Tom and Zane had 88 marbles in total. Zane had 54 marbles more than Tom at first. After Tom and Zane played a game with Yoko, Tom had ²₁₁ as many marbles as Zane. If Tom lost as many marbles as Zane to Yoko, find the number of marbles that Tom lost to Yoko.

	Tom	Zane	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 = 88
2 u = 88 - 54
2 u = 34

1 u = 34 ÷ 2 = 17

Since Tom lost the same number of marbles as Zane, the difference in the number of marbles between Tom and Zane 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 Tom lost to Yoko
= 1 u - 2 p
= 17 - 2 x 6
= 17 - 12
= 5

Answer(s): 5