3. A grocer would mix 12 cwt. of fugar at 10 dols. per cwt. with 3 cwt. at 8 dols. per cwt. and 8 cwt. at 7 dols. per cwt. what will 5 cwt. of this mixture be worth?

Aní. 44 dols. 78 cts. 2 mills.

4. A refiner melts 2 lb. of gold, of 20 carats fine, with 4 lb. of 18 carats fine; how much alloy muft he put to it, to make it 22 carats fine ? Anf. It is not fine enough by 3 carats, so that no alloy must be put to it, but more gold.

5. A maltfter mingles 30 quarters of brown malt, at 28s. per quarter, with 46 quarters of pale, at 30s. per quarter, and 24 quarters of high dried ditto, at 25s. per quarter; what is the value of 8 bufhels of this mixture? Anf. £.1 8s. 21d.}

6. If I mix 27 bushels of wheat, at 5s. 6d. the bushel, with the fame quantity of rye, at 45. per bufhel, and 14 bushels of barley, at 25. 8d. per bushel, what is the worth of a buthel of this mixture? Anf. 4s. 3 d.

7. A grocer mingled 3 cwt. of fugar, at 56s. per cwt. 6 cwt. at £1 17 4 per cwt. and 3 cwt. at £.3 14 8 per cwt. what is I cwt. of this mixture worth? Anf. £.2 11 4

8. A mealman has flour of several forts, and would mix 3 bush. els at 35. 5d. per bufhel, 4 bufhels at 5s. 6d. per bufhel, and 5 bushels at 4s. 8d. per bufhel, what is the worth of a bufhel of this mixAnf. 45. 7d.

ture ?

9. A vintner mixes 20 gallons of Port at 5s. 4d. per gallon, with 12 gallons of White wine at 55. per gallon, 30 gallons of Lisbon at 6s. per gallon, and 20 gallons of Mountain at 4s. 6d. per gallon, what is a gallon of this mixture worth?

IO.

Anf. 55. 3d., 18.

A farmer mingled 20 bushels of wheat at 5s. per bushel, and 36 bushels of rye at 35. per bufhel, with 40 bushels of barley at 25. per bufhel, I defire to know the worth of a bufhel of this mixture? Anf. 3 fhillings.

11.

A perfon mixing a quantity of oats at 2s. 6d. per bushel, with the like quantity of beans at 45. 6d. per bufhel, would be glad to know the value of 1 bufhel of that mixture?

12.

Anf. 35. 6d.

A refiner having 12 lb. of filver bullion of 6 oz. fine, would melt it with 8 lb. of 7 oz. fine, and 10 lb. of 8 oz. fine, required the fineness of 1 lb. of that mixture?

Anf. 6 oz. 18 dwt. 16 grs.

13. If with 40 bushels of corn at 4s. per bufhel, there are mixed 10 bufhels at 6s. per bufhel, 30 bushels at 5s. per bufhel, and 20 bufhels at 35. per bufhel, what will 10 bufhels of that mixture be worth? Anf. £.2 35.

ALLIGATION ALTERNATE

Is the method of finding what quantity of any number of fimples, whofe rates are given, will compofe a mixture of a given rate; fo that it is the reverfe of Alligation Medial, and may be proved by it.

RULE.

each other.

1. Write the rates of the fimples in a column under

2. Connect or link with a continued line the rate of each fimple 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 lefs.

3. Write the difference between the mixture rate and that of each of the fimples, opposite the rates with which they are linked.

4. Then if only one difference ftand against any rate, it will be the quantity belonging to that rate; but if there be feveral, their fum will be the quantity.

I.

EXAMPLES.

A merchant would mix wines at 14s. 195. 15s. and 225. per gallon, so as that the mixture may be worth 18s. the gallon; what quantity of each must be taken ?

NOTE. Queftions in this rule admit of a great variety of answers, according to the manner of linking them.

2. How much wine, at 6s. per gallon, and at 4 fhillings per gallon, must be mixed together, that the compofition may be worth 55. per gallon ? Anf. 1 qt. or 1 gal. &c. 3. How much corn, at 2s. 6d. 8d. and 45. 8d. bufhper el, must be mixed together, that the compound may be worth 35. 10d. per bufhel? Anf. 12 at 2s. 6d. 12 at 3s. 8d. 18 at 4s, and 18 at 4s.

