Translating Equations and Word Problems

One - third of the sum of a number and 24 is equivalent to 10.  

• 1⁄3(x + 24) = 10 

• 1⁄3x + 24 = 10 

• 1⁄3(x - 24) = 10 

• 1⁄3x + 10 = 24 

Twice the difference of a number and 16 is equivalent to 28.

• 2x + 16 = 28

• 2x - 16 = 28 

• 2(x + 16) = 28 

• 2(x - 16) = 28

Three-halves the difference of a number of 22 is equivalent to 45.  

• 3⁄2(x + 22) = 45

• 3⁄2x - 22 = 45

• 3⁄2(x - 22) = 45

• 3⁄2x + 22 = 45

A rectangle has a perimeter of 70 feet. Its length is five more than twice its width. Which equation can be used to determine the width of the rectangle?

• 2x + 5 = 70 

• 3x + 5 = 70 

• 6x + 10 = 70 

• 5x + 2 = 70

A rectangle has a perimeter of 100 inches. Its length is one more than two and a half times its width. Which equation can be used to determine the width of the rectangle? 

• 2.5x + 1 = 100 

• 3.5x + 1 = 100 

• 5x + 2 = 100 

• 7x + 2 = 100 

Lexi's Great Grandmother is twelve years older than six times her age. The sum of their ages is 117. Which equation can be used to determine Lexi's age?

• 6x - 12 = 117

• 7x - 12 = 117

• 7x + 12 = 117

• 6x + 12 = 117

The sum of three consecutive integers is 147. Which equation can be used to find the first integer?

• 3x = 147

• x + 3 = 147 

• x + x + 1 + x + 2 = 147 

• x ⋅ x ⋅ x = 147 

The sum of four consecutive odd integers is equivalent to 232.  Which equation can be used to find the first integer? 

• 4x = 232 

• x + x + 2 + x + 4 + x + 6 = 232 

• x + x + 1 + x + 3 + x + 5 = 232 

• x ⋅ x ⋅ x ⋅ x = 232 

Five times a number is equivalent to thirty-two less than nine time the same number. 

• 5x - 32 = 9x 

• 5x = 9x - 32 

• 5x = 9x + 32 

• 5x - 9x = 32 

Eight less than three times a number is equivalent to ten more than one and half times the same number. 

• 3x - 8 = 0.5x + 10 

• 8 - 3x = 1.5x + 10 

• 3x - 8 = 1.5x + 10

• 8 - 3x = 0.5x + 10