after 2 o'clock.
0. First. tin.c,:;2,^ n.inu.e.: after 8 o'clock; second time. o4 , ,
luiiuites after 8 o'clock.
10. 5 minntes too fast. 12. 'J nules.
11. minutes too slow. L'^- 24 minutes.
Exercise XVI-
1 . S Urn.
2. 20 per ''fnt.
:\. .^> miles, 110 rods
4. :\[\}. i)or cent.
5. 20 jtt;r cent
8. 12 per cent.
•». 40 cents.
U). 12 rods.
11. (a) 1842 lbs., 4i",y ozs. (h) 9 sq.
ft., 1)0 sq. in.
) ]i\t Jtt r cent. ' , rt,(, Mi
^: (.)lVstiu.eistoC'stimeas 12. rjrapes.8nO<U) .pples,S.>)...<
^ 14-<» (M^^1120, IVs-ain. c-lu'rnes,.^...).00-
,,, , ^ . i:; .^40. (»o.
7. lll.\ percent. '•'•
Exercise XVII-
1. .^11,020.
2. §180.
:i. 18 acres. 120 s(i. rods.
4. 'M\ children purposed iS,Anv^
and 15 went.
.•"). 10 11)S., 2 O'AH.
0. 8 pur cent.
7. ^i^r,.
8. 25 per cent. gain,
t). 10 per cent.
10. 24000 ])ricks ; and 0|^%.
11. Ix'V-s.
12. 7o:ur!)nd 911)7.
13. ^4800.
rd
ANSWERS.
Exorcise XVIII.
r • ■n
f*'
1. :;♦;".»('» galli.na (or H7i l>l>ls.)
2. 19.
3. ir);',,02i»,r)2(), L-c.M.
4. 8 avcrug(i 111011.
5. 'riui circuitous, by $2.
<>. 7^ (gallons.
7. JXiij cunts a busli., 35 J ^ Ibx, 13. G balls
pi!r bush.
8. Ilalt'-aiid-lialf; or 50 por cont.
br;indy.
9. $i;210.
10. .^lO'.KS.oO.
11. A, i^SO ; B, 8240.
12. 14 inches.
Exercise XIX.
1. 12 per confc.
2 i?2(i9.75.
3. 6^ per cent.
4. 3 hoiir.s, 8 miu., 55. ,'',.^5^ .soc.
5. (\-isli, by .s,-)(>.
<;. S792(), i'.. of C. Stock.
8. 38.") conla.
9. $10.
JO. Sii!|()(M) M.; $m^ W.; 81S0 v>.
11. 1() per ciMit. discount.
12. 8 (lorccnl. cii fonncr.md 10
[H-v coiit. oil lattor.
7. A, *750 ; r., .«200 ; (.', .i?315 ; 13. ((f) 70 conts ; (b) 450.
D, $400 ; E, f 210.
Exercise XX.
• ■• .1
1. $7776.
2. mk.
3. $.32,000.
4. $m.
8. 13 yoar.s.
9. 3:1.
10. 2()i inin.,28:^min.
11. *5(>,()0.
5. lOOlbs. (7?)45cts.;100lbs. (?$ 12. T..tal Com. $715.00; No. bbls.
60 cts. ; 300 Iba. @ 90c. rcmittod, 4147.
6. £(•», r>.sli, 5d. 13. 21(;0 balls.
7. 30 casks.
Exercise XXI.
1. {<() Town clock 15 minutes slow ; and (/>) 10 milij3.
2. 75 bushels.
3. 40 yards.
4. 3 feet deep.
5. 13 minutes, 52.^ seconds.
6. 25,000.
ANSWKRS.
n
7. Or)(;r>LM7:'.ni:U)i:M7SL»0()8f>. (5, tho fonrHi remainder, is ^ of IR
Ihosecoii.l n-m.-iiiiilcr ; tlun-»)f()ro .\ of <), Hie third nunibor in (juo-
tiunt,, is 2 which is tlio uoxb Hl^iuc to sot down in thtMiuotient, etc.)
