RULE. Write the rates of the simples in a column under each other, reduced into one denomination. Connect or link with a continued line the rate of each simple, which is less than that of the compound, with one or any number of those that are greater than the compound, and each greater rate with one or any number of the less. Place the difference between the mean price, (or mixture rate,) and that of each of the simples, opposite to the rates with which they are connected. If then only one difference stands against any rate, it will be the quantity belonging to that rate; but if there be several, their sum will be the quantity. EXAMPLES. 1. How many pounds of tea, at 140 cts. a pound, 150 cts. a pound, and 190 cents a pound, must be mixed together, that one pound may be sold for 170 cents? 170 140- 190 20 at 140 cts. Ans. 30+20=50 at 190 cts. NOTE. Questions in this rule admit of a variety of answers, owing to the manner of linking or connecting them. Observe again, suppose you reject the ciphers, or units' place of the above answer, and say, 2 pounds at 140, 2 at 150, and 5 at 190 cents per pound, will do; or, if you add another cipher, and say, 200 pounds at 140 cents, 200 at 150, and 500 at 190 cents per pound, all will answer; or any three numbers in the same proportion to each other, as the above 20, 20, and 50, have to themselves. This rule is the proof of Alligation Medial. 2. How much wheat at 80 cents, rye at 60 cents, and buckwheat at 40 cts. per bushel, will make a mixture worth 50 cents per bushel? Ans. 10 of wheat, 10 of rye, and 40 of buckwheat. 3. A grocer mixed three sorts of sugar together, viz. one sort at 10 cents per pound, another at 7 cents, and a third at 6 cents. How much of each sort must he take, that the whole mixture may be sold at 8 cents per pound? Ans. 3 lbs. at 10 cts. 2 at 7, and 2 at 6. 4. A distiller hath several sorts of whiskey, viz. one sort at 80 cents per gallon, another at 70 cts. another at 60 cts. and a fourth at 40 cents, and he is desirous to mix so much of each sort together, that the whole may be at 50 cents a gallon. I demand how much of each sort he must take? Ans. 10 gallons at 80 cents, 10 at 70 cts. 10 at 60 cts. and 60 at 40 cents per gallon. 5. A goldsmith has gold of 17, 18, 22 and 24 carats fine; how much must he take of each sort, to make it 21 carats fine? Ans. 3 of 17, 1 of 18, 3 of 22, and 4 of 24 carats fine. ALLIGATION PARTIAL, By some called Alternation, is when the rate of all the things, the quantity of but one of them, and the mean rate of the whole mixture, are given to find the several quantities of the rest, in proportion to the quantity given. RULE. Take the difference between each rate and the mean rate, and place them alternately, as before; then say, as the difference of the same name, with the quantity given, is to the rest of the differences severally, so is the quantity given, to the several quantities required. EXAMPLES. 1. A grocer would mix 40 pounds of sugar, at 21 cents a pound, with some at 19, 13, and 11 cts. a pound: how much of each sort must he take to mix with the 40 pounds, that he may sell the mixture at 17 cents a pound? 2. A farmer would mix 10 bushels of wheat, at 65 cents per bushel, with rye at 43 cents, corn at 31 cts. and barley at 25 cents per bushel, so that a bushel of this mixture may What quantity of each must he take? be sold for 33 cents. 3. How many gallons of water must be mixed with wine worth 60 cts. per gallon, so as to fill a vessel of 100 gallons, that a gallon may be sold at 50 cents? 50 {60} 10 As 60: 100 :: 10 : 163 gallons water. 60: 100 :: 50 : 831 gallons wine. 60J 50 - 60 Ans. 163 galls, water, and 834 galls. winė. 4. A grocer would mix sugar at 4 cents, 6 cents, 9 cents, and 11 cents per pound, and he would make a mixture of 240 pounds, so that it might be afforded at 8 cents a pound. What quantity of each did he take? Ans. 96 lbs. at 11 cts. 72 lbs. at 4 cts. 48 lbs. at 9 cts. and 24 lbs. at 6 cts. per pound. 