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?

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Answer 1 · 2016-04-24T13:04:33

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

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

We are told
$color(white)("XXX")x=15y$
and
$color(white)("XXX")y+10=3/17(x+10)$

$color(white)("XXXXXX")rarr 17y+170=3x+30$

$color(white)("XXXXXXXXXXXXXX")=45y+30$ (since $x=15y$ )

$color(white)("XXXXXX")rarr140=28y$

$color(white)("XXXXXX")rarry=5$

$color(white)("XXX")x=15y=65$

Grandfather is 1515 time the age of his grandson today, in 1010 years the grandson will be 3/173/17 the age of the grandfather. How old are the grandfather and grandson?