8. A, .ii?l(»2.-J<), B, §r)S.4!), 0,iBr)!.75, and D, .S'.)l.25.
\). SCO!) and sy^o, rospoctivoly.
10. A, «1 1.7() ; P., a^2.00.
11. x = ;,i»,f y.
12. 1.
13. (a) ^4 and ii?:V20 n^sjMHitively. (^) Man's rate 7^ iniU;s an ho\ii'.
Stream's rate 2.^ niilofl an hour.
Exercise XXII.
8. 1^140.
9. (a) :;1278 halls ; (/>) /^^f of
1. $25.
2. 25 yards.
3. 2m yards. '''" ''^'^
4. KJiiidics. 10. 2H50.
5. \r. i»(M- I'tMit. (or 81 a sham). 11.2 milos an honr.
0. 270.4S cnltic inciuvs. 12. <> h.ills.
7. .',. 13. A's, by i?.S40.00.
Exercise XXIII.
X, 1140. 7. 203 cubic yards, 19 cubic feot.
2. (iOlf) ^nillons, 2 quarts, 1 pint. 8. $4.34;^.
3. 441 boxes. 1). I.
4 8:;t;(;0 whoh^ profit and 82ir)0 10. 4 cwt., 10 lbs., 2^ ozs.
B'sshan-. 11. 8<5".U.
5. (<i) m cents ; (b) 77J. cents. 12. .1?20(;o5.()0.
6. 41 gallons. 13. 3 cubic feet, 514 cubic inches.
Exercise XXIV.
6. (") .j'j. (Ni.B. — The .tftm of tho numerator and donotninator
of the fraction, representing^ the simple interest forms the denomina-
tor of the fractions representing the true discount) (/>) ^405.75
simple interest.
7. (a) $20 : (h) i^l ; («) .^1. 10. $04.82„V
8. SSOS. 11. 3^ years.
9. Oyrs., 73 day.s, and por 12. 5 percent.
cent. 13. ^420.
mmam
80
AN.SVVKKS.
1
W
f
' «
'4
t ~
lit
■' II ' I I
" It
id
Exerci«« XXV.
1. 2210.
2. 2 hours, ;iO niiMut<!S.
'A. r» Ilt-t. at cents. <> liis. at H tviifs, .'{ lbs. at IG cunts, aud 2 llw.
at 10 cunts (otliui- sets of ans\v.'r.> may bo got).
4. ><.S() hi-Ht, ami Si 20 secoiul.
5. ^4(11.20.
0. A. >;ii;o ; }\ 8270 ; C, !$240.
7. 5(( ut^uts a lb.
8. 6i<).
0. 1^5 mill's an liour.
10. 8;")'. ♦2. 7-' ;*.).■}.
II. 120 lbs.
12,. 10 ai\.l 25.
i:i 88 yai'ds.
Exercise XXVI.
1. -SKiOO. 8. .,-. of cost f^.?^ R. P.).
2. 12iiur('('nt. 0. 2;"") pur cunt, (or .[ f)f coat).
.*}. s:5;;oan.l si;i20. m. .«i44.
4. ^270:; au<l 88100. II. 1,1 [K-r . Tilt.
5. $2()'.«>.00(or8l.l<^5"„l'^'i'^*'>'j •-• '-'i'l |"'i<"iit.
0. 85520.
7. t\-
1. 180 f out.
2. 81125.
13. (a) 8 180. (K; 3 ; (h) 24 days.
Exercise XXVII.
4. :n\:uh.
5. i pur cut.: 80 cents on C'lOO.
0. 8180.
7. IM yards.
8. (a) '0()17niOO; (/>) •1-12857; (- The n>if>nr of th,- ihnonii-
/)Yf^)/• of the \iili;ar frauti<tii to which 11 correspi'iids. If the denomi-
nator is maije ii]/ of //()()///./• /((r/'(C.s t han 2« and 5's, the duciiual
will bi' tinite : if viilher 2 or 5 with other factors, it will bun ikiixud
rujH'tend ; if neither 2 nor 5, it will bu a |tiii(' repelcnd. {d) Finite
(lucimals : ami funy anil uiixid rtpfl 'y.
