1216. Slate Problems.

1. A certain number is multiplied by 3; 7 is subtracted from the product; the remainder is divided by 16, giving a quotient of 3. What is the number?

2. Three-eighths of what number is 60 less than the number itself?

3. Four persons are of the same age. If the first were age older, the second of his age older, the third older, and the fourth

his

would be 99 years.

4. A man spends

of

of his age

of his age older, the sum of their ages

What is the age of each?

of his earnings on board and lodging, on clothing and repairs, and on sundries. At the end of the year he has $280 left. What are his yearly earnings?

5. A boy gave

of his marbles to one companion, and of them to another. He then bought as many as he originally had, and had 4 marbles more than he had at first. How many did he have at first?

6. A father's age and a son's age added together amount to 138 years. Twelve years ago the father was twice as old as the

son.

How old is each now?

Let x = son's age 12 years ago.

How many

7. John has 80 cents, and William has 60 cents.

cents will William have to give John so that the latter shall have 21 times as much money as the former?

After William gives John x cents, the former has (60 — x) cents, and the latter has (80+ x) cents.

8. In how many years will a man, now 25, be double the age of his 11-year-old brother?

Let x=

number of years. 25+ x and 11 + x =

ages after x years.

9. A man has a cask of 60 gallons' capacity. He draws off one-fourth of its contents, and then fills it. If it takes 24 gallons to fill it, how many gallons did the cask originally contain?

10. A number is divided by 3, and 40 is subtracted from the quotient, leaving a remainder of 104. What is the number?

11. The difference between two numbers is 430. When the greater is divided by the less, the quotient is 4, and the remainder is 76. What are the numbers?

12. A person pays $103 with 29 $2 and $5 bills. How many are there of each denomination?

13. A father is 30 years older than his daughter. In 4 years, his age will be four times her age. What are their present ages? present ages. x +4 and x + 34 = ages 4 years later.

x and x + 30

=

14. The product of two numbers is 180. If the smaller number be increased by 3, the product of the two numbers will be 225. What are the numbers?

15. A man's wages are $1 per day more than his son's. For 33 days' work, the father receives $12 more than the son earns in 40 days. Find the wages of each.

16. The sum of two numbers is 47; their difference is 17. What are the numbers?

17. A mother is 41 years old. many years will the son's age be

Her son's age is 5. In how of his mother's?

TWO UNKNOWN QUANTITIES.

1217. Preliminary Problems.

1. I paid a dollar for two 25 balls and five bats. How much

did I pay apiece for the latter?

2. When three times one number is added to five times another, the sum is 84. If the second number is 12, what is the first number?

3. A girl paid 75 for coffee. The coffee cost 20 the tea per pound?

pound of tea and 2 pounds of per pound. What was the price of

4. A man sold pigs at $5 each and lambs at $8 each, receivHow many pigs did he sell?

ing $42. He sold 4 lambs.

5. Four times a father's age amounts to 180 years. the father's age?

age added to twice his daughter's The girl is 10 years old. What is

6. Eight peaches and seven pears cost 44. The peaches cost 2 each. What is the cost of a pear?

7. Two pieces of cloth and eleven pieces of silk contain 152 yards. There are 10 yards in each piece of cloth. How many yards in each piece of silk?

8. Two-thirds of a yard of linen and three-fourths of a yard of lace cost 40. The price of the lace is 32 a yard. Find the price of the linen.

9. Three and one-half times one number added to four and one-third times a second number equals 60. The second number is 9. What is the first number?

10. 32x+50y=2,600. y = 20.

1219. A boy gave 17 for 3 lemons and 4 oranges, another boy paid 25 for 3 lemons and 8 oranges. How much did the lemons cost apiece?

How much apiece was paid for the lemons?

11. If 3 coats and 14 vests cost $78, and 2 coats and 14 vests, at the same rate, cost $66, how much does 1 coat cost? What is the price of a vest?

First multiply (2) by 2, making it 4x+6y=50. Why?

13. What is the value of x in equation (1), when the value found for y is substituted therein? Substitute the same value for y in equation (2) and find the value of x.

1220. Find the values of x and y in the following equations: