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Question #cf87c

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Nov 14, 2016

Jason is $15$ $15$

Explanation:

Let
$XXX J$ $color(white)("XXX")J$ be Jason's age
$XXX S$ $color(white)("XXX")S$ be Jason's sister's age
$XXX M$ $color(white)("XXX")M$ be Jason's mother's age

We are told
[1] $XXX J = S + 6$ $color(white)("XXX")J=S+6$
[2] $XXX M = J + S + 15$ $color(white)("XXX")M=J+S+15$
[3] $XXX M = 39$ $color(white)("XXX")M=39$

Combining [2] and [3], we have
[4] $XXX J + S + 15 = 39$ $color(white)("XXX")J+S+15=39$

Using [1], we can substitute $S + 6$ $S+6$ for $J$ $J$ in [4]
[5] $XXX S + 6 + S + 15 = 39$ $color(white)("XXX")S+6+S+15=39$

Simplifying
[6] $XXX 2 S + 21 = 39$ $color(white)("XXX")2S+21=39$

[7] $XXX 2 S = 18$ $color(white)("XXX")2S=18$

[8] $XXX S = 9$ $color(white)("XXX")S=9$

Using [8], we can substituting $9$ $9$ for $S$ $S$ in [1]
[9] $XXX J = 9 + 6 = 15$ $color(white)("XXX")J=9+6 =15$

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