Luis and John had 94 marbles in total. Luis had 18 marbles less than John at first. After Luis and John played a game with Dana, Luis had ³₅ as many marbles as John. If Luis lost as many marbles as John to Dana, find the number of marbles that John lost to Dana.

	Luis	John	Difference
Before	1 u	1 u + 18	18
Change	- ?	- ?
After	3 p	5 p	2 p

Total number of marbles at first
= 1 u + 1 u + 18 
= 2 u + 18

2 u + 18 = 94
2 u = 94 - 18
2 u = 76

1 u = 76 ÷ 2 = 38

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

Difference in the number of marbles in the end
= 5 p - 3 p
= 2 p

2 p = 18

1 p = 18 ÷ 2 = 9

Number of marbles that Luis lost to Dana
= 1 u - 3 p
= 38 - 3 x 9
= 38 - 27
= 11

Since John lost the same number of marbles as Luis, the number of marbles that each lost to Dana is the same.

Number of marbles that John lost = 11

Answer(s): 11