0. 828 : 150. 00.
10. ii;i7.10.
11. 437 reams, 10 quires.
12. 4 per cunt.
lU. {a) 24.75 ; (/.) 'M\ ; (r) 4213 ; ,1) 2807 ; {c) 5(K)4 ; (f) 7010.
ANSWERS.
Exercise XXVIII.
1. L, 24 ft. ; B, 18 ft. ; 11. !> ft.
2. (a) $h:'.7.00 ; (h) 22|;:: per ocnt. ; (c) 211 -^^ P^'^ Cf^»i*-
3. ^202.00.
4. 7 feet.
5. H^.
(). 8r)2'.>:'..r)0.
7. 2<»tl sucks ; 20 cents.
H. ,i:!'.)4<i.<s(».
\). 1".> ciil,. feet, 4:32 cul). iiiclics.
1 1. !ifL';'>U(> ((/' 5 pel- .(Mit .*<;}r)0(> 6< 7 per cont.
12. (d) .'{♦i.l-t uiin. [);i-*t7 ; (/') 42 uiiii. |»:i,st 7.
i:;. A, 00 ; B, .^75 ; C, 8r»<) ; I >, s-O ; K, ^'20.
81
I
1. 5 per cent.
2. $11<K).
n. 8201 )().
4. 822.
5. «Uino(l 8105.
«>. Gained $76.
7. 6400 bushala.
Exercise XXIX.
8. 8i;oo.
1). .s«.> 40'.
10 8f'00.
11. '.100 Larrols.
12. 5 per cent.
13. 6 per cent.
Exerc;i.se XXX.
1. (n) £5, 8sh., 9(1 ; (6) §1.00. 9. 8159.25.
2. H()48 sfpiare y.vrds. 10. Ifj ni.irea.
3. 8l.(«>. 1' $901M).00.
4. 1 s([u:ire font, ^81 scj. iiiclips. 12. S<;o2.0H.
5. 8 per cent, loss. l."». (<(; 39 scp rods, 11 sfj. yds.,
(). 13 S(]. ro.la, 20 s(|. \,iids, liiS h<|. iiiclh'H ; (h) Piodiict.
2 s«|. feet, 3r>N(|. iiiihcs. 47'-^.0.S7,O2l,724„r>83,7r)»5; ,pi..-
7. 5 H(|. n.ds, 5 s.|. \ds ,r. s.|. ft. Meat, 53,593,r)0O,l)U0.
8. 2s(|. ntds> P.> st|. yds., 2 sq.
ft., IIG 8U. inei"*»"
^m?^mmsm
ii I
' i tfi,
*VI*
82
ANSWKftS.
Exercise XXXI
1. 25 lbs. for ;i d.^ll.-ir. 7.. <iO'S()7 feet.
2. (1) 45 tons ; fhiSi bushels.
(Se.- I'.S. Aritti. p. 88).
:i. i71 fwt., 92 lbs., 7 OZ8.
4. r>[ bfirrels.
f). -'50 aoivjR.
6. 6840^8-855.
8. 2l0;t barrela.
9. $120.
10. $18,5)00.
11. $80.
12. 14 gallons.
13. {a) 15 Ciiiita ; (6) 792 yards.
Bxerojfcje XXXII.
7. 05.
8. 72 j^'allous.
1. .«;.3s.r»(j.
2. Hi.
3 18. ». 9^ years.
4 :i4 Ibi., 11 OZ3., 14 dwts., 10. 8120.
9gT3. 11. $-bH()0.
5. lH201l>s. 12. 5Gc ; .i. per cent.
<;. *2(i.25. i.s. y'iiWB.
.Aiter the tirst division wi' have 15 a.s rHinaiudt.'r, which is one-fourth
f»f 12, th( immcM'ator of till' fi'acti'Ui ; now, complete the repetend
from this [utiiit by ie<lucniL( nath remainder to tenths oi the next
lower order ami di\idini4 by 4, «.«/. ; —
||=z= '0, and 2 H.s ntauimh'r; now 2 is ^ of 12.
