A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

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A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

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Answer 1 · 2016-08-11T21:30:39

boy is $9$ $9$ years old
sister is $12$ $12$ years old

Explanation:

Let the age of boy be $b$ $b$ and the age of his sister be $s$ $s$
So given $s = b + 3$ $s=b+3$
and $b - 3 = \frac{2}{3} (s - 3)$ $b-3=2/3(s-3)$
or
$3 (b - 3) = 2 (s - 3)$ $3(b-3)=2(s-3)$
by putting $s = b + 3$ $s=b+3$ in the equation $3 (b - 3) = 2 (s - 3)$ $3(b-3)=2(s-3)$
We get
$3 (b - 3) = 2 (b + 3 - 3)$ $3(b-3)=2(b+3-3)$
$3 b - 9 = 2 (b + 0)$ $3b-9=2(b+0)$
or
$3 b - 9 = 2 b$ $3b-9=2b$
or
$3 b - 2 b = 9$ $3b-2b=9$
or
$b = 9$ $b=9$ -------------boy is $9$ $9$ years old
Since $s = b + 3$ $s=b+3$
or
$s = 9 + 3$ $s=9+3$
or
$s = 12$ $s=12$ -------------------------sister is $12$ $12$ years old

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A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

1 Answer

Explanation:

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