Solving Linear Equation 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

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

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

For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

• 4x=472

• 9x=472

• 4+9x=472

• 4+x=472

After paying $5.12 for a salad, Kamauri has $27.10. How much money did he have before buying the salad?

• n + $5.12 = $27.10

• n - $5.12 = $27.10

• n - $5.12 = -$27.10

• $5.12 - n = $27.10

Which equation would describe "two times a number plus five equals 15"?

• x + 5 = 15

• 2x + 5=15

• x + 2(5) = 15

• 2(x + 5) = 15