Translating Algebraic Equations and Word Problems

Rachel swims 3 laps each minute.  Write an equation to show the relationship between number of laps (n) and time (t).

• 3n = t

• 3 + n = t

• 3t = n

• 3 + t = n

Five less than twice a number is equivalent to 47. 

• 5 - 2x = 47 

• 2x - 5 = 47 

• 5x - 2 = 47 

• 2 - 5x = 47 

10 less that half a number is equivalent to 8.  

• 10 - 1⁄2x = 8 

• 1⁄2x + 10 = 8

• 1⁄2x - 10 = 8

• 10x - 0.5 = 8

Justin is purchasing a new iPhone.  The sales clerk says that if he pays $100 now his monthly payments will be $25 and his total cost will be $600.  Which equation can be used to determine how many months Justin will be paying for his phone? 

• 25x + 100 = 600

• 25x - 100 = 600 

• 600 - 100x = 25

• 600 + 25x = 100 

A gymnastics center charges a $60 registration fee and $15 per class. Olivia registers to take a class and pays a total of $210. Which equation can be used to determine how many classes Olivia signed up for?

• 60 - 15x = 210 

• 15x - 60 = 210

• 15x + 60 = 210 

• 210 + 15x = 60 

Three times the sum of a number and 7 is equivalent to 57. 

• 3x + 7 = 57 

• 3(x + 7) = 57

• 7x + 3 = 57 

• 7(x + 3) = 57

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