Question #c7676

Dec 14, 2017

$16$ (years)

Explanation:

Let $J$ equal June's current age and $S$ be June's sister's current age. Now we begin:

$J - 10 = 0.5 \left(S - 10\right)$

$\implies 12 J - 120 = 6 S - 60$

$\implies 12 J - 60 = 6 S$

and

$J + 20 = \frac{6}{7} \left(S + 20\right)$

$\implies 7 J + 140 = 6 S + 120$

$\implies 7 J + 20 = 6 S$

Subtract the bottom equality from the top to get

$5 J - 80 = 0$

$\implies J = 16$

You can check that this answer is correct by plugging back into the initial equations/relationships that were given.