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1. A is indebted to B £.120, whereof one half is to be paid in months, one quarter in 6 months, and the remainder in 9 months, what is the equated time for the payment of the whole ? Anf. 5 months and 7 days.

3. Cowes D 1400 dollars, to be paid in 3 months, but D being in want of money, C pays him, at the expiration of 2 months, 1000 dollars, how much longer than 3 months ought C, in equity, defer the payment of the reft? Anf. 24 months.

Those who are exact in thefe calculations, find the prefent worth of each particular fum, then find on what time these present worths will be increased to the total of the particular fums payable at the particular times to come; and that is the true equated time for payment of the whole.

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BARTER

Is the exchanging one commodity for another on fuch terms as may be agreed on.

for

EXAMPLES.

1. How many quintals of fish, at 2 dols. per quintal, will pay 140 hhds. of falt, at 4 dals. 70 cts. per hhd.

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2. A buys of B 4 hhds. of rum containing 410 gallons, at 1 dol. 17 cts. per gallon; and 253 lb. of coffee, at 21 cts. per lb. in part of which he pays 21 dollars in cash, and the balance in boards, at 4 dols. per thousand; how many feet of boards did the balance require ? Anf. 127957 feet.

3. B has C's note for 250 dols. with 6 months interest due on it, and to redeem it C delivers him 60 bushels of wheat at 7s. 6d. per bufhel, 50 bushels of corn at 5s. 3d. per bushel, and the balance in ftaves at 30 dols. per thousand; what number of staves did B receive ? Anf. 5550 ftaves, or 4 m. 6 hun, and 10 cafts.

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4. B bought of D the hull of a schooner of 70 tons, at 16 dols. per ton, and paid him in cash 500 dols. 3 hhds. of molaffes containing 350 gallons, at 64 cts. and is to pay the balance in New-England rum at 74 cts. per gallon; how many gallons is D to receive? Anf. 535 gallons.

5. A buys of B 250 quintals of fifh, at 255. per quintal; in payment B takes 100 dols. in cafh, 2 hhds. of molaffes containing 87 and 92 gals. at 35. 8d. per gallon, 1 pipe of brandy containing 120 gals. at 75. 6d. per gallon, and gives 3 months credit for the remainder; required the balance due, and what cash would pay it, allowing the intereft of it for the time at 6 per cent. per annum, as discount for prompt payment ?

Anf. the balance is 672 dols. 4 cts. 2 m.

6. C fells to D 28,674 feet of boards at 8 dols. 50 cts. per thoufand, and takes in payment cash, 4 barrels N. E. rum containing 128 gallons at 78 cents per gallon, 1 barrel of fugar weighing neat 2 cwt. 2 qrs. 4 lb. at 10 dollars per cwt. and the balance in coffee at 25 cts. per lb.; how much money and coffee is C to receive?

39 Anf. 37 dols. 28 cts. 9 mills, and 149 lb. of Coffee.

7. C has nutmegs worth 75. 6d. per lb. in ready money, but in barter he will have 8s.; D has tobacco worth 9d. per lb.; how much must he rate it per lb. that his profit may be equal to C's? Ans. 9fd.

8. A has tea, which he barters with B at 10d. per b. more than it cost him, against cambrick which ftands B in 10s. per yard, but puts it at 12s. 6d. ; I would know the first cost of the tea. Anf. 35. 4d. per

he

lb.

bufhel;

9. A has 240 bushels of rye, which coft him go cts. per this he barters with B at 95 cts. for wheat that ftands B in 99 cents per bufhel; how many bushels of wheat is he to receive in barter, and at what price is it to be rated, that their gains may be equal? Anf. 218 bufhels, at 104 cts. per bufhel.

10. A and B barter fome goods-A put his ar 30 and gains 8 per cent. B puts his at 24 fame rate; what was the first cost of the goods?

11.

fhillings,

fhillings, and gains at the

Anf. 28s. and 22s. 6d.

A and B barter; A has cloth that coft 28d. B's coft him 22d. and he puts it at 25d.; how high muft A put his to gain 10 per cent more than B ?

Anf. 35d.

12. C and D barter-C makes of 75. 6s. 8d. D makes of 7s. 6d. 75. 3d.; w :o has lost most, and by how much per cent?

Anf. Clofes 1 per cent. more than D.

LOSS AND GAIN

Is a rule that discovers what is gained or loft in buying or felling goods, and inftructs merchants and traders to raise or fall the price of their goods so as to gain or lofe fo much per cent. &c.

EXAMPLES.

1. Bought a piece of broadcloth containing 53 yds. at 4 dols. 65.cts. per yd. and fold at 5 dols. per yd. what is the profit on the whole ?

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2. If 1 lb. of coffee coft 28 cts. and is fold for 31 cts. what is the profit on 3 bags, weighing 293 lbs. neat ?

