John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age is 35, and John's age will be twice Mary's current age. How do you find their ages now?

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John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age is 35, and John's age will be twice Mary's current age. How do you find their ages now?

1 Answer

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Answer 1 · 2015-09-24T20:17:15

John is 20 and Mary is 15 now.

Explanation:

Let $J$ $J$ and $M$ $M$ be the present age of John and Mary respectively:

$J = M + 5$ $J=M+5$
$2 (J + 10) - (M + 10) = 35$ $2(J+10)-(M+10)=35$
$2 (M + 5 + 10) - (M + 10) = 35$ $2(M+5+10)-(M+10)=35$
$2 M + 30 - M - 10 = 35$ $2M+30-M-10=35$
$M = 15$ $M=15$
$J = 20$ $J=20$

Check:
$2 \cdot 30 - 25 = 35$ $2*30-25=35$
Also in ten years John's age will be twice Mary's current age:
$30 = 2 \cdot 15$ $30=2*15$

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John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age is 35, and John's age will be twice Mary's current age. How do you find their ages now?

1 Answer

Explanation:

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