Michael, Paul and Charlie shared a sum of money. The amount received by Paul was ⁴₅ the amount of money received by Charlie. After Michael had given $54 to Paul and $29 to Charlie, Paul gave $2 to Charlie. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Michael and Paul had at first.

	Michael	Paul	Charlie
Before	4 u + 135	4 u	5 u
Change 1	- 54	+ 54
Change 2	- 29		+ 29
Change 3		- 2	+ 2
After	4 u + 52	4 u + 52	5 u + 31

Amount that Paul had in the end = 4 u + 52 

Amount that Charlie had in the end = 5 u + 31

Amount that Michael had at first 
= 4 u + 52 + 54 + 29
= 4 u + 135

Amount that Paul and Charlie had in the end is the same.

4 u + 52 = 5 u + 31
5 u - 4 u = 52 - 31

1 u = 21

Amount that Michael and Paul had in the end is the same.

Amount that Michael had in the end
= 4 u + 52
= 4 x 21 + 52
= 84 + 52
= $136

Amount that Michael had at first
= 136 + 54 + 29
= $219

Difference in the amounts between Michael and Paul at first
= 219 - 84
= $135

Answer(s): $135