Ahmad and Gabriel had 82 marbles in total. Gabriel had 12 marbles more than Ahmad at first. After Ahmad and Gabriel played a game with Lynn, Ahmad had ¹₃ as many marbles as Gabriel. If Ahmad lost as many marbles as Gabriel to Lynn, find the number of marbles that Ahmad lost to Lynn.

	Ahmad	Gabriel	Difference
Before	1 u	1 u + 12	12
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of marbles at first
= 1 u + 1 u + 12 
= 2 u + 12

2 u + 12 = 82
2 u = 82 - 12
2 u = 70

1 u = 70 ÷ 2 = 35

Since Ahmad lost the same number of marbles as Gabriel, the difference in the number of marbles between Ahmad and Gabriel 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 = 12

1 p = 12 ÷ 2 = 6

Number of marbles that Ahmad lost to Lynn
= 1 u - 1 p
= 35 - 1 x 6
= 35 - 6
= 29

Answer(s): 29