# Milene is 3 years older than john. In 7 years, john's age will be 6/7 of Milene's age. How old they are now?

Nov 6, 2016

John is 11 years old and Milene is 14 years old.

#### Explanation:

Let $m$ = Milene's current age, and let $j$ = John's current age.

Equation A: $m = j + 3$
Equation B: $j + 7 = \frac{6}{7} \left(m + 7\right)$

Substituting equation A into equation B:
$j + 7 = \frac{6}{7} \left(\left(j + 3\right) + 7\right)$
$j + 7 = \frac{6}{7} \left(j + 10\right)$
$j + 7 = \frac{6}{7} j + \frac{60}{7}$
$\frac{1}{7} j = \frac{11}{7}$
$j = 11$

Substituting j=11 into equation A:
$m = 11 + 3$
$m = 14$