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`

Step-by-step 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`