# VARIABLES AND EXPRESSIONS WORKSHEET

Question 1 -4 : Write each algebraic expression in words in two ways.

1) x + 5

2) y - 9

3) 2 · m

4) a ÷ 6

5) Thomas reads 22 pages per hour. Write an expression for the number of pages he reads in m hours.

6) John is 2 years younger than Kay, who is k years old. Write an expression for John’s age

7) Peter runs a mile in 15 minutes. Write an expression for the number of miles that Peter runs in y minutes.

Questions 8-10 : Evaluate each expression for x = 7, y = 4, and z = 2.

8) x + y

9) y/z

10) xyz

11) Approximately ten 25-ounce plastic drink bottles must be recycled to produce 1 square foot of carpet.

a. Write an expression for the number of bottles needed to make x square feet of carpet.

b. Find the number of bottles needed to make 20, 50, and 200 square feet of carpet.

The sum of x and 5.

x is increased by 5.

The difference of y and 9.

9 less than y.

2 times m.

The product of 2 and m.

a divided by 6.

The quotient of a and 6.

m represents the number of hours that Thomas reads.

Think : m groups of 25 pages.

25 · m or 25m

k represents Kay's age.

Think : 'younger than' means 'less than'.

k - 2

y represents the total time Peter runs.

Think : How many groups of 15 are in y.

y ÷ 15 or y/15

Evaluate each expression for x = 7, y = 4, and z = 2.

x + y = 7 + 4

= 11

y/z = 4/2

= 2

xyz = 7 · 4 · 2

= 56

a. The expression 10x models the number of bottles needed to make x square feet of carpet.

b. Evaluate 10x for x = 20, 50, and 200.

x = 20 ----> 10(20) = 200

x = 50 ----> 10(50) = 500

x = 200 ----> 10(200) = 2000

To make 20 ft2 of carpet, 200 bottles are needed.

To make 50 ft2 of carpet, 500 bottles are needed.

To make 200 ft2 of carpet, 2000 bottles are needed.

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