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24.2. If 481. ferve for the maintenance of 12 men S days, how long will 2881. ferve for 4 men?-Anf. 144 days.

Qu. 3. If, when a bufhel of wheat cofts 6s. 8d. a penny loaf weighs 6 ounces, how much will a loaf weigh that costs 10d. when the wheat is 10s. the bufhel?-Anf. 42 ounces.

"Rule 1. Let the principal caufe of lofs or gain, intereft or decrease, action or paffion, be put in the first place.

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2. Let that which betokeneth time, diftance, or place, and the like, be in the fecond place; and the remaining one in the third. "3. Place the other two terms under their like in the fuppofition. 4. If the blank falls under the third term, multiply the firft and fecond terms for a divifor, and the other three for a dividend; but, "5. If the blank falls under the first or fecond term, multiply the third and fourth terms for a divifor, and the other three for the dividend; and the quotient will be the answer. '

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"Example 1. If 14 horfes eat 56 bushels of oats in 16 days, how many bushels will be fufficient for 20 horfes for 24 days?

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That this rule is not founded on mathematical principles is evident from inspection; for by a different statement of the queftion (though exactly agreeable to the rules) a different anfwer will arife. Thus, how eafily might the learner, required to work this queftion by one ftatement, order the numbers as follows:

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According to this flatement the answer will be 58 bufhels; whereas, the true answer is 120 bufhels. The queftion is, nevertheless, stated in this laft cafe agreeable to the rules.

Qu. 4. If 96 pioneers in 24 days caft a trench 96 yards long, how many pioneers will caft a trench 536 yards long in 8 days?-Anf. 1008 pioneers.

Qu. 5. If 10 men mow 40 acres in § days, how many days will it require 3 meu to mow 450 acres?—Auf, 100 days.

This rule may be proved by two fingle rules.

.I

The following rules in this chapter, except vulgar fractions and the extractions of roots, are wrought either by fome of the rules of proportion, delivered in the four preceding fections, or by the rule of practice, hereafter to be fpoken of.

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FELLOWSHIP is that rule whereby merchants and others, trading in company, and employing a joint capital stock, are enabled to afcertain each partner's particular lofs or gain, according to his fhare in the fame joint flock.

This rule alfo ferves to divide a bankrupt's eftate among his creditors; to pay legacies, when there is a deficiency of the teftator's effects: and, in fine, to divide the lofs or profit of any joint concern among the lofers or proprietors.

The rule of fellowship is either fingle or double, that is, without regard to time, or with time.

Fellowship without time, or fingle fellowship, is when different perfons employ their refpective ftocks for the fame time.

Rule.

Rule. As the whole stock of all the partners is to the whole gain or lofs, fo is each man's particular stock to his particular share of the gain or lofs.

Proof. By adding each perfon's gain or lofs together.

Therefore, the whole ftock of all the partners is to be made the first number in the rule of three, the whole gain or loss the second number, and the particular stock of any one partner the third number; then the fourth number, or anfwer, is that partner's lofs or gain, whofe ftock was the third number. This operation in the rule of three must be repeated if there be more than two partners, and performed as often as there are partners concerned.

Example 1. Three perfons enter into trade together: A put into the trade iool. B 170l. and C 300l.; at the making up their accompts, they find they have gained 550%. profit: what is each person's share?

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If there be any remainders, fuch remainders in the proof must be added together (if they be fractions of the same denomination), and divided by the common divifor of each question (¿. e. the total stock); and the quotient, which is units of the fame denomination, added to the particular fhares: thus, in the foregoing example, I added the three remainders, 330, 390, and 420, together, and dividing the total by 570, the common divifor, the quotient is 2, which are farthings, as they are fractions of a farthing.

Qu. 2. Four perfons place their money in the public funds: A put in 360%. B 480l. C 70cl. and D 860l. When the capital came to be fold out, the principal and intereft amounted to 4200l. what is each man's fhare of the net profit?-Anfer, A 270l. B 360l. C 5251. D 6451

Qu. 3. A bankrupt is indebted to four creditors in the Following fums: to A 5511. Ss. to B 608l. 145. to C 3041. and to D 2081. 125. The bankrupt's eftate is worth only 3372. 175. how much will each creditor receive?-Anf. A 111l. 75. 5d. B 122/. 185. 101d. C 617. 85. old, and D 421. 25. 7ąd.

Qu. 4. A hip being loft value 1730l.; of which A paid 3461. B 5197. C 6924. and D 1737. towards building her; the was infured to the amount of 1360l. what was each person' lofs? Answer, A 741. B 111. C 148. D 377.

In the fecond example, the whole ftock first placed in the funds is to be found by adding each person's stock together, and that made the first number in the rule of three; the whole gain is to be the second number, the particular stock of any one perfon the third number, and the fourth number is his fhare.

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