Paul and Xavier had 106 marbles in total. Xavier had 36 marbles more than Paul at first. After Paul and Xavier played a game with Kimberly, Paul had ¹₄ as many marbles as Xavier. If Paul lost as many marbles as Xavier to Kimberly, find the number of marbles that Paul lost to Kimberly.

	Paul	Xavier	Difference
Before	1 u	1 u + 36	36
Change	- ?	- ?
After	1 p	4 p	3 p

Total number of marbles at first
= 1 u + 1 u + 36 
= 2 u + 36

2 u + 36 = 106
2 u = 106 - 36
2 u = 70

1 u = 70 ÷ 2 = 35

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

Difference in the number of marbles in the end
= 4 p - 1 p
= 3 p

3 p = 36

1 p = 36 ÷ 3 = 12

Number of marbles that Paul lost to Kimberly
= 1 u - 1 p
= 35 - 1 x 12
= 35 - 12
= 23

Answer(s): 23