For the 21. I multiply the given number by 2, and the product 832 is pounds; then for the 8s. I multiply the given number by 4, fetting the double of the unit figure apárt for fhillings, as directed in the fourth cafe; for the 1s. I take the eighth part of the 8s. line; for the 3d. I take the fourth part of the 1s. line; and for the I take the fourth part of the 34. line: and the fum of thefe is the answer.

Qu. 28. What is the value of 1894 pieces of finen, at 41. 15s. 10 d. per piece?-Anf. 90772. 75.2."

Cafe 8. When the number of integers whofe value is required is a whole number with fractions annexed, find the value of the whole number by fome of the foregoing rules, to which add the value of the parts represented by the fractions.

Example 29. What is the value of 278cwt. 84lb. of foap, at il. 195. 4d. per cwt.?

In this example, after finding the value of the 278 cwt. at the given price, I find that 84lb. is of an cwt. I therefore take of the given price, viz. 19s. 8d. for the cwt. and for the other cwt. I take of the price, 9s. 10d.

Qu. 30. What is the value of 568 pieces of cloth, at 21. 1cs. 6d. per piece?-Anf. 1435l. 9s. 3d.

Cafe 9. When the quantity whofe value is fought is of feveral denominations, firft, find the value of the greatest denomination; and for the other denominations, take an equivalent part or parts of the given price; and add the feveral fums together for the anfwer.

Example 31. What is the value of 10cwt. 2qrs. 21lb. of tobacco, at 41. 55. 6d. per cwt. ?

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 14lb. by taking half the price of a qr. or a fourth part of 2qrs. and half this price for the other 7lb.; thefe fums added together give the answer.

Qu. 32. What is the value of 28yds. 31qrs. of superfine cloth, at 30s. per yard? Anf. 431. 65. 3d.

BARTER is that rule which inftructs traders to exchange oue cominodity for another, fo that neither party may fuftain any lofs.

Rule. Find the value of that commodity whofe quantity is given, by the rule of three or practice; then by the rule of three, practice, or divifion, find what quantity of the other commodity fhould be given in exchange.

Example 1 How many gallons of brandy, at 6s. per gallon, must be given in barter for 7cwt. 2qrs. 14lb. of fugar, at 27. 10s. per cwt. ?

In this example, I first 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 questions 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 resolved by the rule of three.

Qu. 2. A grocer has 120lb. of tea, which coft him 6s. per Ib. but he intends to barter it at the rate of 8s. per lb. with a distiller, for Hollands that coft him 45. 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. 4d, 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 8. what will 4. require?-Answer 53. 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 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 45. 6d. per gallon, with B for 61b. of tea at 5s. per lb. and for fugar at 8d. per Ib.; how much fugar will A receive?—Answer 11cwt. 1qr.

Qu. 5. A vintner barters 608 gallons of brandy at 145. per gallon, for fugar at 31. 10s. per cwt. and 125 125. in cash: how much fugar should the vintner receive?— Answer S5cwt. 2qrs. 24lb.

SECT. XVI.

OF LOSS AND GAIN.

Loss and gain is that rule which discovers the lofs or gain from buying and felling goods; and inftructs 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 1. At how much per lb. must a grocer sell tea which coft him 45. 10d. 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 intereft has a 5 or a cypher on the right hand, as is moft commonly the cafe, the aufwer may be readily found, by adding to or fubtracting from the given price fuch a part as the intereft is of the principal; thus, if it be required to gain or lofe 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 i and 20 per cent. is; and 25 per cent. is 1, &c. Qu. 2. A grocer bought 8cwt. of fugar, which coft 317. 14s. Ed.; but, it being damaged, he is willing to lofe 127. 10s. per cent. in the fale of it; at how much per lb. must he fell it?-Answer 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 74. the price of 1lb.

Qu. 3. A wholefale factor in Ireland made linen, which coft him 1244. per yard, the expenfe of fending it to London 1. per yard, it was fold in London at 1s. 9d. per yard, and the retail trader was allowed 26 per cent. profit, what profit had the wholefale factor?-Anf. 24 per cent.