35. 45.

8d.

4. A goldsmith has gold of 17, 18, 22, and 24 carats fine; how much muft he take of each to make it 21 carats fine?

Anf. 3 of 17, 1 of 18, 3 of 22, and 4 of 24. 5. It is required to mix brandy at 8s. wine at 75. cider at Is. and water together, so that the mixture may be worth 5s. per gallon? Anl. 9 gals, of brandy, 9 of wine, 5 of cider, and 5 of water.

When the whole compofition is limited to a certain quantity.

RULE. Find an answer as before by linking; then say, As the fum of the quantities, or differences thus determined, is to the given quantity, fo is each ingredient, found by linking, to the required quantity of each.

EXAMPLES.

6. How many gallons of water must be mixed with wine worth 35. per gallon, fo as to fill a veffel of 100 gallons, and that a gallon may be afforded at 2s. 6d. ?

Anf. 83 gallons of wine, and 163 of water.

7. A grocer has currants at 4d. 6d. 9d. and 11d. per lb. and he would make a mixture of 240 lb. fo that it might be afforded at 8d. per lb. how much of each fort must he take?

Anf. 72 lb. at 4d. 24 at 6d. 48 at 9d. and 96 at 11d. 8. How much gold of 15, of 17, of 18, and of 22 carats fine, muft be mixed together, to form a compofition of 40 oz. of 20 carats fine? Anf. 5 oz. of 15, of 17, and of 18, and 25 oz. of 22.

When one of the ingredients is limited to a certain quantity.

RULE. Take the difference between each price and the mean rate, as before; then,

As the difference of that fimple, whofe quantity is given, is to the reft of the differences feverally, fo is the quantity given, to the feveral quantities required.

EXAMPLES.

9. How much wine, at 5s. at 5s. 6d. and at 6s. the gallon, must be mixed with three gallons, at 45. per gallon, fo that the mixture may be worth 5s. 4d. per gallon ?

Anf. 3 gallons at 5s. ; 6 at 5s. 6d. ; and 6 at 6s.

10. A grocer would mix teas at 125. 10s. and 6s. with 20 lb. at 4s. per lb. ; how much of each fort muft he take to make the compofition worth 8s. per lb. ?

Anf. 20 lb. at 4s.; 10 lb. at 6s.; 10 lb. at 10s.; and 20 lb. at 125.

11. How much gold of 15, of 17, and of 22 carats fine, must be mixed with 5 oz. of 18 carats fine, fo that the composition may be

20 carats fine ?

POSITION is a rule, which, by falfe or fuppofed numbers, taken at pleasure, discovers the true one required. It is divided into two parts, SINGLE and DOUBLE.

Is, by using one fuppofed number, and working with it as the true one, you find the real number required by the following

RULE. As the total of the errors is to the given fum, fo is the fuppofed number to the true one required.

PROOF. Add the feveral parts of the refult together, and if it agrees with the given fum, it is right.

S

EXAMPLES.

I. A fchool-mafter, being asked how many scholars he had, faid, If I had as many, half as many, and one quarter as many more, I fhould have 264; how many had he?

2.

A perfon, after fpending and of his money, had 60 dollars left; what had he at firft?

Anf. 144 dols.

3. A certain fum of money is to be divided between 4 persons, in fuch a manner, that the first shall have of it, the fecond, the third, and the fourth the remainder, which is 28 dollars; what was the fum ? Anf. 112 dols.

4. A perfon lent his friend a fum of money unknown, to receive intereft for the fame, at 6 per cent. per annum, fimple intereft, and at the end of 5 years he received for principal and intereft 644 dols. 80 cents; what was the fum lent ? Anf. 496 dollars.

DOUBLE POSITION

Is, by making ufe of two supposed numbers, which, if both prove falfe, are, with their errors, to be thus disposed;

RULE. I. Place each error against its respective pofition. 2. Multiply them cross-wife.

3. If the errors are alike, that is, both greater or both less than the given number, divide the difference of the products by the difference of the errors, and the quotient is the answer: Bnt if the errors be unlike, divide the sum of the products by the fum of the errors, and the quotient will be the anfwer.