Question

Question #e832a

Answer 1

Boy is 2 years old
Father is 22 years old.

Explanation:

Let b = boys age. and f = fathers age.

Sum of boy's age and father's age.

`b+f=24`

Quarter of the product of ages equal to boy's age plus 9 years.

`(bf)/4=b+9`

`(bf)/4=b+9= bf =4b +36`

`bf =4b +36 color(white)(*)[1]`

Fathers age:

`f=24-bcolor(white)(*)[2]`

Substituting this into `[1]`

`b(24-b)=4b+36=24b-b^2-4b-36=0`

Collecting terms and multiplying by `-1`

`b^2-20b+36=0`

Factor:

`(b-18)(b-2)=0=> b=18 or b=2`

Using `b=18` in `[2]`

`f=24-18=6->` father is 6 years old ( not possible)

Using `b=2` in `[2]`

`f=24-2=22->` father is 22 years old.