Question

A mother's age is 2 more than the square of the son's age and the sum of their ages is 44. Find the son's age.

• A. 7
• B. 6
• C. 5
• D. 4

Answer 1

The correct option is B 6

Let the son's age be $x$.
Since the sum of their ages is 44. Let the mother's age be $44-x$.
Using the given relation, we have the following equation.
$44-x=x^2+2$
$\Rightarrow$$x^2+x-42=0$
$\Rightarrow$$x^2+7x-6x-42=0$
$\Rightarrow$$x(x+7)-6(x+7)=0$
$\Rightarrow$$(x-6)(x+7)=0$
$\Rightarrow$$x=6,x=-7$
Since age cannot be negative, $x=6$.
That is, the son is 6 years old.