> 
> Suppose $P$ and $Q$ are both prime numbers
>  $$5P+7Q= 109$$
>  Find the value of $P$.
> 
> 
> 

I thought about examining all terms for parity, and I approached it by this:

Suppose $5P$ was an even number. However, the only even prime number is $2$, so that would make $5P$ = $10$ and $7Q =99$. However, since $7$ doesn't divide fully into $99$, this means that $7Q$ must be even. But how do I approach it from there?

P.S. I'm only an Year 7 and this is Year 9 work. Please explain clearly how you found the solution.