14. A vintner buys 596 gallons of wine, at 6s. 3d. per gallon, in ready money, and sells it immediately at 6s. 9d. per gallon, payable in 3 months, how much is his gain or loss, supposing he allows the interest for the time, at 6 per cent. per annum, as discount for present payment ? Ans. £.11 17 8 gained.

15. What would be the gain or loss on the aforesaid wine, supposing the discount for present payment to be made at 2 per cent. without any regard to time? Ans. £.10 17 6 gain..

16. A merchant bought a parcel of cloth at the rate of 1 dol.. for every 2 yds. of which he sold a certain quantity at the rate of 3 dols. for every 5 yds. and then found he had gained as much as 18 yards cost, how many yards did he sell? Ans. 90 yds.

17. Bought rum at 1 dol. 25 cts. per gallon, which not proving so good as I expected, I am content to lose 18 per cent. by it, how must I sell it per gallon? Ans. 1 dol. 2 cts.

18. H sells a quantity of corn at 1 dollar a bushel, and gains 20 per cent. some time after he sold of the same, to the amount of 37 dols. 50 cts. and gained 50 per cent. how many bushels were there in the last parcel, and at what rate did he sell it per bushel ? Ans. 30 bushels, at 1 dol. 25 cts. per bushel.

19. A distiller is about purchasing 10000 gallons of molasses, which he can have at 43 cents per gallon, in ready money, or 50 cents with two months credit, it is required to know which is more advantageous to him, either to buy it on credit, or to borrow the money at 8 per cent. per annum to pay the cash. price? Ans. He will gain 136 dols. by paying the cash.

20. A tobacconist buys 4 hogsheads of tobacco weighing 38 cwt. 2 qrs. 8 lb. gross, tare 94 lb. per hhd. at 9 dols. per cwt. ready money, and sells it at 111d. per lb. allowing tare at. 14 lb. per cwt. to receive two-thirds in cash, and for the remainder a note at 90 days credit; his gain or loss is required, supposing the note is discounted at a bank where discount is made for 60 days. Ans. 283 dols. 43 cts. gain.

M.2

ALLIGATION MEDIAL

Is when the quantities and prices of several things are given, to find the mean price of the mixture compounded of those things.

RULE. As the sum of the quantities or whole composition is to their total value, so is any part of the composition to its mean price.

EXAMPLES.

1. A grocer would mix 25 lb. of raisins, at 8 cents per ib. and 35 lb. at 10 cents per lb. with 40 lb. at 12 cents per lb.― What is 1 lb. of this mixture worth?

2. A goldsmith mixes 8 lb. 53oz. of gold, of 14 carats fine, with 121b. 8 oz. of 18 carats fine; what is the fineness of this Lixture? Ans. 16 carats.

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3. A grocer would mix 12 cwt. of sugar, at 10 dols. per cwt. with 3 cwt. at $3 dols, per cwt, and 8 cwt. at 73 dols. per cwt. what will 5 cwt. of this mixture be worth?

Ans. 44 dols. 78 cts. 2 ms. 4. A refiner melts 23 lb. of gold, of 20 carats fine, with 4 b. of 18 carats fine; how much alloy must he put to it to make it 22 carats fine? Ans. It is not fine enough by 3 carats, so that no alloy must be put to it, but more gold.

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and

5. A malster mingles 30 quarters of brown malt, at 288. per quarter, with 46 quarters of pale, at 30s. per quarter, 24 quarters of high dried ditto, at 258. per quarter; what is the value of 8 bushels of this mixture? Ans. £.1 8s. 24d.

6. If I mix 27 bushels of wheat, at 5s. 6d. the bushel, with the same quantity of rye, at 4s. per bushel, and 14 bushels of barley, at 2s. 8d. per bushel, what is the worth of a bushel of this mixture? Ans. 48. 3 d.

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

8. A mealman has flour of several sorts, bushels at 3s. 5d. per bushel, 4 bushels at and 5 bushels at 4s. 8d. per bushel, what bushel of this mixture?

and would mix 3 5s. 6d. per bushel, is the worth of a. Ans. 4s. 7 d. 4

9. A vintner mixes 20 gallons of Port, at 5s. 4d. per galJon, with 12 gallons of White wine, at 5s. 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? Ans. 5s. 3 d. 2

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10. A farmer mingled 20 bushels of wheat, at 5s. per bushel, and 36 bushels of rye, at 3s. per bushel, with 40 bushels of barley, at 2s. per bushel, I desire to know the worth of a bushel of this mixture? Ans. 3 shillings.

11. A person mixing a quantity of oats, at 2s. 6d. per bushel, with the like quantity of beans, at 4s. 6d. per bushel, would be glad to know the value of 1 bushel of that mixture? Ans. 3s. 6d.

12. A refiner having 12 lb. of silver 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? Ans. 6 oz. 18 dwt. 16 grs.

13. If with 40 bushels of corn, at 4s. per bushel, there are mixed 10 bushels, at 6s. per bushel, 30 bushels, at 5s. per` bushel, and 20 bushels, at 3s. per bushel, what will 10 bushels of that mixture be worth? Ans. £.2 35.

ALLIG ATION ALTERNATE

Is the method of finding what quantity of any number of simples, whose rates are given, will compose a mixture of a given rate; so that it is the reverse of Alligation Medial, and may be proved by it.

RULE. 1. Write the rates of the simples in a column under each other.

2. 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.

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

4. Then if only one difference stand 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. A merchant would mix wines at 14s. 19s. 15s.. and 228. per gallon, so that the mixture may be worth 18s. the gallon;, what quantity of each must be taken?

NOTE. Questions in this rule admit of a great variety of answers, accord ing to the manner of linking them..

2. How much wine, at 6s. per gallon, and at 4s. per gallon, must be mixed together, that the composition may be worth 5s. per gallon? Ans. 1 qt. or 1 gal. of each, &c.

3. How much corn, at 2s. 6d. 3s. 8d. 4s. and 4s. 8d. per bushel, must be mixed together, that the compound may be worth 3s. 10d. per bushel ?

Ans. 12 at 2s. 6d. 12 at 3s. Ed. 18 at 4s, and 13 at 4s. 3d. 4. A goldsmith has gold of 17, 18, 22 and 24 carats fine ;how much must he take of each to make it 21 carats find? Aus 3. of 17, 1 of 18, 3 of 22, and 4 of 24.

5. It is required to mix brandy at 8s. wine at 7s. cider at 1s. and water together, so that the mixture may be worth 5s. per gallon?

Ans. 9 gals. of brandy, 9 of wine, 5 of cider, and 5 of water.

When the whole composition is limited to a certain quantity.

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

6.

EXAMPLES.

How many gallons of water must be mixed with wine worth 3s. per gallon, so as to fill a vessel of 100 gallons, and that a gallon may be afforded at 2s. 6d. ?.

Ans. 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. so that it might be afforded at 8d. perlb. how much of each sort must he take? Ans. 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, must be mixed together, to form a composition of 40 oz. of 20 carats fine?

Ans. 5 oz. of 15, of 17, and of 18, and 25 oz. of 22.