TRANSLATING PHRASES TO ALGEBRAIC EXPRESSIONS OR EQUATIONS WORKSHEET

Problem 1 :

Write each verbal phrase as an algebraic expression.

1) the sum of 8 and t

2) the quotient of g and 15

3) the product of 5 and b

4) the difference of 32 and x 

Solution

Problem 2 :

5) Eight more than x

6) Six less than p

7) 14 less than f

8) p more than 10

9) 3 more runs than Pirates scored

10) 12 less than some number

Solution

Translate the verbal phrase to algebraic equations.

PART B

Problem 3 :

Arthur is 8 years younger than Janet

Solution

Problem 4 :

Kelly’s test score is 6 points higher than Mike’s

Solution

Problem 5 :

The product of 7 and b is equal to 63.

Solution

Problem 6 :

The quotient of x and 7 is equal to 13.

Solution

Problem 7 :

The sum of r and 45 is 79.

Solution

Problem 8 :

The quotient of x and 7 is equal to 13.

Solution

Problem 9 :

In a cross-country race you run at a steady rate of 7 minutes per mile. After 21 minutes, you finish in fourth place. How long is the race?

Solution

Problem 10 :

For a science project, you record the high temperature each day. The high temperature on Day 1 was 6° less than on Day 4 and 4° less than on Day 10. The high temperature on Day 10 was 62°F. What was the high temperature on Day 1?

Solution

Problem 11 :

Students and faculty raised $6042 for band uniforms. The faculty raised $1780. Write an equation you can use to find the amount a raised by the students.

Solution

Problem 12 :

Together you and a friend have $52. Your friend has $28. Write an equation you can use to find how much money you have.

Solution

Problem 12 :

You hit a golf ball 90 yards. It travels three-fourths of the distance to the hole. Write an equation you can use to find the distance d from the tee to the hole.

Problem 13 :

Which expression is equivalent to 8(x + 3)?

a) 8x + 3      b) 8x + 24     c) 8x + 11      d) x + 24

Solution

Problem 14 :

Evaluate the expression when a = 7

a)   6 + a       b)  a − 4        c)  4a      d) 35/a

Solution

PART C

Translate the verbal phrase to algebraic expressions.

1) Six less than twice a number x is four        Solution

2) Four more than the product of 2 and a       Solution

3) Nine times a number decreased by four     Solution

4) Seven more than the quotient of a number and 2 is 10          Solution

5) One less than the product of four and a number is 11.      Solution

6) Ten more than the quotient of a number and 3 is 12.      Solution

7) The sum of 9 and the quotient of x and 7 is 11.      Solution

8) The product of 8 and the difference of n and 3.    Solution

9) Two less than the quotient of 15 and a number.    Solution

10) Five times the sum of six and some number.    Solution

11) The quotient of 7 and d decreased by 9.   Solution

12) Twice the difference of y and three   Solution

13) The difference of 9 and the quotient of s and –4   Solution

14) The sum of 5 and product of 7 and x   Solution

15) Three more than quotient of 5 and a    Solution

16) The product of 4 and the difference of x and 3     Solution

Problem 17 :

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.

Solution

Problem 18 :

While catching fire flies, 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 fire flies you and your friend caught together.

b. The competition ends after 5 minutes. Who has more fire flies?

Solution

Problem 19 :

A square wrestling mat has a perimeter of (12x − 32) feet. Write an expression that represents the side length of the mat (in feet).

Solution

Problem 20 :

A table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of each rectangular leaf is 3 feet. The extended table is rectangular with an area of (18 + 6x) square feet.

a. Make a diagram of the table and leaves.

b. Write an expression that represents the length of the extended table. What does x represent?

Solution

PART C ANSWERS

1) 2x - 6 = 4 2) 4 + 2a 3) 9x - 4 4) (x/2) + 7 = 10 5) 4x - 1 = 11 6) (x/3) + 10 = 12 7) (x/7) + 9 = 11 8) 8(n - 3)

9) (15/x) - 2 10) 5(x + 6) 11) 7/(d - 9) 12) 2(y - 3) 13) 9 + (s/4) 14) 5 + 7x 15) 3 + (5/a) 16) 4(x - 3) 17)  Total amount in both accounts is 55w + 145. 18)  a)  7m + 19 b)  You have more fire flies. 19)  (3x - 8) feet 20)   b)   length of table is 6 + 2x.