Find a remainder when dividing some number $n\in \mathbb N$ with 30 
A number n when you divide with 6 give a remainder 4, when you divide with 15 the remainder is 7. How much is remainder when you divide number $n$ with $30$?

that mean $n=6k_1+4$, $n=15k_2+7$, and $n=30k_3+x$, so I need to find  $x$. And $30=6*5$ or I can write $30=2*15$, maybe this can do using congruence bit I stuck there if I use that $4n\equiv x \pmod{30}$, and I can write $n\equiv x\pmod{2*15}$, since  $n\equiv 7 \pmod{15}$ and using little Fermat's little theorem  $ n\equiv 1 \pmod 2 $ so then $n\equiv 7 \pmod{30}$ is this ok?  

Alternatively:
$$n\equiv 4 \pmod{6} \Rightarrow 5n\equiv 20 \pmod{30};\\
n\equiv 7 \pmod{15} \Rightarrow 2n\equiv 14 \pmod{30}.$$
Add the two:
$$7n \equiv 34\equiv 4 \pmod{30} \Rightarrow \\
91n\equiv n\equiv 52 \equiv 22 \pmod{30}.$$
