In this example, I firft find the value of the given quantity of fugar 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 queftions that concern only one price of each fort, of two different kinds of goods, may be wrought by practice and divifion only, as the foregoing; but thofe of a more complex nature must be refolved by the rule of three,

Qu. 2. A grocer has 120lb. of tea, which coft him 6s. per lb. but he intends to barter it at the rate of 8s. per lb. with a diftiller, for Hollands that coft him 4. per gallon. At what price muft the diftiller 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?-Anfwer, he must rate his Hollands at 55. 4. per gallon, and give 180 gallons for the tea.

In refolving this question, firft find what the Hollands must be rated at, by the rule of three, faying, if 6s. require 8s. what will 45. require?-Answer 5s. 4d. Then by practice (as in the first example) find the value of the tea at 8s. per lb. 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 fugar 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 5lb. of tea at 5s. per lb. and for fugar at 8d. per lb.; how much fugar will A receive?-Anfwer towe. qr.

Qu. 5. A vintner barters 608 gallons of brandy at 145. per gallon, for fugar at 37. 10s. per cwt. and 1251. 12s, in cash: how much fugar should the vintner receive ?—dafwer S5cwt, zqrs. 24lb.

Loss and gain is that rule which discovers the loss or gain from buying and felling 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 At how much per lb. must a grocer sell tea which cost him 45. rou. per lb. fo as to gain 27 per cent,” profit?

As

When the gain or lofs is required at any rate per cent, where the interest has a 5 or a cypher on the right hand, as is moft commonly the cafe, the answer may be readily found, by adding to, or fubtracting from the given price fuch 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 fubtracting from the given price one twentieth part; and if the gain or lofs be 10 per cent. then it is one tenth part; and if 15 per cent. it is; and 20 per cent. is ; and 25 per cent. is ‡, &c. Qu. 2. A grocer bought 8cwt. of fugar, which coft 31. 145. 8d.; but, it being damaged, he is willing to lofe 127. 10s. per cent. in the fale of it; at how much per lb. muft he fell it?-Anfwer 7d. per lb.

In this example I fubtract the lofs per cent. from the principal, and the remainder is the fecond number in the rule of three, the principal the first number, the whole price of the fugar 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 1lb.

Qu. 3. A wholesale factor in Ireland made linen, which coft him 12 d. per yard, the expense of fending it to London

d. per yard, it was fold in London at 15. 9d. per yard, and the retail trader was allowed 26 per cent. profit, what profit had the wholefale factor?-Anf. 24 per cent.

In refolving this question, I fay, as 15. 2d. the expense of making and exporting the linen, is to 1s. 9. the retail price, fo is 100l. to 150l.; thus there is 50 per cent. profit, which, after deducting 26 per cent. the retail trader's profit, leaves 24 per cent. for the factor.

Qu. 4. A merchant bought 100 gallons of brandy, at 6s. per gallon, of which quantity 40 gallons were loft; at what price per gallon must he fell the remainder, that he may gain 10 per cent. profit upon the money it coft him?-Anf. 115. per gallon.

SECT. 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, fo that neither party may fuftain any lofs..

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 fum 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 fum of 200l. to be paid as follows: 60l. in 4 months, 40%. in 6 months, and 100%. in 10 months; what is the equated time to pay the whole?

Qu. 2. A owes B 1000l. of which is to be paid in 6 months, in 8 months, and the remainder in 10 months; what is the equated time to pay the whole?-Anfwer 7 months.

In this example, of 1000l. multiplied by 6 months produces 2, and multiplied by 8, produces 3, and (the remainder of the 1000l.) multiplied by 10, produces 210; and thefe three products added together gives 713 months for the answer.

And, note, when the fums or times of payment are given in fractions, the fum of the products is not to be divided by the fum of the debts, as it is in whole numbers.

2u. 3. A tradefman owes his creditor 144.; 447. he pays in ready money; 6ol. is to be paid at the expiration of 6 months, and the remaining 401. at the expiration of 8 months; but the tradefman defiring to have more time for the payment of the laft 40%. pays his creditor the 6ol. due 6 months after, in ready money; how long may he defer paying this laft 40%. to make him amends for this prompt payment?-Anf. 17 months.

In this example, the 441. to be paid in ready money is neglected; but for the 60l. paid 6 months before due, I find by the rule of three what intereft it would gain at any rate per cent. in that time, and then how long the 401. may be lent for that 'intéreft at the fame rate, which I find is 9 months, and which added to S months, its time of payment, gives 17 months for the answer *.

*This rule, though greatly used by men of bufinefs, is not mathematically exact. The reafon of the rule given by many writers, is, that for the debtor paying a fum before the time it is due, an equal fum should be forborn, for as long a time after it is due; but this is a mistake, for by the debtor paying money before it is due, he has the discount. only; but keeping the money after it is due, he gains the intereft, which is greater than the discount.

SECT.