40. In what time will $750, at 62% per annum, double itself at simple interest?

41. In what time will a dollars at r per cent, simple interest, treble itself?

42. At what rate will $750 in 6 years, at simple interest, amount to $1020?

43. At what rate will m dollars in n years, at simple interest, double itself?

I bought a $100 bond, bearing 5% interest, for $80. What per cent of my investment did I gain annually? x= the annual gain per cent,

Let

44. Bought railroad stock, par value $50 a share, for $45 a share; the company declared a dividend of 6%. What per cent did I receive on my investment?

45. At what price must I buy railroad stock, par value $100 a share, in order that a 6% dividend will bring me an income of 8% on my investment?

46. I bought a $50 share for $40; the company declared a dividend which I found was 72% of my investWhat per cent of the par value was it?

ment.

47. If 25% of the par value of stock equals 40% of the market value, what is the par value of stock that is selling at $622 a share?

48. If stock bought at 90 yields an income of 5%, at what price would it yield 6% ?

49. What capital invested in 5's at 80 will yield the same income as $4500 invested in 6's at 90?

How far may a person ride in a coach, going at the rate of 5 miles an hour, that he may walk back at the rate of 2 miles an hour and be gone 5 hours?

50. If a boat sailed down a stream at the rate of 10 miles an hour and returned at the rate of 6 miles an hour, and was gone 6 hours, how far did it sail down the stream?

51. A boat whose rate of sailing in still water is 10 miles an hour, goes down a stream whose rate is two miles an hour, and returns, making the round trip in 5 hours. How far does it go down the stream?

52. A boat whose rate of sailing in still water is 6 miles an hour, goes a miles down the stream in one half the time it requires to return. What is the rate of the current?

A can do a piece of work in 5 days and B can do it in 8 days. In what time can they do it working together? the number of days required,

Let

53. A can do and C in 6 days. together?

x = 31/13

a piece of work in 4 days, B in 5 days, In what time can they do it working

54. Two pipes can fill a cistern in 5 hours, and one alone can fill it in 8 hours. In what time can the other fill it?

55. There are 3 pipes connected with a reservoir: the first can fill it in 10 hours, the second in 8 hours, and the third can empty it in 6 hours. In what time will it be filled if all run together?

56. A can do a piece of work in 21 days, working 8 hours a day, and B can do it in 3 days, working 9 hours a day. In how many days, working 6 hours a day, can they together do it?

57. A has $800 and B has as much. must A give to B in order that A may have as B?

How much

as much

58. B has $300 more than A, and earns $5 a day; A earns $8 a day. How much must each earn in order that they may have the same sum ?

59. A man has two horses, and a saddle worth $10. The first horse and saddle are worth 3/4 as much as the second horse, and the second horse and saddle 29/20 as much as the first horse. Required the value of each horse.

60. A general draws up his army in the form of a square, and has 140 men over; he then endeavors to increase each side by 2 men, and finds he lacks 24 men to complete the square. How many men has he?

61. A is 15 years old and B is 30. will of A's age equal, of B's?

2

In how many years

62. A man loaned $1500, a part at 5% and the rest at 6%; his annual interest was $81. How much did he loan at 5% ?

63. How many pounds of sugar at 10 cents a pound must be mixed with 25 pounds worth 8 cents a pound to make a sugar worth 83 cents a pound?

64. A man agreed to work one year for $180 and houserent free. At the expiration of 9 months he was deprived of work by sickness for the rest of the year, but retained the house; he was paid $120 in money for his services. What was the house-rent valued at ?

65. What time of day is it when 2/3 of the time past noon equals 3/4 of the time to midnight?

Suggestion.-Let x = the number of hours past noon.

66. At what time of day is the time past noon / of the time past midnight?

67. At what time between 4 and 5 o'clock are the minute and hour hands of a clock together? At right angles? Opposite each other?

Suggestion.—At 4 o'clock the minute-hand must gain 20 minutespaces, 5 or 35 minute-spaces, and 50 minute-spaces respectively.

68. A son's age is 25 that of his father's, but in 16 years it will be / that of the father's. What are the ages now?

69. A and B together can do a piece of work in 24 days, A and C in 30 days, B and C in 40 days. In what time can they do it all working together?

70. A boy spent 11⁄2 his money and 1/2 a cent; then, 11⁄2 of the remainder and 1/2 a cent; then, 12 of what then remained and 1⁄2 a cent, and had 9 cents remaining. How much money had he at first?

Simple Equations of Two Unknown Quantities.

Definitions and Principles.

161. A single equation of two unknown quantities may be satisfied by any number of values of the unknown quantities, and is therefore said to be Indeterminate.

Thus, 2xy= 10 is true when x=6 and y = 2; when x and y = 4; when x = 8 and y = 6; etc.

162. Two simultaneous simple equations of two unknown quantities can be satisfied by only one pair of values of the unknown quantities.

Thus, x+2y=7 and 5x-3y=9 are satisfied only by x3 and y = 2.

163. Generally, when there are as many independent simultaneous equations given as there are unknown quantities involved, their solution can be effected by elimination. (See page 96.)

164. There are three easy methods of elimination :

1. By addition and subtraction. 2. By substitution. 3. By comparison.

Note. For elimination by addition and subtraction, see pages 59 and 96.