7. The difference between three times a certain number and nine times the same number is 66. What is the number?

8. $27,000 is divided among three children, the second of whom receives twice as much as the first, and the third of whom receives three times as much as the second. What is the share of each?

9. The sum of two numbers is 72, and the greater is 5 times the other. What are the numbers?

10. John, Henry, and James have 54 marbles. Henry has twice as many as John, and James has as many as the other two. How many has each?

11. The sum of the ages of mother and daughter is 42 years. What is the age of each, if the mother's age is six times that of her daughter?

12. A man paid $96 for an equal number of hats and coats, paying $2 apiece for the former and $10 apiece for the latter. How many of each did he buy?

13. Divide 41 into four parts, the first being twice the secon‹l, the second three times the third, and the third four times the fourth..

(Let x = the fourth.)

14. The sum of three numbers is 180. The first is double the second, and the third is three times as large as the sum of the other two. What are the numbers?

15. Mr. Smith paid 81 cents for sugar and flour, the same quantity of each. For the sugar he gave 5¢ per pound, and for the flour 4 per pound. How many pounds of each did he buy?

16. The length of a rectangular field is 24 rods, its breadth is x rods, its area is 456 square rods. Find the value of x.

17. It takes 340 feet of fence to enclose a square lot. What are the dimensions of the lot?

18. Mrs. B. divides $120 between her son and her daughter. She gives the latter twice as much as she gives the former. What is the share of each?

19. The earnings of a man and his son during January amounted to $175, both having worked the same number of days. The father's wages were $4 per day, and the son's wages were $3 per day. How many days did they work?

20. The sum of $240 is divided among four children, two boys and two girls. Find the share of each, if each girl's share is double that of each boy.

21. A man worked twice as many days as his son. Their combined earnings amounted to $165. Find the number of days each worked, if the father earned $4 per day and the son threefourths as much per day.

22. A boy's bank contains 78 in dimes, nickels, and cents. There are twice as many nickels as there are dimes, and three times as many cents as there are nickels. How many are there of each?

23. I paid 75 more for a roll of 15-cent ribbon than I did for a roll of 12-cent ribbon of the same length. How many

yards did each roll contain?

24. A rectangular field whose length is four times its breadth requires 250 rods of fence to enclose it. What are the dimensions of the field? (Make diagram.)

25. A girl paid 60 cents for a speller and a reader, the cost of the former being one-third that of the latter. Find the cost of each.

26. The sum of two numbers is 72, and the smaller is onefifth of the other. What are the numbers?

27. Mary, Susan, and Jane have 54 hickory nuts. Susan has one-half as many as Mary, and Jane has as many as the other two. How many has each?

5. If of a number is 30, what is the number?

6. One-half a number added to 4 of the same number equals what fraction of the number?

7. One-half a number added to of the same number equals 30. What is the number?

8. One-third of a number + one-sixth of the number fraction of the number?

9. One-third of a number added to of the number fraction of the number?

10. x+4x=what fraction of x? +=?

X х
3 4

852. When x = 32, find the value of three-fourths of x;

3x

i.e.,

4

When (3x divided by 4) = 24, what is the value of

3x 4

4 z
5

Given the equation 20; by what whole number can we

multiply the first member to get rid of the fraction? If we multiply one member of an equation by any number, what must we do to the second member in order to preserve the equality?

Find the value of the unknown quantity (x).

In each of the following equations, multiply both members by the least common denominator of the fractions.

1. The sum of two numbers is 90, and the smaller number is one-fifth of the larger one.

What are the numbers?

(x + 1 = 90.)

2. Divide 100 into two parts, one of which shall be 21 times the other.

3. After losing of his money, a man has $714. How many dollars had he at first?

4. A horse was sold for $240, the seller thereby gaining onethird of what he originally paid for it. How much did he pay for it?

5. One-half of a number added to one-fourth of the same number equals 663. What is the number?

6. The difference between of a number and of the same number is 15. Find the number.

7. One number is of another. Their sum is 55. What are the numbers?

8. Find a fraction equivalent to 7, the sum of its numerator and its denominator being 60.

9. Find a fraction equivalent to, the difference between its numerator and its denominator being 24.