divisibility - Help - remainders when number is divided

Please, give me hints, I've no idea ;):

Find greatest number $x$ such that $x<1000$ and $x$ divided by $4$ gives remainder $3$, divided by $5$ gives remainder $4$, and divided by $6$ gives remainder $5$.

I already know that for some natural $a, b, c$, $x=4a+3=5b+4=6c+5$, but what next? Help please.

Answer

You know that $x+1$ is divisible by $4$, $5$, and $6$ so $x+1$ is divisible by $60$. The largest number under $1000$ that is divisible by $60$ is $960$. So $x=959$.