Ryan and Luke had 65 marbles in total. Luke had 15 marbles more than Ryan at first. After Ryan and Luke played a game with Gabby, Ryan had ¹₄ as many marbles as Luke. If Ryan lost as many marbles as Luke to Gabby, find the number of marbles that Ryan lost to Gabby.

	Ryan	Luke	Difference
Before	1 u	1 u + 15	15
Change	- ?	- ?
After	1 p	4 p	3 p

Total number of marbles at first
= 1 u + 1 u + 15 
= 2 u + 15

2 u + 15 = 65
2 u = 65 - 15
2 u = 50

1 u = 50 ÷ 2 = 25

Since Ryan lost the same number of marbles as Luke, the difference in the number of marbles between Ryan and Luke 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 = 15

1 p = 15 ÷ 3 = 5

Number of marbles that Ryan lost to Gabby
= 1 u - 1 p
= 25 - 1 x 5
= 25 - 5
= 20

Answer(s): 20