Agear 50 inches in diameter turns a smaller gear 30 inches in diameter. if the larger gear makes 15 revolutions, how many revolutions does the smaller gear make in that time? (a) 9 (b) 12 (c) 20 (d) 25 (e) 30

Well thinking about this just logically, since the larger gear makes 15 revolutions then the smaller gear would have to make more so you could eliminate A and B.

But to solve this problem you need to find the "distance" that the circumference makes.  One revolution is equal to the circumference and since C = d(pi) then the circumference for the larger gear is 50(pi).  If it makes a total of 15 revolutions then 50(pi) * 15 = 750(pi), which is the total distance the circumference is turning. 

The smaller gear needs to travel the same distance but you don't know how many revolutions it does so you need to use the same formula but solve for revolutions.

30(pi) * x = 750(pi) 

divided both sides by 30(pi) we get x = 25 revolutions. D

I’m confused what’s happening