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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 xa and the person's age a years in future will be x + a. An example will illustrate.

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
x + 30 = 2(x + 10)
x + 30 = 2x + 20
x = 10
Hence, Steve is 10 years old, and the answer is (C).


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