combinatorics - How many positive integers less than 1000 are multiples of 5 and are equal to 3 times an even number?

Question: How many positive integers less than 1000 are multiples of 5 and are equal to 3 times an even number?

So Multiples of $5$ and $6$

If a number is a multiple of $5$ and $6$ then it is a multiple of $30$ as well. Because of the law,

Multiple of $a$ and $b$ $\implies$ multiples of lcm$(a, b)$

lcm($5, 6$) = $30$

$$1000 \equiv 10 \pmod{30}$$

I am trying to solve this problem using number-theory, any help? The answer is $33$

Also, how does $1000/30$ give the right answer?

Thanks!