Age Problems
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€“ a and the person's age a years in future will be x + a.
An example will illustrate.
Since "in 10 years, Steve's age will be half that of John's," we get
x + 30 = 2(x + 10)
x + 30 = 2x + 20
x = 10
Hence, Steve is 10 years old, and the answer is (C).
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?

2

8

10

20

25
Solution
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 