Age Problem

Ella is 6 years younger than Amanda.  Zoe is twice as old as Amanda.  The total of their ages is 54.  Which equation can be used to find Amanda's age?
A.)  x + (x - 6) + 2(x - 6) = 54
B.)  x - 6x + (x + 2) = 54
C.)  x - 6 + 2x = 54
D.)  x + (x - 6) + 2x = 54
E.)  2(x + 6) + (x + 6) + x = 54

---

Amanda's age is being used to describe the other two, Ella and Zoe.  Therefore, let the variable, x, represent Amanda's age.  In many word problems, whatever comes after the word "than" is usually what you should let the variable represent.

x = Amanda's age
x - 6 = Ella's age   {Ella is 6 years younger than Amanda}
2x = Zoe's age   {Zoe is twice as old as Amanda}

The total of their ages is 54.

x + (x - 6) + 2x = 54   {added the ages and set equal to 54}

Answer is D.)

Ask Algebra House