Age Word Problem (simultaneous equations)

Question

I am working on this word problem and I can’t figure it out for the life of me and the textbook doesn’t seem to help at all. The question is:

Six years ago, Katie was four times as old as her daughter Melanie. In 10 years, Katie will be two times as old as Melanie is in 8 years time. Use simultaneous equations to determine Katie and Melanie’s current ages.

Any help on how to complete it would be appreciated.

Answer 1

Let $K = $ Katies current age and $M = $ Melanies current age.

Let's translate each sentence one by one.

"Six years ago, Katie was four times as old as her daughter Melanie."

So $K-6 = 4(M-6)$.

" In 10 years, Katie will be two times as old as Melanie is in 8 years time. "

So $K + 10 = 2(M+8)$.

So $K-6 = 4(M-6)$ and $K+10 = 2(M+8)$.