Liam and John had 64 beads in total. John had 12 beads more than Liam at first. After Liam and John played a game with Marion, Liam had ¹₃ as many beads as John. If Liam lost as many beads as John to Marion, find the number of beads that Liam lost to Marion.

	Liam	John	Difference
Before	1 u	1 u + 12	12
Change	- ?	- ?
After	1 p	3 p	2 p

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

2 u + 12 = 64
2 u = 64 - 12
2 u = 52

1 u = 52 ÷ 2 = 26

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

Difference in the number of beads in the end
= 3 p - 1 p
= 2 p

2 p = 12

1 p = 12 ÷ 2 = 6

Number of beads that Liam lost to Marion
= 1 u - 1 p
= 26 - 1 x 6
= 26 - 6
= 20

Answer(s): 20