Luke, Riordan and Mark shared a sum of money. The amount received by Riordan was ²₃ the amount of money received by Mark. After Luke had given $51 to Riordan and $23 to Mark, Riordan gave $8 to Mark. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Luke and Riordan had at first.

	Luke	Riordan	Mark
Before	2 u + 117	2 u	3 u
Change 1	- 51	+ 51
Change 2	- 23		+ 23
Change 3		- 8	+ 8
After	2 u + 43	2 u + 43	3 u + 31

Amount that Riordan had in the end = 2 u + 43 

Amount that Mark had in the end = 3 u + 31

Amount that Luke had at first 
= 2 u + 43 + 51 + 23
= 2 u + 117

Amount that Riordan and Mark had in the end is the same.

2 u + 43 = 3 u + 31
3 u - 2 u = 43 - 31

1 u = 12

Amount that Luke and Riordan had in the end is the same.

Amount that Luke had in the end
= 2 u + 43
= 2 x 12 + 43
= 24 + 43
= $67

Amount that Luke had at first
= 67 + 51 + 23
= $141

Difference in the amounts between Luke and Riordan at first
= 141 - 24
= $117

Answer(s): $117