^ of V» (tirst tigurn in decimal), etc.
= 9 -r 4 r^ tl and 1 over, -10 x 1-1-2 = 12.
12 -r 4 -= It and o ,.ver,--10xO-H3^ 3.
3 -:- I O and ;• ar, -10 x3-H0 ~ 30.
30 ^ 4 ^ r and 2 over, 10 x 2 -1-7 - 27.
27 -^ ^ « and :; ov.r, -10 X 3 + —36.
36 -^ 4 -»an<l ovtu', etc.
Dec.-- •«!.';;! >7<;<»'j, etc
^ •»L':;o7o.
lii
(N.JJ. — The operation .should be performed tiu'idally.)
ANSWEUS.
83
Exercise XXXIII.
1. $22.00. 8. 300:J4 square root.
2. $1040. 9. 6^-J ; Rem. = Divi.lond
3. 42^' per cejit. (Divisor x (,»ii(>t,iciit.)
4. Focal date, April 0, 1887 ; 10. 15 rods.
Bal. due, Jan. iOth, 1887. 11. $1742.25.
5. 4000 barrels. 12. 280 do/ens.
6. 20 per cent. 13. $190. 37 per acre.
7. £40, lOs., 6d.
Exercise XXXIV.
1. $1200.
2. B, $1200; C. $1700.
.*{. $14400.
4. $98.55.
5. 25 per cent, discount.
6. $280.
7. 28 lbs., 1 oz., 10 dwta.
8. IB boys.
9. $48.44.
10. or. csvt., 15 lbs.
11. ti acres, 28 sq. rods, 15 sq. yds.,
1 sq. foot, 18 sq. inches.
12. 93|.
13. $6.00.
Exercise XXXV.
1.
29 i^ per cent.
8.
$350.
2.
June J7tli, 1893.
9.
49 lbs.
3.
$5915.
10.
1188.
4.
$81.25.
11.
225 uiiles.
5.
'l per cent.
12.
$820: ^i8l>()().
<).
53^ cents.
13.
$300 first ; $240 second
7.
3031bij., 12oza.
. Exercise XXXVI.
1. $108.04.
2. $L'<M)oo ; $225,000.
3. $9!)().
7. $101 2. no.
8. 46 and 40.
9. $79.50.
4. Bal. due Xov. 25(li, 1892. 10. 90 cnnts.
(Focal (1m te, l)e<;. 0, 1892.) 1 L. 72.
5. $1<;(;0. 12. !^80.96.
0. $10,000. 13. $.39;iO.
b4
AN.^WKIlS.
Exercise XXXVIL
1. $4l>(>.
2. - <»/,.s., 2 (IvvL.. 14 gr.s,
8. .slO.l.lU).
4. 1^5 fciiiui.s: ;') li'iui-s, 'AO min.
5. i?52.0L'!.
«;. i4(»() miles.
7. •( >2( K H'4( ) 1 <)()( )8{>r)4«;08.
8. itpti.
'.> .^108.
10. -i M(;tros.
11. If);; \I.. r, <lin.; $115.20.
12. 0M;:.«);i«ir)i>52.
13. 8'>oo.
Exercise XXXVIII.
j_ f?1.0(). '.). (.'(>mj>()iui<l Rules ; 1 cubic
2. ■0(HMt;(>44'.tLMS7r). inetri! (voliinui or capacity) •=
8. ^\H'A). 1 trvamiMo (^wtMLflit), or c/ipa-
4. A, $80 ; H, i<lL'0 ; C, §160. city : woi^ht: ;! cu. cm.ilg.
5. 1 Kl., 4 HI., 5 Dl., 2 L., 10. iC;
145 Mg., 2 Kg. 11. *47-754 lutuiest ; $297-754
6. $2475. atiu.ant.
7. 6Du'.,7G.,yag.,2cg.,lmg. li^. 23.
3. 08 Kg. 13. $1560.
■i
20.
1 cubic
[)acity) =
or capa-
m. : Ig.
$297-754
Rm