Nick and Simon had 106 marbles in total. Nick had 54 marbles less than Simon at first. After Nick and Simon played a game with Raeann, Nick had ²₁₁ as many marbles as Simon. If Nick lost as many marbles as Simon to Raeann, find the number of marbles that Simon lost to Raeann.

	Nick	Simon	Difference
Before	1 u	1 u + 54	54
Change	- ?	- ?
After	2 p	11 p	9 p

Total number of marbles at first
= 1 u + 1 u + 54 
= 2 u + 54

2 u + 54 = 106
2 u = 106 - 54
2 u = 52

1 u = 52 ÷ 2 = 26

Since Nick lost the same number of marbles as Simon, the difference in the number of marbles between Nick and Simon at first and in the end remains the same.

Difference in the number of marbles in the end
= 11 p - 2 p
= 9 p

9 p = 54

1 p = 54 ÷ 9 = 6

Number of marbles that Nick lost to Raeann
= 1 u - 2 p
= 26 - 2 x 6
= 26 - 12
= 14

Since Simon lost the same number of marbles as Nick, the number of marbles that each lost to Raeann is the same.

Number of marbles that Simon lost = 14

Answer(s): 14