the of which equaled what he put in; C, a sum equal to g of what he put in; and B the remainder. Find the amount B and C put in, and each one's share of the gain. Ans. B put in $2457; C, $1820.

A's gain $2730; B's, $2086; C's, $2184.

ART. 266. 44. A mixes sugar at 2 cts. per lb., with sugar at 5 cts. per lb., so that the mixture is worth 3 cts. per lb.: how much of each does he take?

SOLUTION. By taking 1lb., at 2 cts., he gains 1 ct., and by taking 1lb. at 5 cts., he loses 2 cts.; hence, that the gains and losses may be equal, he takes 1lb. at 2 cts., and 1⁄2 lb. at 5 cts., and in the same ratio for any quantity of the mixture; thus, 2 lb. at 2 cts., and 1lb. at 5 cts.; 4lb. at 2 cts., and 2 lb. at 5 cts., and 80 on, will make a mixture worth 3 cts. a lb. Art. 259.

45. In what ratio must I mix sugar at 4 cts. a lb., with sugar at 8cts. a lb.; the mixture to be worth 5 cts. a lb.? Ans. 3lb. at 4 cts. to 1 lb. at 8 cts. 46. In what ratio must I mix sugar at 3 cts. a lb., with sugar at 8cts. a lb.; the mixture to be worth 6 cts. a lb.? Ans. 21b. at 3 cts. to 31b. at 8cts.

47. How many pounds of tea, at 25 cts. per lb., must be mixed with 15 lb. at 30 cts. per lb.; the mixture to be worth 28 cts. per lb.?

SOLUTION. The ratio of the ingredients necessary for a mixture worth 28 cts. a lb., shows that for cach 11⁄2 lb. at 30 cts., we must take 1lb. at 25 cts. But 15 lb. 1 lb. 10; hence, it will

take 10lb. at 25 cts.

48. How many pounds of sugar, at 8cts. a lb., must I mix with 101b. at 11 cts. a lb., to make a mixture worth 10 cts.

lb.?

Ans. 5 lb.

49. Mix two kinds of tea at 20 and 25 cts. a lb., to make a mixture of 25 lb. worth 24 cts. a lb.

SOLUTION.-First find that 1lb. at 20 cts. and 41b. at 25 cts. a lb., make a mixture worth 24 cts. a lb. Then (Art. 252), dividing 25 into two parts having the ratio of 1 to 4, will give 5 lb. at 20 cts. per lb., and 201b. at 25 cts. per lb.

The above examples are usually placed under a rule called Alligation Alternate. They properly belong to Algebra.

ART. 267. 50. The sum of, }, and of a certain number is 26: what is that number?

SOL.-The sum of 1, 1, and is 13; hence, 13 of the number is 26, and is of 26=2; and the number is 12X2-24. Ans.

51. One-third of a number exceeds of it by 8: find the number. Ans. 96.

52. Seven-tenths of a number exceeds is that number?

53. I spent

of it by 7: what Ans. 70.

and of my money, and had $35 left:

what had I at first?
54. What number, increased by,, and
gives the sum 73?

55. A boy lost of his money, spent 15 cts. left how much had he at first?

Ans. $75.

of itself, Ans. 30.

20 cts., and had Ans. 63 cts. of the rest for Ans. 75 cts.

56. I spent of my money for books; paper; I had 10 cts. left: what had I at first?

57. A received $2 for each day he worked, and lost $1 for each day idle; he worked 3 times as many days as he was idle; at the end of the time he received $25: how many days did he work? ·

Ans. 15 da. 58. In an orchard, the trees bear apples;, peaches; and, cherries; the remaining 4, pears: how many trees in the orchard?

Ans. 80.

59. A teacher, when asked the number of his pupils, replied, that if he had as many more, half as many more, and 1 fourth as many more as he now had, he would have 110 what the number of pupils? Ans, 40.

60. A traveler spent the 1st day, of his money; the 2d day, of the remainder, and so on, the 3d and 4th days, when he had $1.62 left: what sum had he at first? Ans. $5.12

61. A merchant increased his capital the first year by of itself; the 2d, he increased this sum by of itself; the 3d, he lost of all he had, which left him $3375. How much had he at first? Ans. $1875.

NOTE. The examples in this article are sometimes placed under the rule of Position, now but little used, as Algebra is generally studied by the higher classes in common schools.

XXI. EXCHANGE OF CURRENCIES.

ART. 268. EXCHANGE or REDUCTION OF CURRENCIES, is the process of changing the currency of one country to that of another, without altering its value.

The currency of a country is its money or circulating medium.

ART. 269. To change one currency to another, the different denominations in each must be known; also, the unit value of a denomination in one currency, in a denomination of the other.

TABLE OF ENGLISH, OR STERLING MONEY.

4 farthings (far.). make 1 penny,

....

marked d.

12 pence

1 shilling,

8.

