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The cwt. being the greatest denomination, is found first, by multiplying the price of an cwt. by 10, and for the value of the

2qrs. I take half the price of an cwt. then for the 21lb, I first' find the value of 141b. by taking half the price of a qr. or a fourth part of 2qrs. and half this price for the other 71b.; these sums added together give the answer.

Qu. 32. What is the value of 28yds. 3 Iqrs. of superfine cloth, at gos. per yard ? + Anf. 431. 6s. 3d.

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BARTER is that rule which inftruets traders to exchange oue cominodity for another, so that neither party may sustain

any loss.

Rule. Find the value of that commodity whose quantity is given, by the rule of three or practice; then by the rule of three, practice, or division, find what quatitity of the other commodity should be given in exchange.

Example'r. How many gallons of brandy, at 6s. per gallon, must be given in barter for ycwt. sqrs. 1416. of sugar, at 21. 105. per cwt. ?

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72)4575(63 gallons.

432
255
216
39

8
72)312 (434 pints.
288

Answer 63 gallons 4} pints.
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1

In this example, I first find the value of the given quantity of sugar by the rule of practice, which I reduce into pence, and it produces 4575 pence; these pence are then divided by 72, the pence in 1 gallon of brandy, and it quotes 63 gallons and 4 of a pint for the answer.

Thus it appears that questions that concern only one price of each fort, of two different kinds of goods, may be wrought by practice and division only, as the foregoing; but those of a more complex nature must be resolved by the rule of three.

Qu. 2. A grocer has 120lb. of tea, which cost him oso per lb. but he intends to barter it at the rate of 8s. per Ib. with a distiller, for Hollands that cost him 4s, per gallon. At what price must the distiller rate his Hollands, that he may have as much profit as the grocer; and how many gallons muft he give for the 120lb. of tea ? - Answer, he must rate his Hollands at 56, 4d. per gallon, and give 180 gallons for the tea.

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In resolving this question, first find what the Hollands must be rated at, by the rule of three, saying, if 6s. require 85. what will 45. require ? - Answer 55. 4d. Then by practice (as in the first example) find the value of the tea at 8s. per Ib. which, divided by the price of 1 gallon of Hollands, as before, quotes the answer.

Qu. 3. A vintner barters 196 gallons of wine for 14cwt. of sugar worth 6d. per lb. how much was the wine worth at that rate ?-Anf. 45. per gallon.

Qu. 4. A barters 320 gallons of gin, at 4s. 6d. per gallon, with B for blb. of tea at gs. per Ib. and for sugar at 8d. per ib.; how much sugar will A receive ? - Answer 11cwt. iqr.

Qu. 5. A vintner barters 608 gallons of brandy at 145. per gallon, for sugar at 31. 10s. per cwt. and 1251. 125. in cath: how much sugar should the vintner receive ? -Anfwer Sscwt, 2qrs. 241b.

SECT. XVI.

OP LOSS AND GAIN.

Loss and gain is that rule which discovers the loss or gain from buying and selling goods; and instructs traders how to fix their price, in order to gain or lose any certain fum.

Rule. By the rule of three direct. Though questions in this rule may often be answered by practice, or other rules.

Example i, At how much per lb. must a grocer sell tea which cost him 45. 10d. per lb. so as to gaiu 2-7 per cent.

profit?

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When the gain or loss is required at any rate per ceut. where the intereft has a g or a cypher on the right hand, as is moft commonly the case, the answer may be readily fouud, by adding to or subtracting from the given price such a part as the interest is of the principal; thus, if it be required to gain or lose 5 per cent. (as 5 is the twentieth part of an hundred) the answer is found by adding to or subtracting from the given price one twentieth part; and if the gain or loss be 10 per cent. then it is one tenth part; and if 15 per cent. it is zo ; and 20 per cent.is ; and 25 per cent. is *, &c.

23. 2. A grocer bought 8{cwt. of sugar, which cost 31l. 145. &d.; but, it being damaged, he is willing to lose 121. 10s. per cent. in the sale of it ; at how much per lb. mutt he fell it? - Answer 7d. per lb.

In this example I subtract the loss per cent. from the principal, and the reinainder is the second number in the rule of three, the principal the first number, the whole price of the sugar the third number; and the fourth number will be the whole price at the reduced rate, which divided by the number of pounds, gives -7d. the price of ilb.

Qu. 3. A wholesale factor in Ireland made linen, which coft him 124. per yard, the expense of fending it to London 13d. per yard, it was sold in London at 1s. 9d. per yard, and the retail trader was allowed 26 per cent. profit, what profit had the wholesale factor ? -- Anf, 24 per cent.

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In resolving this question, I say, as is. 2d. the expense of making and exporting the linen, is to is. Jd. the retail price, so i, rool to 150l.; thus there is so per cent. profit, which, after deducting 26 per cent. the retail trader's profit, leaves 94 per cent. for the factor.

Qu. 4. A merchant bought 100 gallons of brandy, at 65. per gallon, of which quantity 40 gallons were loft; at what price per gallon must be fell the remainder, that he may gain 10 per cent. profit upon the money it cost him Ang. 116, per gallon.

ŞECT. XVII.

OF EQUATION OF PAYMENTS.

EQUATION of payments is that rule whereby is discovered the time to pay at one payment several sums due at different times, so that neither party may sustain any loss.

Rule. Multiply each debt by the time at which it is due, and add all the products together ; divide the sum of the products by the sum of all the debts, and the quotient will be the answer, or the equated time to pay the whole.

Example 1. A is indebted to B in the sum of 200l. to be paid as follows: 6ol. in 4 months, 401. in 6 months, and 100l. in 10 months; what is the equated time to pay the whole ?

in

Debts.

Months. Products. 601.

4

245 40

6

240 100

10

1000 200

2,00)1,70 Answer 7 months.

7

VOL. I.

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24.

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