34. A man and his wife ate a bu. of meal in 6 da.; when the man was absent, it lasted the woman 15 da.: how long would it last the man?

35. A cistern has 3 pipes; the 4 min., the 2d in 8min., the 3d in will all empty it?

Ans. 10 da.

1st will empty it in 15 min.: in what time Ans. 2 min. 15 sec. 53

36. A can mow of a meadow in 6 days, and B, 5 in 10 da. in what time can both mow it? Ans. 5 da. 37. Divide 35 cents between two boys, giving to one 9 more than the other. Ans. 13 and 22. SUG.-Subtract 9 from 35, divide the remainder equally; then 9, added to one of the equal parts, will give the greater share. 38. Divide $3000 into two parts, one being $500 more Ans. $1250 and $1750.

than the other.

39. A man left $3500 to his wife, son, and daughter; to the wife, $800 more than to the son; to the son, $300 more than to the daughter: find the share of cach.

Ans. wife, $1800; son, $1000; daughter, $700. 40. The hour and minute hands of a watch are together at 12 o'clock at what time are they next together?

SOL. The min. hand moves over 60 min. while the hour hand moves over 5 min.; therefore, the min. hand moves over 12 min. while the hr. hand moves over 1 min. Hence, in moving over 12

min., the min. hand gains 11 min. on the hr. hand.

Now, 12 is 12 of 11, that is, the distance moved over by the min. hand, is 12 of the distance gained. When the min. hand is at 12, and the hr. hand at 1, the former must gain 5 min. to overtake the latter: 1 of 5 min.=60=5,5. Ans. 55 min. past 1.

41. At what time between 5 and 6 o'clock are the hr.

and min. hands together?

42. At what time between

opposite to each other?

Ans. 273 min. after 5.

8 and 9 o'clock, are they Ans. 1010 min. after 8.

43. A, B, and C are the partners: A put in $3276;

the of what A put in was equal to of what B put in; 矗

and the difference between of what B put in, and of what C put in.

the whole of what A put in, equaled

They gained $7000; A received for his share a sum,

the of which equaled what he put in; C, a sum equal tog 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 1 lb. at 2 cts., and 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.; 4 lb. at 2 cts., and 2 lb. at 5 cts., and so 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 3cts. a lb., with sugar at 8cts. a lb.; the mixture to be worth Gets. a lb.? Ans. 2lb. at 3 cts. to 3lb. 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 each 1 lb. at 30 cts., we must take 1lb. at 25 cts. But 15 lb.÷11 lb. = 10; hence, it will take 10 lb. at 25 cts.

48. How many pounds of sugar, at 8 cts. a lb., must I mix with 10lb. at 11 cts. a lb., to make a mixture worth 10 cts. a 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 4 lb. 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

number is 26: what is that number?

, and of a certain

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

13

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

Ans. 96.

52. Seven-tenths of a number exceeds 3 of it by 7: what is that number?

53. I spent

Ans. 70.

and of my money, and had $35 left: Ans. $75.

what had I at first?

54. What number, increased by 1, 1, and of itself, gives the sum 73?

Ans. 30. 55. A boy lost of his money, spent 20 cts., and had 15 cts. left: how much had he at first? Ans. 63 cts. 56. I spent of my money for books; 3 of the rest for paper; I had 10 cts. left: what had I at first? Ans. 75 cts.

57. A received $2 for each day he worked, and lost $1 foi 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. 10.

4

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 3 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 4 farthings (far.) . make 1 penny,

12 pence

20 shillings

21 shillings

..

..

1 shilling,

MONEY.

marked d.

1 pound, or sovereign £.
1 guinea,

g.

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

Ans. £11 6s.

3. Add £3 61d., £5 10s. 41d., £1 15s. 11d.

4. £17 6s. 5d.,-£8 5s. 11d. 5. Multiply £3 12s. 2d. by 8. 6. £25 101d.÷6,—what?

Ans. £9 5d.

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?

269

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 X 12=$58.08 Ans.

2. Reduce £5 6s. 3d. to U. S. Money.

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 $4.84 to the value of the given sum in dollars.

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