John, Michael and Bobby shared a sum of money. The amount received by Michael was ³₄ the amount of money received by Bobby. After John had given $52 to Michael and $24 to Bobby, Michael gave $5 to Bobby. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that John and Michael had at first.

	John	Michael	Bobby
Before	3 u + 123	3 u	4 u
Change 1	- 52	+ 52
Change 2	- 24		+ 24
Change 3		- 5	+ 5
After	3 u + 47	3 u + 47	4 u + 29

Amount that Michael had in the end = 3 u + 47 

Amount that Bobby had in the end = 4 u + 29

Amount that John had at first 
= 3 u + 47 + 52 + 24
= 3 u + 123

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

3 u + 47 = 4 u + 29
4 u - 3 u = 47 - 29

1 u = 18

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

Amount that John had in the end
= 3 u + 47
= 3 x 18 + 47
= 54 + 47
= $101

Amount that John had at first
= 101 + 52 + 24
= $177

Difference in the amounts between John and Michael at first
= 177 - 54
= $123

Answer(s): $123