Paul, Caden and Gabriel shared a sum of money. The amount received by Caden was ³₄ the amount of money received by Gabriel. After Paul had given $50 to Caden and $21 to Gabriel, Caden gave $5 to Gabriel. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Paul and Caden had at first.

	Paul	Caden	Gabriel
Before	3 u + 116	3 u	4 u
Change 1	- 50	+ 50
Change 2	- 21		+ 21
Change 3		- 5	+ 5
After	3 u + 45	3 u + 45	4 u + 26

Amount that Caden had in the end = 3 u + 45 

Amount that Gabriel had in the end = 4 u + 26

Amount that Paul had at first 
= 3 u + 45 + 50 + 21
= 3 u + 116

Amount that Caden and Gabriel had in the end is the same.

3 u + 45 = 4 u + 26
4 u - 3 u = 45 - 26

1 u = 19

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

Amount that Paul had in the end
= 3 u + 45
= 3 x 19 + 45
= 57 + 45
= $102

Amount that Paul had at first
= 102 + 50 + 21
= $173

Difference in the amounts between Paul and Caden at first
= 173 - 57
= $116

Answer(s): $116