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149. When the price is pounds, shillings, pence, and farthings. RULE. Multiply the given number by the pounds, take parts for the rest of the price, and proceed as in the former rules".

105. What will 571 cwt. of sugar cost, at 21. 12s. 9d. per ewt.? OPERATION.

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150. When the given number consists of a whole number and

parts.

RULE. Work for the whole number according to the direc tions given in the former rules, and add in such a part of the price as the question requires ".

b If the given number be multiplied by the pounds each costs, the product will evidently be the value for the pounds; the reasons on which the method of taking the aliquot parts for the remainder of the price is founded, have been already explained.

The price of will evidently be (half the price of 1, or) half the given

113. What is the value of 1094 dozen of wine, at 21. 6s. 6d. per dozen ?

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114. 237 yards of cambric, at 12s. 4d. per yard?

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116. 2734 at 7s. 6d. Answer 1021. 9s. 4d..

117. 234 at 17s. Answer 1991. 10s. 9d.

118. 120 at 5l. 15s, 5d. Answer 6961. 16s. 6d..

151. When the given number is of several denominations. RULE. Multiply the given price by the highest denomination of the given number, and take the remaining denominations of the given number in aliquot parts of the highest, and of one another, and work as in the preceding rules “.

price; in like manner the price of any part will evidently be the same part of the given price: the rule is therefore manifest.

a The reason of the rule will appear from an examination of the 119th Example; where, since I cwt. costs 87. 12s. 4d. it is plain that 15 cwt. will cost 15 times 87. 12s. 4d. (or 1297. 5s.); 1 quarter will cost of 81. 12s. 4d. (or 21. 3s. 1d.), and 14 lb. will cost half what a quarter costs, (or 11. Is. 6d.†); and that these several quotients being added together, the sum will be the

answer.

The Examples under this rule should be proved by The Rule of Three.

149. When the price is pounds, shillings, pence, and farthings. RULE. Multiply the given number by the pounds, take parts for the rest of the price, and proceed as in the former rules".

105. What will 571 cwt. of sugar cost, at 21. 12s. 9d. per ewt. ? OPERATION.

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150. When the given number consists of a whole number and

parts.

RULE. Work for the whole number according to the direc tions given in the former rules, and add in such a part of the price as the question requires".

b If the given number be multiplied by the pounds each costs, the product will evidently be the value for the pounds; the reasons on which the method of taking the aliquot parts for the remainder of the price is founded, have been already explained.

The price of will evidently be (half the price of 1, or) half the given

113. What is the value of 1094 dozen of wine, at 21. 6s. 6d. per dozen ?

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114. 237 yards of cambric, at 12s. 4d. per yard?

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116. 2734 at 7s. 6d. Answer 102l. 9s. 4d..

117. 234 at 17s. Answer 1997. 10s. 9d.

118. 120 at 5l. 15s, 5d. Answer 6961. 16s. 6d..

151. When the given number is of several denominations. RULE. Multiply the given price by the highest denomination of the given number, and take the remaining denominations of the given number in aliquot parts of the highest, and of one another, and work as in the preceding rules".

price; in like manner the price of any part will evidently be the same part of the given price: the rule is therefore manifest.

a The reason of the rule will appear from an examination of the 119th Example; where, since I cwt. costs 87. 12s. 4d. it is plain that 15 cwt. will cost 15 times 87. 12s. 4d. (or 1291. 5s.); 1 quarter will cost of 87. 12s. 4d. (or 21. 3s. Id.), and 14 lb. will cost half what a quarter costs, (or 11. Is. 6d.†) ; and that these several quotients being added together, the sum will be the

answer.

The Examples under this rule should be proved by The Rule of Three.

119. What will 15cwt. 1qr. 14lb. of tobacco cost, at

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Having put down the given price, I multiply it by 15, that is, by 5 × 3, the number of cwts.; I then say, 1 qr. is of a cwt., and 14 lb. of a qr.; I divide the top line by 4, and the quotient 27.3s. Id. by 2, and add the whole together for the answer.

The proof is stated thus, 1127b. 81. 12s. 4d. :: 15cwt. 1qr. 14lb.

• The following tables of aliquot parts will be necessary in solving these

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To find the aliquot parts of any number, divide it successively by 2, 3, 4, &c. to half the given number, and reserve all the quotients which arise without remainders, then each of these quotients, and its divisor, will be aliquot parts one by the other; thus in 1 cwt, or 112 lb. I find that 14 will go 8 times, therefore 14 lb. is, and 8 lb. of an hundred weight.

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