# Find age of John

Ten years before Alice's age is 4 times John's age. Ten years later, Alice's age is 2 times John's age. How old is John?

John is

20. Ten years earlier, John was 10 and Alice was 40. Ten years from now, Alice will be 60 and John will be 30.

John is

20

Equations

Let age of Alice now be a and age of John now be j. Therefore 10 years ago,
$$a-10=4(j-10)$$

and

After 10 years
$$a+10=2(j+10)$$

Solving two equations we get

j = 20 and a = 50. So today age of John is 20 years.

This proves that this is a $6^{th}$ grade math problem.