TRANSLATING PHRASES INTO EQUATIONS AND INEQUALITIES WORKSHEET

Translating Sentence into Equations

1)  The sum of a number and 10 is 15.          Solution

2)  28 decreased by a number is18.            Solution

3)  The product of a number and 25 is 100.      Solution

4)  The quotient of 49 and a number is 7.          Solution

5)  The area of the rectangle is less than or equal to 50 meters. Write an inequality for the area using the dimensions in the diagram.

Solution

6)  The distance between your house and the amusement park s 110 miles. Your rate of travel is 55 miles per hour. Use the formula d = rt to write an equation. Use mental math to solve the equation for the time you spend traveling.

Solution

7)  Translate into mathematical symbols “the difference of a number and 4 is 10”. Let n represent the number.

A)  n - 4 = 10    B)  4 - n = 10    C)  10 - 4 = n    D)  10 – n = 4

Solution

8)  MULTIPLE CHOICE   Which is the correct algebraic translation of “Howard’s hourly wage h is $2 greater them Marla’s hourly wage m?”

A)  h < m+2   B)  h = m+2   C)  m = h+2   D)  h > m+2

Solution

9)  Find the volume of a cube when each side x is 10 feet.      Solution

10)  The rectangle shown at the right has an area of 32 square units. Write an equation to find the width x.

Solution

Translating Phrases into Equations and Inequalities

1)  The sum of 20 and a number is 30.   Solution

2)  A number increased by 10 is greater than or equal to 44.    Solution

3)  18 decreased by a number is 6.     Solution

4)  35 is less than the difference of 21 and a number.      Solution

5)  The product of 13 and a number is greater than 60.    Solution

6)  7 times a number is 56.    Solution

7)  A number divided by 22 is less than 3.       Solution

8)  The quotient of 35 and a number is 7.       Solution

9)  A number x divided by 9 is less than 17.       Solution

10)  The product of 10 and a number x is 50.       Solution

11)  A number y plus 10 is greater than or equal to 57.        Solution

12)  A number y minus 6 is 15.        Solution

Problem 13 :

Ten servers decorate 25 tables for a wedding. Each table is decorated as shown. Let c be the total number of white and purple candles. Which equation can you use to find c ?

a) c = 25 + (4 × 6)       b) c = 25(4 + 6)      c) c = 10(25 + 4 + 6)    d)  c = 10(4 + 6)

Solution

Problem 14 :

In a magic square, the sum of the numbers in each row, column, and diagonal is the same. Write and solve equations to find the values of a, b, and c.

Solution

Problem 15 :

You are fishing and are allowed to catch at most 3 striped bass. Each striped bass must be no less than 18 inches long.

Solution

Problem 16 :

• A bus ride costs $1.50.
• A 30-day bus pass costs $36.

Write an inequality to represent the number of bus rides you would need to take for the bus pass to be a better deal.

Solution

Problem 17 :

Fifty people are seated in a movie theater. The maximum capacity of the theater is 425 people. Write an inequality to represent the number of additional people who can still be seated.

Solution

Answers :