Carl and Peter had 53 beads in total. Peter had 15 beads more than Carl at first. After Carl and Peter played a game with Fanny, Carl had ¹₄ as many beads as Peter. If Carl lost as many beads as Peter to Fanny, find the number of beads that Carl lost to Fanny.

	Carl	Peter	Difference
Before	1 u	1 u + 15	15
Change	- ?	- ?
After	1 p	4 p	3 p

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

2 u + 15 = 53
2 u = 53 - 15
2 u = 38

1 u = 38 ÷ 2 = 19

Since Carl lost the same number of beads as Peter, the difference in the number of beads between Carl and Peter at first and in the end remains the same.

Difference in the number of beads in the end
= 4 p - 1 p
= 3 p

3 p = 15

1 p = 15 ÷ 3 = 5

Number of beads that Carl lost to Fanny
= 1 u - 1 p
= 19 - 1 x 5
= 19 - 5
= 14

Answer(s): 14