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Is finding the equated time to pay at once, several debts due at different periods of time, so that no loss shall be sustained by either party.


Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time for the payment of the whole.


1. A owes B 380 dollars, to be paid as follows-viz. 100 oilars in 6 months, 120 dollars in 7 months, and 160 doilars in 10 months: What is the equated time for the payment of the whole debt. ?.

100 X 6 = 600
7 = 840

120 X
160 × 10

= 1000


)3040(8 months. Ans.

2. A merchant hath owing him 500l. to be paid as follows: 50l. at 2 months, 100l. at 5 months, and the rest at 3 months; and it is agreed to make one payment of the whole; I demand the equated time? Ans. 6 months.

3. F owes H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5, months, and the rest at 15 months, but they agree to make one payment of the whole; demand when that time must be? Ans. 8 months. 4. A merchant has due to him a certain sum of money, o be paid one sixth at 2 months, one third at 3 months, nd the rest at 6 months; what is the equated time for ne payment of the whole? Ans. 44 months.


S the exchanging of one commodity for another, and diects merchants and traders how to make the exchange thout loss to either party.


Find the value of the commodity whose quantity is ven; then find what quantity of the other at the pro

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posed rate can be bought for the same money, and it gives the answer.


1. What quantity of flax at 9 cts. per lb. must be giv en in barter for 12 lb. of indigo, at 2 dols. 19 cts. per Ib.

12 lb. of indigo at 2 dols. 19 cts. per lb. comes to 26 dols. 28 cts. therefore, As 9 cts. : 1 lb. :: 26,28 cts. : 292 the answer.


2. How much wheat at 1 dol. 25 cts. a bushel, must be given in barter for 50 bushels of rye, at 70 cts. a bushel ? Ans. 28 bushels. 3. How much rice at 28s. per cwt. must be bartered for Scwt. of raisins, at 5d. per Ib. ?

Ans. 5cwt. Sqrs. 913lb.

4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at 12s. 34d. per gallon ? Ans. 201lb. 13270z.

5. A and B bartered: A had & cwt. of sugar at 12 cts. per lb. for which B gave him 18 cwt. of flour; what was the flour rated at per lb. ? Ans. 5 cts.

6. B delivered 3 hhds. of brandy, at 6s. 8d. per gallon, to C, for 126 yds. of cloth, what was the cloth per yard?

Ans. 10s.

7. D gives E 250 yards of drugget, at 50 cts. per yd. for 319 lbs. of pepper; what does the pepper stand him lb. ? Ans. 23cts. 51m.



8. A and B bartered: A had 41 cwt. of rice, at 21s. per cwt. for which B gave him 201. in money, and the rest in sugar at 8d. per lb.; I demand how much sugar B gave A besides the 201.? Ans. 6cwt. Ogrs. 19 lb. 9. Two farmers bartered: A had 120 bushels of wheat, at 1 dols. per bushel, for which B gave him 100 bushels of barley, worth 65 cts. per bushel, and the balance in oats at 40 cts. per bushel; what quantity of oats did A reAns. 287 bushels.

ceive from B.?

10. A hath linen cloth worth 20d. an ell ready money; but in barter he will have 2s. B hath broadcloth worth 14s. 6d. per yard ready money, at what price ought B to rate his broadcloth in barter, so as to be equivalent to A's bartering price? Ans. 17s. 4d. Syrs.

11. A and B barter: A hath 145 gallons of brandy at 1 dol. 20 cts. per gallon ready money, but in barter he will have 1 dol. 35 cts. per gallon: B has linen at 58 cts. per yard ready money; how must B sell his linen per yard in proportion to A's bartering price, and how many yards are equal to A's brandy?

Ans. Barter price of B's linen is 65cts. 23m. and he must give A 300 yds. for his brandy.

12. A has 225 yds. of shalloon, at 2s. ready money, per yard, which he barters with B at 2s. 5d. per yard, taking Indigo at 12s. 6d. per lb. which is worth but 10s. how much indigo will pay for the shalloon; and who gets the best bargain?

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Ans. 43lb. at barter price will pay for the shalloon,
and B has the advantage in barter.
Value of A's cloth at cash price, is
Value of 43lb. of indigo, at 10s. per 1,

B gets the best bargain by £0 15

£22 10
21 15


Is a rule by which merchants and traders discover their profit or loss in buying and selling their goods: it also instructs them how to rise or fall in the price of their goods, so as to gain or lose so much per cent, or otherwise. Questions in this rule are answered by the Rule of Three


1. Bought a piece of cloth containing 85 yards, for 191 dols. 25 cts. and sold the same at 2 dols. 81 ets. per yard; what is the profit upon the whole piece?

