Problem Solving using Algebra

Question

If Peter is $7$ years older than Sharon and John is twice as old as Peter, work out how old Peter is if the average of their ages is $19$.

Thanks! :)

Answer 1

HINT:

If the age of Peter is $x$ years,

the age of Sharon will be $x-7$ years and that of John will be $2x$ years

So, $$\frac{x-7+x+2x}3=19$$

Answer 2

Hint: Let $P$ be Peter's age; $S,$ Sharon's; $J,$ John's. The problem then gives you three equations in (at most) three variables each, once translated into terms of $P,S,J$ (for example, $P=S+7$). You are asked to solve this system for $P,$ in particular.