Counters conundrum

Question

Amir has 240 more counters than Brett.

Amir gives 25% of his counters to Brett.

Brett now gives 60% of the counters he now has back to Amir.

in the end Amir had 300 counters more than Brett.

How many counters did Amir have at the start?

Answer 1

First off, it's always easier to solve these types of equations if you give someone an easy amount to go off of. So, let's say that Brett starts off with 100 counters. That would mean that Amir has 340 counters, since Amir has 240 more than Brett. Amir then gives 25% of his counters (25% of 340 = 85) to Brett. Now Amir has 255 counters while Brett has 185. Brett then gives back 60% of his 185 (60% of 185 = 111) counters to Amir. Now Amir has 366 counters while Brett has 74. However, this doesn't satisfy the ending statement that Amir had 300 counters more than Brett, because Brett would have ended up with 66 rather than 74. It is close enough to 300, though, that we can test the theory by adding 8 to the original 100 that Brett had and seeing if that works out in the end. So, if we start over, Brett has 108 counters while Amir has 348. Once Amir gives Brett his 25%, Brett is left with 195 (108 + 87, which is 25% of 348) and Amir has 261. Brett gives back 60% of his counters (117) and he is left with 78 while Amir has 378. This satisfies the end result of Amir having 300 more counters than Brett, which means the answer is 108 counters.