3. How much is the discount of 650L. at 4 per cent.? Ans. 26L.

4. Bought goods on credit, amounting to 1656 dollars; how much ready money must be paid for them, if a discount of 5 per cent. be allowed? Ans. $1573.20. 5. A holds B's note for 175L. 10s. he agrees to allow B a discount of 3 per cent. for present payment; what sum must B pay? Ans. 170L. 4s. 8d.

EQUATION.

Equation is a method of reducing several stated times, at which money is payable, to one mean or equated time.

RULE.

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

PROOF.

The interest of the sum payable at the equated time, at any given rate, will equal the interest of the several payments, for their respective times, at the same rate.

EXAMPLES.

1. C owes D 100 dollars, of which 50 dollars is to be paid at 2 months, and 50 at 4 months; but they agree that the whole shall be paid at one time, when must it be paid? Ans. 3 months.

50×2=100
50X4=200

100)3100

3 months.

2. A owes B 380L. of which 100L. is to be paid at 6 months, 120L. at 7 months, and 160L. at 10 months; but they agree that the whole shall be paid at one time: when must it be paid? Ans. at 8 months. 3. A merchant has owing to him 300L. to be paid as

follows: 50L. at 2 months, 100L. at 5 months, and 150L. at 8 months; it is agreed to make one payment of the whole: at what time must it be paid? Ans. 6 months.

4. Fowes H 2400 dollars, of which 480 dollars are to be paid at present, 960 dollars at 5 months, and the rest at 10 months, but they agree to make one payment of the whole, and wish to know the time.

Ans. 6 months. 5. A merchant has purchased goods to the amount of 2000 dollars, of which sum 400 dollars are to be paid at present, 800 dollars at 6 months, and the rest at 9 months; but it is agreed to make one payment of the whole: what is the equated time? Ans. 6 months. 6. G owes K 420L. which will be due 6 months hence: it is agreed that 60L. shall be paid now, and that the rest remain unpaid a longer time than 6 months; when must it be paid? Ans. in 7 months.

BARTER.

Barter is the exchanging of one commodity for another, according to the price or value agreed upon by the parties concerned.

Questions relating to barter are solved, either by the Rule of Three or by Practice.

Note. When a given quantity of any commodity at a given price, is to be bartered for another commodity at a given price, find the value, in money, of that commodity whose quantity is given; then find what quantity of the other may be had for that value.

EXAMPLES.

1. How much sugar at 11d. per lb. must be given in barter for 1100lb. of rice, at 3 d.

per lb.? Ans. 350lb.

2. How much sugar at 9d. per lb. must be given in barter for 492lb. of rice, at 3d. per lb.? Ans. 164lb. 3. How much tea at 64 cents per lb. must be given in barter for 4481b. of coffee, at 20 cents per lb.?

Ans. 140lb.

4. What quantity of tea, at 10s. per lb. must be given' for 720lb. of chocolate, at 4s. 2d.

per lb.?

Ans. 300lb. 5. How much wheat at Idol. 25cts. per bushel, is equal in value to 50 bushels of rye, at 70 cents per bushel? Ans. 28 bushels. 6. B has 75 yards of muslin, at 1s. 4d. per yard, which he is to give to H for linen, at 5s. per yard; how much linen will he receive? Ans. 20 yards. 7. A has sugar at 9d. per lb. for a quantity of which F is to give him 225lb. of tea, at 6s. per lb.; how much sugar must F receive for his tea? Ans. 1800lb. 8. How much sugar at 8d. per lb. must be given in barter for 20cwt. of tobacco, at 3L. per cwt.? Ans. 16cwt. Oqrs. 8lb. 9. A merchant has 1000 yards of canvas, at 94d. per yard, which he is to barter for serge, at 104d. per yard; how many yards of serge should he receive?

Ans. 92644 yards. 10. A grocer bartered 5cwt. of sugar at 6d. per lb. for cinnamon at 10s. 8d. per lb.; how much cinnamon did he receive? Ans. 26lb. 4oz.

11. A has 41ewt. of hops, at 30s. per cwt. for which B is to give him 20L. in money, and the rest in prunes, at 5d. per lb.: what quantity of prunes must A receive? Ans. 1992lb.

12. A and B barter: A has 320lb. of chocolate, at 4s. 6d. per lb. for which B is to give him 30L. in money, and the rest in cotton at 8d. per lb. How much cotton is B to give A? Ans. 1260lb.

