Charlie and Nick had 64 marbles in total. Nick had 6 marbles more than Charlie at first. After Charlie and Nick played a game with Diana, Charlie had ¹₄ as many marbles as Nick. If Charlie lost as many marbles as Nick to Diana, find the number of marbles that Charlie lost to Diana.

	Charlie	Nick	Difference
Before	1 u	1 u + 6	6
Change	- ?	- ?
After	1 p	4 p	3 p

Total number of marbles at first
= 1 u + 1 u + 6 
= 2 u + 6

2 u + 6 = 64
2 u = 64 - 6
2 u = 58

1 u = 58 ÷ 2 = 29

Since Charlie lost the same number of marbles as Nick, the difference in the number of marbles between Charlie and Nick 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 = 6

1 p = 6 ÷ 3 = 2

Number of marbles that Charlie lost to Diana
= 1 u - 1 p
= 29 - 1 x 2
= 29 - 2
= 27

Answer(s): 27