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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.

 
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?

  1. 2
  2. 8
  3. 10
  4. 20
  5. 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
 
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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