13. L has 41cwt. of hops, at 4dols. 50cts. per cwt. for which M is to give him 28dols. 50cts. in money, and the rest in salt, at 80cts. per bushel; what quantity of salt is M to give L.? Ans. 195 bushels.

14. G has 284lb. of tea, at 11s. 6d. per lb. for which B is to give him 40 yards of linen, at 7s. 4d. per yard, and the rest in money; how much money must G receive? Ans. 1L. 14s. 5d.

15. R gave 189 yards of linen, at 6s. 8d. per yard, to C for 42 yards of cloth; what was the cloth per yard? Ans. 30s.

16. A has 608 yards of cloth at 14s. per yard, for which B is to give him 125L. 12s. in money, and 85 cwt. 2qrs. 24lb. of bees wax. At how much is the bees wax valued per cwt.? Ans. 3L. 10s. 17. C has wheat at $1.25 cents per bushel, ready money; but in barter he will have $1.50 per bushel; D has cotton at 20 cents per lb. ready money: what price must the cotton be in barter, and how much cotton must be given for 100 bushels of wheat?

Ans. SThe cotton must be 24cts. per lb. and 625lb. must be given for 100 bushels of wheat.

LOSS AND GAIN.

Loss and Gain instructs merchants and traders, so to estimate their goods in buying and selling, as to know what they gain or lose in dealing.

Questions in Loss and Gain are solved by the Rule of Three, or by Practice.

EXAMPLES.

1. A storekeeper sold 100 yards of silk, at $1.50 per yard, which cost him $1.25 per yard: how much did the gain by the saler

$1.50

$1.25

25 gain per yard.

yd.

yds.

cts.

1 : 100 :: 25

100

Whole gain $25.00 2. If a grocer buy 265lb. of tea for 79L. 10s. and afterwards sell the whole at 7s. per lb. how much will

he gain by the transaction?

265
7

210)18515

92L. 15s.

3. A shopkeeper bought 53 yards of silk, at 12s. per yard, and afterwards sold it at 14s. per yard; how much did he gain by the sale?

Ans. 5L. 6s.

4. G bought 650lb. of sugar, at 10 cents per lb. and sold it at 12 cents per lb.; how much did he gain? Ans. $13.00. 5. If I buy 765 yards of baize, at 3s. 44d. per yard, and sell it at 3s. 9d. per yard, how much do I gain? Ans. 14L. 6s. 10 d. 6. Bought 2016lb. of rice at 3d. per lb. and sold it at 3 d. per lb.; how much was gained by the transaction? Ans. 4L. 4s. 7. If I lay out 1000 dollars in hats, at 4 dollars each, and sell them afterwards at 4dols. 50cts. each, how much will I gain? Ans. 125dols. 8. A merchant bought 1300lb. of coffee, at 22cts. per lb. and was afterwards obliged to sell it at 20cts. per lb.; how much did he lose? Ans. $26.00. 9. B laid out 250L. in cloth, at 30s. per yard, and, afterwards, finding it was damaged, sold it at 26s. 3d. per yard; how much did he lose? Ans. 31L. 5s. 10. A shopkeeper bought 42 yards of muslin for 4L. 14s. Sd. and sold it at 2s. 6d. per yard; whether did he gain or lose, and how much? Ans. He gained 10s. 4d.

11. A draper bought 100 yards of cloth for 56 dollars, how must he sell it per yard, to gain 19 dollars in the whole? Ans. 75 cents. 12. If a grocer buy a quantity of tea for 125L and sell it again for 100L. how much will ho gain per cent.? Ans. 20 per cent. 13. If a yard of mantua be purchased for $1.20, and sold again for $1.50, what is the gain per cent.? Ans. 25 per cent. 14. If a yard of velvet be bought for 16s. and sold again for 12s. what is the loss per cent.?

Ans. 25 per cent. 15. Bought a chest of tea, weighing 490lb. for 326 dollars, and sold it for $370.10, what was the profit on each lb.? Ans. 9 cents. 16. If I buy 100 yards of cambric for 56L. at how much must I sell it per yard, to gain 15 per cent.? Ans. 12s. 10 d. 17. Bought 12 pieces of white cloth, for 6L. 10s. per piece, and paid 20s. 10d. per piece for dying it; how much must each piece be sold for, to gain 20 per Ans. 9L. 1s.

cent.?