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.