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.

12. The original price of a cowboy hat is d dollars. You use a coupon and buy the hat for (d − 2) dollars. You decorate the hat and sell it for (2d − 4) dollars.

Write an expression that represents your earnings from buying and selling the hat. Interpret the expression.

13. You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and (45w + 25) dollars in your checking account. Write an expression that represents the total in both accounts.

14. While catching fi refl ies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fire flies and your friend has (4m + 6) fire flies.

a. Write an expression that represents the number of fi refl ies you and your friend caught together.

b. The competition ends after 5 minutes. Who has more fi refl ies?

15. The expression 17n + 11 represents the perimeter (in feet) of the triangle. Write an expression that represents the measure of the third side.

Detailed Solutions and Answers

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.

12. Answer : 

Cost price = (d − 2) dollars

Selling price = (2d − 4) dollars

Earning = Selling price - cost price

= (2d - 4) - (d - 2)

= 2d - 4 - d + 2

= d - 2

You earn (d − 2) dollars. You also paid (d − 2) dollars, so you doubled your money by selling the hat for twice as much as you paid for it.

13. Answer : 

Amount in savings account = 10w + 120

Amount in checking account = 45w + 25

Total amount = 10w + 120 + 45w + 25

= 10w + 45w + 120 + 25

= 55 w + 145

So, the required total amount is 55 w + 145.

14. Answer : 

Number of fireflies you have = (3m + 13)

Number of fire flies your friend has =  (4m + 6)

a) total number of fire flies = 3m + 13 + 4m + 6

= 3m + 4m + 13 + 6

= 7m + 19

b) Number of fire flies you have after 5 minutes = 3(5) + 13

= 15 + 13

= 28 fireflies

Number of fire flies your friend has after 5 minutes = 4(5) + 6

= 20 + 6

= 26 fireflies

So, you have more number of fire flies.

15. Answer : 

Perimeter = 17n + 11

Sum of all sides = perimeter

5n + 6 + 4n + 5 + third side = 17n + 11

9n + 11 + Third side = 17n + 11

Third side = 17n + 11 - 9n - 11

= 17n - 9n

= 8n