Suppose $x$ is an integer such that $3x \equiv 15 \pmod{64}$. Find remainder when $q$ is divided by $64$. Suppose $x$ is an integer such that $3x \equiv 15 \pmod{64}$. If $x$ has remainder $2$ and quotient $q$ when divided by $23$, determine the remainder when $q$ is divided by $64$.
I tried a couple things. By division algorithm, know $x = 23q + 2$. So $3(23q + 2) \equiv 15 \pmod{64}$. Not sure how to go from there.
Another thing I tried is $3x = 64q + 15$. If we let $q$ be zero, then $x$ is obviously $5$. This also doesn't wind up being that helpful, and I think $x$ can have other values asides from $5$.

$3x\equiv 15\pmod{64}$ means
$64\mid (3x-15)$
$64\mid 3(x-5)$ 
Since $64$ and $3$ have no common factors, it follows that $64$ must divide the remaining factor $x-5$ :
$$x\equiv 5\pmod {64}$$ 
Directly plugin the given info $x=23q+2$ :
$$23q+2\equiv 5 \pmod{64}$$
Subtract $2$ both sides and see if you can try the rest.
