2nd. Find a number, of which the, the, and the , make 52.

SOLUTION.

118

I take 12, of which the, the 4, and the make 13; now I have this proportion, 13: 12:: 52: the number asked = 48.

3d. A man dying, leaves a sum of 36000, £. to be divided among five persons, in the following manner; he gives to the first of the sum, to the second 1, to the third,, to the fourth r', to the fifth %, what will be each man's share?

SOLUTION.

It must be observed that the several legacies exceed the estate left, since 1 +} + ÷ +15+ ‡, make more than 1; but, as their parts must be in the same ratio with these fractions, the question must be solved in this manner.

2

Let us suppose that the whole sum is 12£. of which++ ¦ + ‚1⁄2 + 2, make 18.£. then we have this proportion; 18: 12 :: 36000: a=24000;

Σ

now dividing this number conformably with the intention of the testator, we easily find the several person's shares, the sum of which really amounts to 36000£.

Put a cypher at the right of the 5, in order to have an

even number of decimais.

Tare and trett are allowances made by the seller to the buyer, on some particular commodities.

Tare is the weight of the barrel, box, bag, or whatever contains the goods.

Trett is an allowance for the waste and dust, of 4lb. in every 104lb.

Gross is the weight of the goods, together with that in which they are contained.

Neat is the weight of the goods, after all allowances are deducted.

FIRST CASE.

Find the value of goods, allowances done for tare only.

RULE.

It is evident that we must subtract the whole tare from the whole gross weight, and multiply the difference, which is the neat, by the price, as taught for compound multiplication.

QUESTIONS,

1st. At 1£. 10s. 6d. per cent. what is the value of 24 hogsheads of tobacco, each weighing 6C, 2gr. 17lb. gross weight, and the whole tare being 17C. 3qr. 27lb? Ans, 216£. Os. 4d.

2nd. At 2£. 14s. per cent. what is the value of 12 casks of raisins, each weighing 3C. 2qr. 10lb. gross, and tare 20lb. per cask? Ans. 110£. 10s. 1d.

3d. Sold 9 hogsheads of sugar, each 6C. 2qr. 12/6. gross, tare 1716. per hundred weight: what is the neat weight, and what sum must be paid at 2£. 12s. 6d. per Cwt.? Ans. neat 50C. 1qr. 22tb.* amount 132 8s. 54d.

* In fuch questions as thefe, the ounces are neglected.

SECOND CASE.

When the trett is allowed with tare,

RULE.

Deduct the tare as before, the remainder is called suttle, which divided by 26,* the quotient will be the trett; subtract this from the suttle, and the remainder will be the neat, which, multiplied by the price, gives the answer.

QUESTIONS.

1st. In 27 bags of coffee, each 2C. Sqr. 1776. gross, tare 13/6. per Cwt; irett 4lb. per 104 h; what is the neat, and what is its value at 3£. 18s. 9d. per Cwt.? Ans. Neat 66C. 2qrs. 11lb. value 262£. 45. 74d.

2nd. At 8. per pound, what is the value of the neat weight of 8C. 3qrs. 20lb. gross, tare 38.b, trett 46. in every 104lb.? Ans. 32£. 15s. 21⁄2d.

BARTER.

Barter is the exchanging of one commodity for another, by duly proportioning their quantities and values.

From this definition, it follows that the questions relative to barter, depend upon proportions, and are solved by the rule of three.

46. in every 104, is 1b. in evey 26.