Asher and Tommy had 76 beads in total. Tommy had 22 beads more than Asher at first. After Asher and Tommy played a game with Penelope, Asher had ¹₃ as many beads as Tommy. If Asher lost as many beads as Tommy to Penelope, find the number of beads that Asher lost to Penelope.

	Asher	Tommy	Difference
Before	1 u	1 u + 22	22
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of beads at first
= 1 u + 1 u + 22 
= 2 u + 22

2 u + 22 = 76
2 u = 76 - 22
2 u = 54

1 u = 54 ÷ 2 = 27

Since Asher lost the same number of beads as Tommy, the difference in the number of beads between Asher and Tommy 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 = 22

1 p = 22 ÷ 2 = 11

Number of beads that Asher lost to Penelope
= 1 u - 1 p
= 27 - 1 x 11
= 27 - 11
= 16

Answer(s): 16