Mark and Justin had 98 marbles in total. Justin had 22 marbles more than Mark at first. After Mark and Justin played a game with Rachel, Mark had ¹₃ as many marbles as Justin. If Mark lost as many marbles as Justin to Rachel, find the number of marbles that Mark lost to Rachel.

	Mark	Justin	Difference
Before	1 u	1 u + 22	22
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of marbles at first
= 1 u + 1 u + 22 
= 2 u + 22

2 u + 22 = 98
2 u = 98 - 22
2 u = 76

1 u = 76 ÷ 2 = 38

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

Difference in the number of marbles in the end
= 3 p - 1 p
= 2 p

2 p = 22

1 p = 22 ÷ 2 = 11

Number of marbles that Mark lost to Rachel
= 1 u - 1 p
= 38 - 1 x 11
= 38 - 11
= 27

Answer(s): 27