Answer:
The son in 12 years old and the woman is 36 years old
Step-by-step 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 [tex]3 s^{2}-32s-48=0[/tex] By using quadratic equation [tex]s=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}=\frac{-(-32)+\sqrt{32^{2}-4(3)(-48)}}{2(3)}=\frac{-(-32)+\sqrt{1570}}{6}=\frac{71,62}{6}=11.9 \cong 12[/tex] s=12 We know that w=3s w=[tex]3 \times 12[/tex] = 36. Hence, the woman’s age is 36 years and the son’s age is 12 years.