5. A retailer of groceries has four sorts of tea, at 20 cts. 60 cts. 120 cts. and 200 cts. per pound. The worst would not sell, and the best was too high for the common people; he therefore mixed 120 pounds, and so much of each sort, as to sell it at 80 cents per pound. How much of each sort did he take? 6. A goldsmith had two sorts of silver bullion, one of 11 oz. fine, and the other of 6 oz. fine, and having determined to mix a pound of it, so that it shall be 9 oz. fine, how much of each sort must he take? 7. A grocer hath sugars at 9 cents, 17 cents, and 25 cents per pound, and would make a composition of 2 cwt. 16 lbs. worth 21 cents a pound. What quantity of each must he take? Ans. 40 lbs. at 9 cts. 40 at 17, and 160 at 25 cts. 8. How much gold of 16, 18, 19, and 23 carats fine, must be mixed together, to form a mixture of 3 lbs. 4 oz. of 21 carats fine? Ans. 5 oz. of 16, of 18, of 19, and 25 of 23 car. fine. 9. A distiller has whiskey at 70 cents, and at 115 cents per gallon, and has a mind to mix a quantity together, so that a hogshead of 63 gallons may be sold for 50 dollars 40 cents. How many gallons must be taken of each ? Ans. 14 gallons at 115 cents, and 49 at 70 cents. 10. A grocer would mix teas at 240 cents, 200 cents, and 120 cents per pound, with 20 pounds at 80 cents per pound. How much of each sort must he take, to make the mixture worth 160 cents per pound? Ans. 20 lbs. at 80 cts. 20 at 240 cts. 10 at 200 cts. and 10 at 120 cents per pound. 11. A man who made cider had three sorts, one sort at 10 cts. per gallon, another at 8 cts. and the third at 6 cts. He would have a composition of 30 gallons, worth 7 cents a gallon. I demand how much of each sort he must take? Ans. 5 gallons at 10 cents, 5 at 8 cts. and 20 at 6 cts. 12. A vintner hath four sorts of wine, one sort at 2 dolls. per gallon, another sort at 1 dol. 60 cts. another at 1 dollar 20 cents, and a fourth worth but 80 cents. I demand how much of each sort he must take, to make a mixture of 60 gallons, worth 180 cents per gallon. Ans. 5 gallons of 160 cents, 5 of 120 cents, 5 of 80 cts. and 45 of 200 cents per gallon. SECTION VI. EXCHANGE. By this rule, import and export merchants know what sum of money ought to be received in one country, for any sum of different specie paid in another, according to the given course of exchange between the countries so trading. To reduce the monies of foreign countries to that of the United States, see the following tables and examples. ENGLAND AND IRELAND Keep their books and accounts in pounds, shillings, pence and farthings. 4 Farthings (qrs.) make 1 Penny. (d.) 12 Pence 20 Shillings 1 Shilling. (8.) 1 Pound. (1.) A pound sterling is equal by law to 4 dollars 44 cents United States' money, and one pound Irish is also equal by law to 4 dollars 10 cents United States' money. NOTE. This difference of 34 cents per pound sterling, is owing to the difference of exchange between England and Ireland, as 1007. English money is equal to 10831. Irish money, and the difference is called the par of exchange, which is 8l. 6s. 8d. FRANCE Keep their books and accounts, as in the following table: A livre is equal to 18 cents of the currency of United States' money. SPAIN Keep their books and accounts, as in the following table: A piastre is equal to 80 cents United States' money. HAMBURGH IN GERMANY Keep their books and accounts, as in the following table: A Rix dollar is equal to 100 cents, or a dollar United States' money. THE UNITED NETHERLANDS Keep their books and accounts, as in the following table A guilder is equal to 39 cents United States' money. PORTUGAL Keep their books and accounts, as in the following table? A millrea is equal to 1 dollar 24 cents United States' money. EAST-INDIA MONEY. CHINA Keep their books and accounts, as in the following tables A tale is equal to 1 dol. 48 ets. United States' money; a pagodas of India is equal to 1 dol. 94 cts. and a rupee of Bengal is equal to 55 cents. EXAMPLES. 1. Shipped a cargo of goods from Philadelphia to Liverpool, amounting, as per invoice, to 3860 dollars; how much sterling money will my correspondent credit me for in his books? cts. 7. cts. 1. 8. d. |