20 shillings

21 shillings

1 guinea,

g.

NOTES.-1. Farthings are generally written as fractions of penny. Thus, 1 far. is written 1d., 2 far. d., and 3 far. 2 d.

2. The present legal value of the pound sterling, according to act of Congress of 1842, is $4.84

The operations of Reduction, Addition, &c., of sterling money, are performed like those of other Compound Numbers.

1. Reduce £5 3s. 21d. to far.

2. Reduce 8675 far. to £.

Ans. 4953 far.

Ans. £9 83d.

£2 15s. 11d.

Ans. £11 6s. .. Ans. £9 5¿d.

Ans. £28 17s. 8d.

Ans. £4 3s. 5 d.

7. Find the value of £.625 (Art. 188.) Ans. 12s. 6d.

REVIEW.-268. What is Exchange of currencies? What is the currency of a country? 269. What must be known to change one currency to another? Repeat the table.

269. NOTE. How are farthings written? What is the legal value of the pound? How are the operations of reduction, addition, &c., of sterling money performed?

8. The value of .796875 of a £. Ans. 15s. 111d. 9. Reduce 7s. 6d. to the decimal of a £. Ans. .375 10. 8s. 9d. to the decimal of a £. (Art. 189.) Ans. .4375

ART. 270. To compute Int. in pounds, shillings, &c.

Reduce the given shillings, pence, and farthings, to the deci mal of a pound (Art. 189); find the interest as in dollars and cents (Art. 222); reduce the resulting decimal figures to shil lings, pence, and farthings (Art. 188).

11. What is the interest of £75 10s. for 2 yr. 6 mon., at 4 %? Ans. £7 11s. 12. Of £85 12s. 6d. for 1 yr. 9 mon., at 6 %? Ans. £8 19s. 93d.

ART. 271. 1. Reduce £12 sterling to U. S. Money. SOLUTION. Since £1 is worth $4.84, £12 are worth 12 times as much; and $4.84 × 12=$58.08 Ans.

2. Reduce £5 6s. 3d. to U. S. Money.

SUGGESTION. Either reduce the shillings, pence, and farthings, to the decimal of a pound, and multiply $4.84 by the result; or, multiply $1.84 by the pounds, and find the

OPERATION.

£5 6s. 3d.=£5.3125 = $4.84

£1

Ans. $25.7125

value of the lower denominations, by taking aliquot parts (Art. 208).

3. Reduce $40.535 to sterling money.

SOLUTION. Since £1 is $4.84, there will be as many pounds in $40.535 as $4.84 is contained times in $40.535

$40.535$4.84 8.375, and £8.375 £8 7s. 6d. Ans.

RULES.

1. TO REDUCE STERLING TO U. S. MONEY.-Express sterling money in pounds and decimals of a pound: multiply this by the value of £1, ($4.84), the product will be the value in dollars. Or, by PROPORTION. As £1 is to the given sum, so is $1.84 to the value of the given sum in dollars.

2 TO REDUCE U. S. TO STERLING MONEY-Divide the given

sum by the value of £1, ($4.84), the quotient will be the value in pounds and decimals of a pound.

money.

4. Reduce £25 to U. S.
5. £15 8s. to U. S. money.
6. £36 15s. 9d. to U. S. money.
7. $179.08 to sterling money.
8. $124.388 to sterling money.
9. In $1000, how many £?

Ans. $121.

Ans. $74.536 Ans. $178.05+

Ans. £37.

Ans. £25 14s. Ans. £206 12s. 23d.+

NOTE. The law of Congress, of July 31st, 1789, fixed the value of the pound sterling at $43, or $4.444, and $1. at 4s. 6d.

As the then legal or nominal value of the pound was below its real value, such a per cent. was afterward added to the nominal as was necessary to make it express the real value.

As it requires nearly 9 per cent. of $4.444 to be added to it, to make $4.84, when sterling funds or bills are estimated at $43 to a pound, and are 9 per cent. premium, they are really only at par.

ART. 272. In buying or selling exchange on England, it is still customary to regard the pound as $41, and then to add the % premium.

1. What must be paid for a bill of exchange on London of £200, at 9% premium?

=

SOLUTION. £200 X 44 $888.888; $888.888X.09 $80 premium; $888.888 +$80-$968.888 Ans.

2. What for a bill of exchange on Liverpool of £150, at 8% premium? Ans. $720. 3. What for a bill of exchange on London of £80 10s., at 91% premium? Ans. $391.76+

ART. 273. Previous to the adoption of Federal or U. S. Money, in 1786, accounts were kept in pounds, shillings, pence, and farthings.

Owing to the fact that the Colonies had issued bills of credit,

REVIEW.-270. .How compute interest on sterling money? 271. How reduce sterling to U. S. Money? How reduce U. S. to sterling money?

271. NOTE. What was the legal value of the pound sterling in 1789– How was the real value found from this?