Question

Eric works as a manager with an international hotel. Eric has a son who is 30 years younger than him. The product of their ages is 175 years. How old is Eric?

Answer 1

ANSWER

Eric is
$35years$

EXPLANATION

Let Eric's age be
$x \: \: years$

Then his son age will be,

$(x - 30) \: years$

The product of their ages is 175.

This implies that,

$x(x - 30) = 175$

We expand to get,


$x^2- 30x = 175$

We equate everything to zero to obtain,

${x}^{2} - 30x - 175 = 0$

We split the middle term to get,

${x}^{2} +5x- 35x - 175 = 0$

We factor to obtain,

$x(x +5)- 35(x +5) = 0$

We factor further to get,

$(x - 35)( x + 5) = 0$

This implies that,

$x = 35 \: or \: - 5$

Since age is not negative,

$x = 35years$

Therefore Eric is
$35years$