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70. If 13908 men consume 732 bbls. of flour in 2 months, in how long time will 425 men consume 175 bbls.?

71. If the interest of $30 for 12 months is $2.10, how much is the interest of $1560 for 6 months?

72. If the interest of $750 for 8 months is $28, how much is the interest of $16425 for 6 months?

73. A man being asked how much money he had, replied that 3, 4, and of it made $980: what amount did he have?

Analysis. It is plain that ++-4. (Art. 202.) The question then resolves itself into this: $980 are of what sum? Now if $980 are of a certain sum, is, of $980; and $980

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$20, and 24 is $20×24=$480. Ans.

PROOF. of $480=$320; 3 of $480=$360; and of $480 =$300. Now $320+$360+$300=$980, according to the conditions of the question.

469. This and similar examples are placed under the rule of Position. The shortest and easiest method of solving them is by Analysis.

74. A sailor having spent of his money for his outfit, deposited of it in a savings bank, and had $50 left: how much had he at first?

75. A man laid out of his money for a house, for furniture, and had $1500 left; how much had he at first?

76. A man lost of his money in gambling, in betting, and spent in drinking; he had $259 left: how much had he at first? 77. What number is that and of which is 102 ?

78. What number is that, 1, 4, and of which is 450?

79. What number is that

itself, the sum will be 164?

and of which being added to

80. What number is that

of which exceeds of it by 18?

81. A post stands 40 feet above water, in the water, and ♣

in the ground what is the length of the post?

82. What will 376 yds. of muslin cost, at 2s. and 6d.

per yd.?

Analysis.-2s. 6d. £t. Now if 1 yd. costs £3, 376 yds. will

cost 376 times as much; and £X376=£47. Ans.

83. If 1 yard of silk costs 50 cents, what will 256 yards cost?

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Analysis.—50 cts. $. Now if 1 yd. costs $1, 256 yds. will cost 256 times as much; and $4×256=$128. Ans.

470. Examples like the preceding, in which the price of a single article is an aliquot part of a dollar, &c., are usually classed under the rule of Practice.

Practice is defined by a late English author to be "an abridged method of performing operations in the rule of proportion by means of aliquot parts; and it is chiefly employed in computing the prices of commodities."

OBS. After giving several tables of aliquot parts in money, weight, and measure, the same author proceeds to divide his subject into twelve subdivisions or cases, and gives a specific rule for each case, to be committed to memory by the pupil. It is believed, however, that so many specific rules are worse than useless. They have a tendency to prevent the exercise of thought and reason, while they tax the time and memory of the student with a multiplicity of particular directions for the solution of a class of examples, which his common sense, if permitted to be exercised, will solve more expeditiously by Analysis.

TABLE OF ALIQUOT PARTS OF $1, £1, AND 1s.

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Note. If the price itself is not an aliquot part of $1, or £1, &c., it may sometimes be divided into such parts as will be aliquot parts of $1, £1, &c., or which will be aliquot parts of each other. Thus, 871⁄2 cts. is not an aliquot 50+ 25+124 cts. Now 50 cts.=$1; 25 cts.=$; and 50 cts. $1, 25 cts.

part of $1, but 87 cts. 12 cts. $. Or thus: 25 cts.

of 50 cts., and 12 cts. of

84. What will 680 bu. of wheat cost, at 87 cts. per bushel? Analysis. It is plain, if the price were $1 per bu., the cost of 680 bu. would be $680. Hence,

Were the price 50 cts. the cost would be of $680, which is $340

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But since the price is 50+25+12 cents, the cost must be $595 Or, thus: $1X680=$680, the cost at $1 per bushel.

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85. What cost 478 yards of cashmere, at 50 cts. per yard? 86. What cost 1560 lbs. of tea, at 75 cts. per pound? 87. What cost 2400 gals. of molasses, at 37 cts. per gal. ? 88. What cost 1800 yds. of satinet, at 622 cts. per yard? 89. At 25 cts. per bushel, what cost 1470 bu. of oats? 90. At 33 cts. a pound, what cost 1326 lbs. of ginger? 91. At 64 cts. per roll, what cost 3216 rolls of tape? 92. At 8 cts. per pound, what cost 4200 lbs. of lard? 93. At 121 cts. per dozen, what cost 1920 doz. of eggs ? 94. At 16a cts. a pound, what cost 4524 lbs. of figs? 95. At 66 cts. per yard, what cost 1620 yds. of sarcenet? 96. What cost 840 bu. of rye, at $3 per bushel?

