Grandfather is 15 time the age of his grandson today, in 10 years the grandson will be 3/17 the age of the grandfather. How old are the grandfather and grandson?

Apr 24, 2016

Grandfather is $65$ years old.
Grandson is $5$ years old.

Explanation:

Let the grandfather's age be $x$
and the grandson's age be $y$.

We are told
$\textcolor{w h i t e}{\text{XXX}} x = 15 y$
and
$\textcolor{w h i t e}{\text{XXX}} y + 10 = \frac{3}{17} \left(x + 10\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} \rightarrow 17 y + 170 = 3 x + 30$

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXX}} = 45 y + 30$ (since $x = 15 y$)

$\textcolor{w h i t e}{\text{XXXXXX}} \rightarrow 140 = 28 y$

$\textcolor{w h i t e}{\text{XXXXXX}} \rightarrow y = 5$

$\textcolor{w h i t e}{\text{XXX}} x = 15 y = 65$