21. How do you tell whether one negative number is greater or less than another one? Illustrate in the case of the numbers -11

and -2.

22. A frog by slow degrees jumps out of a well; it jumps upward 3 feet the first day and falls back 2 feet; 5 feet the second day and falls back 3 feet; 4 feet the third day and falls back 4 feet. How far is it from the bottom of the well at the end of the third day? Work by using negative numbers.

State the value of each of the following expressions.

SUPPLEMENTARY EXERCISES ON § 27

Carry out the following indicated operations.

21. Solve by inspection each of the following equations.

12. 72 x÷(-36 x).

22. Find the value of each of the following expressions for the values written beside them.

SUPPLEMENTARY EXERCISES ON § 36

Perform the following indicated subtractions.

1. 6x+4y

2x+7 y

2. 3x-2y
-3x-2y

3.

ab+2 5 ab+7

4. From a+3 b take 10 a-9 b.

5. Take 3 x2y-4 from 10 x2y+9.

6. Take -4 a+9 b+7 c from 10 a-3 b+14 c.

7. Subtract a3+3 a2b+3 ab2+b3 from a3-3 a2b+3 ab2—b3.

8. From 3 xy+7 z−9 k take 8 xy+4 k−9 z.

9. From the sum of 3 a2+4 a3+2 a−7 aa+1 and 3+2 a2-4 a+ a3-2 a1 take 6 a3+2 a−a2-3 a1-9.

10. How much larger is 6 x2+9 x+10 than 3 x2-2 x-5?

SUPPLEMENTARY EXERCISES ON § 37

1. State the four Axioms. Why is it that they are very useful in solving equations?

Solve the following equations and check each one.

18. A rectangular field is three times as long as wide. The fence surrounding the field is 144 yards in length. Find the length and width of the field.

19. What is the number which increased by of itself equals 70? 20. The sum of three consecutive numbers is 93. What are the numbers?

21. If a number is increased by 42, the result is 45 more than twice the number.

22. An employer on pay day wishes to have $35 in change. He wishes to have as many quarter dollars as nickels, and twice as many dimes as nickels. How many must he get of each?

23. There are two rows of crosswise seats in a street car, and two long lengthwise seats. If each crosswise seat will hold two persons and each lengthwise seat will hold eight persons, how many crosswise seats must there be in order that the seating capacity of the car shall be 44?

24. If a quantity of grape juice is bottled in 5 bottles, 1 gill remains, but if it is bottled in 2 bottles twice as large, 4 gills remain. How many gills does each bottle contain?

25. A cask is full; 7 gallons are drawn from it and it is now half empty. How many gallons does the cask contain?

26. A person's income is $1290; of his capital is invested at 4% and the remainder at 2%. Find the capital.

27. A man invests $1000, part at 3% and part at 4%. The annual income from the investment is $34. How has he divided the money?

28. 20 per cent of the pupils in a class drop out while 13 new pupils enter. The class is now found to be increased by its original number. How many were there at first?

29. Solve the equation 3(4) - x)2 - 2(x+3) C (x+2)(x-2)+1.

A

FIG. 93.

=

(2 x

3)2

30. The figure represents a rectangle, ABCD, within which are placed two equal squares. The border (shaded) is everywhere 3 inches wide. In order that the area of the border be 159 square inches, B what must be the length of one side of each square?