97. What cost 690 yds. of cloth, at 6s. 8d. per yard?

Analysis.-At £1 per yard the cost would be £690. But 6s. 8d. is £; therefore the cost must be of £690, which is £230. Ans.

98. What cost 360 gals. of wine, at 16s. per gallon?

Analysis.-16s. 10s.+5s.+1s. Now 10s. £; 5s.=£;

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If the price were £1 per gal., the cost of 360 gals. would be £360 At 10s., £1, it will be of £360, or £180

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99. What cost 1240 yds. of flannel, at 3s. 4d. per yard? 100. What cost 2128 lbs. of spice, at 2s. 6d. per pound? 101. What cost 5250 yds. of lace, at 6d. per yard?

102. What cost 56480 yds. of tape, at 12d. per yard?

471. Notwithstanding the law requires accounts to be kept in Federal Money, goods are frequently sold at prices stated in the denominations of the old state currencies.

When the price per yard, pound, &c., stated in those currencies, is an aliquot part of a dollar, the answer may be easily obtained in Federal Money.

TABLE OF ALIQUOT PARTS IN DIFFERENT STATE CURRENCIES.

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Note.-1. In N. Y. currency 8s. make $1; in N. E. currency 6s. make $1. From example 103 to 119 inclusive, the prices are given in N. Y. currency ; from example 120 to 133 inclusive, they are given in N. E. currency. For the mode of reducing the different State currencies to each other and to Federal Money, see Section XVII.

103. At 1s. 4d. per yard, what cost 726 yds. of cambric?

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Analysis. If the price were $1 per yard, the cost would be $1X726=$726. But 1s. 4d.$; therefore the cost must be of $726, which is $121. Ans.

104. What cost 896 bu. of wheat at 6s. per bushel ?

Analysis.-6s. 4s.+2s. Now 4s. $; and 2s.

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of 4s.

Or, thus: 6s=$3; therefore the number of bu. minus of itself, will be the cost, and 896-224 (4 of 896)=672. Ans. $672.

105. What cost 752 yds. of balzorine, at 2s. 8d. per yard? 106. What cost 1232 yds. of calico, at 1s. 6d. per yard? 107. What cost 763 lbs. of pepper, at 1s. 3d. a pound? 108. What cost 1116 bu. of apples, at 1s. 4d. per bushel? 109. What cost 1920 yds. of shirting, at 1s. 2d. per yard? 110. At 6s. a basket, what will 1560 baskets of peaches cost. 111. At 5s. 4d. a pound, what will 1200 lbs. of tea come to? Note.-2. Since 5s. 4d. is less than $1, is plain 1200-400-$800. Ans. 112. At 7s. per yard, what will 432 yds. of crape cost? 113. At 6s. 8d. a pound, what cost 972 lbs. of nutmegs ? 114. At 2s. 8d. a pair, what cost 864 pair of cotton hose? 115. At 12d. a yard, how much will 2800 yds. of tape come to? 116. What cost 1628 yds. of flannel, at 4s. per yard? 117. What cost 2560 bu. of oats, at 2s. per bushel? 118. What cost 9600 lbs. of wool, at 2s. 6d. a pound? 119. What cost 3200 lbs. of sugar, at 6d. per pound? 120. What cost 600 yds. of damask, at 5s., N. E. cur., per yard? Nole.-3. 5s. N. E. cur. is less than $1; hence, 600-100-$500. Ans. 121. What cost 2500 bu. of potatoes, at 1s. 6d. per bushel? 122. What cost 1440 yds. of gingham, at 2s. per yard? 123. How much will 4848 chickens cost, at 1s. apiece? 124. How much will 1680 slates cost, at 1s. 6d. apiece? 125. How much will 920 turkeys cost, at 4s. 6d. apiece? 126. What cost 4860 lbs. of butter, at 1s. 1d. per pound? 127. What cost 1260 melons, at 8d. apiece?

128. What cost 2340 lbs. of tea, at 4s. a pound?

per bushel?

129. What cost 240 bu. of peas, at 4s. 6d. 130. What cost 720 pair of gloves, at 5s. 3d. a pair? 131. What cost 360 bushels of corn, at 3s. per bushel? 132. What cost 7686 lbs. of butter, at 1s. per pound? 133. What cost 960 yds. of silk, at 5s. per yard? 134. What will 75 lbs. of butter cost, at $16.80 per cwt.? 135. What will 125 lbs. of wool cost, at $36 per hundred? 136. What will 15 cwt. of hemp cost at $60 per ton? 137. What will 2500 lbs. of iron cost, at $72 per ton? 138. What cost 14 acre of land, at $120 per acre?

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