Japheth, Oliver and Liam shared a sum of money. The amount received by Oliver was ³₄ the amount of money received by Liam. After Japheth had given $46 to Oliver and $30 to Liam, Oliver gave $5 to Liam. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Japheth and Oliver had at first.

	Japheth	Oliver	Liam
Before	3 u + 117	3 u	4 u
Change 1	- 46	+ 46
Change 2	- 30		+ 30
Change 3		- 5	+ 5
After	3 u + 41	3 u + 41	4 u + 35

Amount that Oliver had in the end = 3 u + 41 

Amount that Liam had in the end = 4 u + 35

Amount that Japheth had at first 
= 3 u + 41 + 46 + 30
= 3 u + 117

Amount that Oliver and Liam had in the end is the same.

3 u + 41 = 4 u + 35
4 u - 3 u = 41 - 35

1 u = 6

Amount that Japheth and Oliver had in the end is the same.

Amount that Japheth had in the end
= 3 u + 41
= 3 x 6 + 41
= 18 + 41
= $59

Amount that Japheth had at first
= 59 + 46 + 30
= $135

Difference in the amounts between Japheth and Oliver at first
= 135 - 18
= $117

Answer(s): $117