Question #c7676

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Answer 1 · 2017-12-14T23:11:46

$16$ (years)

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

$J-10 = 0.5(S-10)$

$=> 12J - 120 = 6S - 60$

$=> 12J - 60 = 6S$

and

$J+20=6/7(S+20)$

$=> 7J + 140 = 6S + 120$

$=> 7J + 20 = 6S$

Subtract the bottom equality from the top to get

$5J - 80 = 0$

$=> J = 16$

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