Question

18 A woman is 3 times as old as her son.

8 years ago the product of their ages was
112. Find their present ages.

Answer 1

The son in 12 years old and the woman is 36 years old

Explanation:

Let the woman’s current age be w years and son’s age be s years. According to the question, the woman is 3 times as old as her son then, w=3s Also, it is given that 8 years ago the product of their ages were 112 Therefore, (w-8)(s-8)=112 (3s-8)(s-8)=112 Solving for s, we get
`3 s^(2)-32s-48=0` By using quadratic equation
`s=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}=\frac{-(-32)+\sqrt{32^(2)-4(3)(-48)}}{2(3)}=(-(-32)+√(1570))/(6)=(71,62)/(6)=11.9 \cong 12` s=12 We know that w=3s w=
`3 * 12` = 36. Hence, the woman’s age is 36 years and the son’s age is 12 years.