Question

Jack is twice as old as Jill. If 4 years ago Jack’s age was thrice as Jill’s. Find their present age.

Answer 1

Task. Jack is twice as old as Jill and 4 years ago Jacks age was thrice as Jills. Find their present age.

Solution. Let $K$ be the age of Jack, and $L$ be the ages of Jill. Then

$K=2L.$

Moreover, by assumption 4 years ago Jacks age was thrice as Jills. At that time Jacks age was $K-4$ and Jill’s age was $L-4$, so

$K-4=3(L-4).$

Substituting $K=2L$ we obtain

$2L-4=3(L-4)\quad\Rightarrow\quad 2L-4=3L-12\quad\Rightarrow\quad 3L-2L=12-4\quad\Rightarrow\quad L=8.$

Hence

$K=2L=2*8=16.$

Answer. Jack is 16 years old, and Jill is 8 years old.