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.

1. Answer :

The sum of x and 5.

x is increased by 5.

2. Answer :

The difference of y and 9.

9 less than y.

3. Answer :

2 times m.

The product of 2 and m. 

4. Answer :

a divided by 6.

The quotient of a and 6.

5. Answer : 

m represents the number of hours that Thomas reads.

Think : m groups of 25 pages. 

25 · m or 25m

6. Answer : 

k represents Kay's age. 

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

k - 2

7. Answer : 

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.

8. Answer : 

x + y = 7 + 4

= 11

9. Answer : 

y/z = 4/2

= 2

10. Answer : 

xyz = 7 · 4 · 2

= 56

11. Answer : 

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.