Problem Solving

sanju09 wrote:Five years ago, Beth's age was three times that of Amy. Ten years ago, Beth's age was one half that of Chelsea. If C represents Chelsea's current age, which of the following represents Amy's current age?
(A) C/6 + 5
(B) 2 C
(C) (C - 10)/3
(D) 3 C - 5
(E) (5/3) C - 10

Let's let a, b, and c represent the current ages of Amy, Beth, and Chelsea, respectively. We can create the equations:

b - 5 = 3(a - 5)

b - 5 = 3a - 15

b = 3a - 10

and

b - 10 = (1/2)(c - 10)

2b - 20 = c - 10

2b - 10 = c

Substituting, we have:

2(3a - 10) - 10 = c

6a - 20 - 10 = c

6a - 30 = c

a - 5 = c/6

a = c/6 + 5

Answer: A