Anf. 8 dols. 79 cts.

3. Bought a piece of baize of 42 yds. for £.4 14 6 and fold it at 2s. 6d. per yd. what is the gain or lofs on the whole piece? Anf. 10s. 6d. gain. 4. A merchant bought 59 cwt. 3 qr. 14 lb. of iron, at 112 dollars per ton, paid freight and charges, 24 dols. lofs, if he fells the whole at 375. 4d. per

cwt. ?

what is the gain or

Anf. 13 dols. 26 cts. gain.

5. If a gallon of wine coft 6s. 8d. and is fold for 75. 2d. what is the gain per cent. ?

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6. When 20 per cent. lofs is made on coffee, fold at 20 cents per lb. what was the first coft?

Anf. 25 cents.

7. At 13 cents profit on the dollar, how much is it per cent, ? Anf. 13 per cent or 13 dols. 50 cts. per 100 dols.

8. A trader fells his goods at 2 much is it per cent. ?

d. profit on the fhilling, how Anl. 20%, or £.20 16 8.

9.

Which is the better bargain, in purchasing fifh, 17 fhillings per quintal, and 4 months credit, or 16s. 8d. cash ?

Anf. They are alike.

PROOF. The prefent worth of 175. found by discount, is equal to 16s. 8d. and 16s. 8d. with 4 months interest will amount to 175.

IO. A bought a piece of fhalloon containing 34 yds. at 35. 4d. per yard, and fold it at 124 per cent. lofs, how much did he fell it Anf. per yard ? 25. 11d. 11. Bought rum at 90 cts. per gallon, at what rate muft it be fold to gain 20 per cent. ? Anf. 108 cts.

12. A trader bought 1 hogfhead of rum, at a certain proof, containing 115 gallons, at 1 doll. 10 cts. per gallon, how many gallons of water must he put into it to gain 5 dols. by felling it at 1 doll. per gallon? Anf. 16 gallons.

13. Bought 4 hog fheads of rum, containing 450 gallons, at dollar per gallon, and fold it at 1 doll. 20 cts. per gallon, and gave 3 months credit; now allowing the leakage of the rum while in my poffeffion to be 10 gallons, I would know the gain or lofs, discounting for the prefent worth of the debt at 6 per cent. per annum.

Anf. 70 dols. 19 cts. gain.

14. A vintner buys 596 gallons of wine, at 6s. 3d. per gallon, in ready money, and fells it immediately at 6s. 94. per gallon, payable in 3 months, how much is his gain or lofs, fuppofing he allows the interest for the time at 6 per cent. per annum, as difcount for prefent payment ? Anf. £.11 17 8 gained.

15. What would be the gain or lofs on the aforefaid wine, fuppofing the discount for prefent payment to be made at 2 per cent. without any regard to time?

Anf. £.10 17 61⁄2 gain.

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16. A merchant bought a parcel of cloth at the rate of 1 dollar for every 2 yards, of which he fold a certain quantity at the rate of 3 dollars for every 5 yards, and then found he had gained as much as 18 yards coft, how many yards did he fell ?

Anf. 90 yards.

17. Bought rum at 1 dollar 25 cents per gallon, which not proving fo good as I expected, I am content to lofe 18 per cent. by it, how muft I fell it per gallon? Anf. 1 dol. 2 cts.

18. H fells a quantity of corn at 1 dollar a bufhel, and gains 20 per cent. some time after he fold of the fame, to the amount of 37 dollars 50 cents, and gained 50 per cent. how many bufhels were there in the laft parcel, and at what rate did he fell it per bufhel ? Anf. 30 bufhels, at 1 dol. 25 cts. per bushel.

A diftiller is about purchafing 10000 gallons of molaffes, which he can have at 48 cts. per gallon, in ready money, or 50 cts. with 2 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 per cent. per annum to pay the cafh price?

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Anf. He will gain 136 dols. by paying the cash. 20. A tobacconist buys 4 hogiheads of tobacco weighing 38 cwt. 2 qrs. 8 lb. grofs, tare 94 lb. per hogfhead, at 9 dollars per cwt. ready money, and fells it at 11d. 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 lofs is required, fuppofing the note is discounted at a bank where discount is made for 60 days?

Anf. 283 dols. 43 cts. gain.

ALLIGATION MEDIAL

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

RULE. As the fum of the quantities or whole compofition is to their total value, fo is any part of the compofition to its mean price.

EXAMPLES.

1. A grocer would mix 25 lb. of raisins, at 8 cents per lb. and 35 lb. at 10 cts. per lb. with 40 lb. at 12 cts. per lb.-what is one pound of this mixture worth?

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2. A goldsmith mixes 8 lb. 5 oz. of gold, of 14 carats fine, with 12 lb. 8 oz. of 18 carats fine; what is the fineness of this mixture?

Anf. 16 carats.

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