Ans. $47, 60 ts. 2. Bought 12 cwt. of rice, at 3 dols. 45 cts. a cwt. and sold it again at 4 cts. a pound; what was the whole gain ? Ans. $12, 87cts. 5m.


3. Bought 11 cwt. of sugar, at 64d. per lb. but could not sell it again for any more than 2l. 16s. per cwt.; I gain or lose by my bargain? Ans. Lost, £2 11s. 4d. 4. Bought 44 lb. of tea for 6l. 12s. and sold it again for 87. 10s. 6d.; what was the profit on each pound?

Ans. 101d

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5. Bought a hhd. of molasses containing 119 gallons,
at 52 cts. per gallon; paid for carting the same Ï dollar
25 cents, and by accident 9 gallons leaked out; at what
rate must I sell the remainder per gallon, to gain 13 dol-
lars in the whole ?
Ans. 69cts. 2m.+

II. To know what is gained or lost per cent.


First see what the gain or loss is by subtraction; then As the price it cost is to the gain or loss: so is 100l. or $100, to the gain or loss per cent.


Sold for 4, 30
Cost 3, 44


1. If I buy Irish linen at 2s. per yard, and sell it again
at 2s. 8d. per yard; what do I gain per cent. or in laying
out 1001. As 2s. 8d.:: 100l.: £33 6s. 8d. Ans.
2. If I buy broadcloth at 3 dols. 44 cts. per yard, and
sell it again at 4 dols, 30 ces. per yard; what do I gain
per cent. or in laying out 100 dollars?

cts. cts.

$ $

As 3, 44: 86 :: 100: 25
Ans. 25 per cent.


per yd. 86

3. If I buy a cwt. of cotton for 34dols. 86 ets. and sell
it again at 41 cts. per lb. what do I gain or lose, and
per cent. ?

1 cwt. at 41 cts. per lb. comes to

8 cts. 46,48 34,86

Prime cost

Gained in the gross, $11,62

As 34,86 11,62 :: 100: 331 Ans. 331 per cent. 4. Bought sugar at 84d. per lb. and sold it again at 4l. per cwt. what did I gain per cent.?


Ans. £25 19s. 53d.

5. If I buy 12 hhds. of wine for 2047. and sell the same
again at 14l. 17s. 6d. per hhd. do I gain or lose, and
what per cent. ?
Ans. I lose 12 per cent.
6. At 13d. profit in a shilling, how much per cent. ?

Ans. £12 10s.

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cent. ?

. At 25 cts. profit in a dollar, how much per
Ans. 25 per cent.
NOTE-When goods are bought or sold on credit, you
st calculate (by discount) the present worth of their
ce, in order to find your true gain or loss, &c.


. Bought 164 yards of broadcloth, at 14s. 6d. per yd.
ly money, and sold the same again for 154l. 10s. on
onths credit; what did I gain by the whole; allow-
discount at 6 per cent. a year?
£. s.
As 103: 100 :: 154 10: 150


£. S.

O present worth. 118 18 prime cost.

Gained £31 2 Answer.

- If I buy cloth at 4 dols. 16 cts. per yard, on eight
ths credit, and sell it again at 3 dols. 90 cts. per yd.
Hy money, what do I lose per cent. allowing 6 per cent.
ount on the purchase price?
Ans. 24 per cent.

II. To know how a commodity must be sold, to gain
Ose so much per cent.


s 100 is to the purchase price so is 100l. or dols. with the profit added, or loss subtracted: to selling price.


If I buy Irish linen at 28. 3d. per yard; how must
I it per yard to gain 25 per cent. ?


As 100%. 2s. 3d. :: 125l. to 25. Id. Sqrs. Ans.
If I buy Rum at 1 dol. 5 cts. per gallon; how must
I it per gallon to gain 50 per cent.?

$1,56acts. Ans.

As $100 $1,05: $150 If tea cost 54 cents per lb. ; how must it be sold per o lose 12 per cent.?

= $100 54 cts.:: $87, 50 cts. : 47cts. 24m. Ans. Bought cloth 17s. 6d. per yard, which not proving od as I expected, I am obliged to lose 15 per cent. ; how must I sell it per yard ? Ans. 148. 10d.

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