Typically, in these problems, we start by letting x be a person's current age and then the person's age a years ago will be x Â–â€“ a and the person's age a years in future will be x + a. An example will illustrate.
Example:
John is 20 years older than Steve. In 10 years, Steve's age will be half that of John's. What is Steve's age?
(A) 2
(B) 8
(C) 10
(D) 20
(E) 25
Steve's age is the most unknown quantity. So we let x = Steve's age and then x + 20 is John's age. Ten years from now, Steve and John's ages will be x + 10 and x + 30, respectively.
Summarizing this information in a table yields
Age now | Age in 10 years | |
Steve | x | x + 10 |
John | x + 20 | x + 30 |
Since "in 10 years, Steve's age will be half that of John's," we get
$\frac{1}{2}$ ( x + 30) = x + 10
x + 30 = 2(x + 10)
x + 30 = 2x + 20
x = 10
Hence, Steve is 10 years old, and the answer is (C).