Whenever you see several inequalities with no common terms, one thing you can at least do is add them. Make sure you flip them around if necessary so that all the inequalities face in the same direction.
In this case we have a ≥ 30 and b ≤ 15. Let's flip the first one (no need to multiply by 1 or anything) to get 30 ≤ a. Then we can just stack and add:
30 ≤ a
b ≤ 15
gets us
30 + b ≤ a +15
The logic is that if 30 and b are the two little guys, and a and 15 are the two big guys, then if we add the two big guys they must still be bigger than if we add the two little guys. Note: you can add inequalities but you can't subtract them! Subtracting shows us the difference between the terms and we have no information about whether the difference between the two little guys is smaller or greater than the difference between the two big ones.
Anyway at this point if we look at the answer choices we note that they all have a and b on the same side of the inequality so let's make ours match:
30 + b ≤ a + 15
15 + b ≤ a
15 ≤ a  b
So it's C.
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