Ken and Andy had 102 beads in total. Ken had 40 beads less than Andy at first. After Ken and Andy played a game with Erika, Ken had ¹₆ as many beads as Andy. If Ken lost as many beads as Andy to Erika, find the number of beads that Andy lost to Erika.

	Ken	Andy	Difference
Before	1 u	1 u + 40	40
Change	- ?	- ?
After	1 p	6 p	5 p

Total number of beads at first
= 1 u + 1 u + 40 
= 2 u + 40

2 u + 40 = 102
2 u = 102 - 40
2 u = 62

1 u = 62 ÷ 2 = 31

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

Difference in the number of beads in the end
= 6 p - 1 p
= 5 p

5 p = 40

1 p = 40 ÷ 5 = 8

Number of beads that Ken lost to Erika
= 1 u - 1 p
= 31 - 1 x 8
= 31 - 8
= 23

Since Andy lost the same number of beads as Ken, the number of beads that each lost to Erika is the same.

Number of beads that Andy lost = 23

Answer(s): 23