Jeremy and Michael had 76 beads in total. Jeremy had 14 beads less than Michael at first. After Jeremy and Michael played a game with Irene, Jeremy had ³₅ as many beads as Michael. If Jeremy lost as many beads as Michael to Irene, find the number of beads that Michael lost to Irene.

	Jeremy	Michael	Difference
Before	1 u	1 u + 14	14
Change	- ?	- ?
After	3 p	5 p	2 p

Total number of beads at first
= 1 u + 1 u + 14 
= 2 u + 14

2 u + 14 = 76
2 u = 76 - 14
2 u = 62

1 u = 62 ÷ 2 = 31

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

Difference in the number of beads in the end
= 5 p - 3 p
= 2 p

2 p = 14

1 p = 14 ÷ 2 = 7

Number of beads that Jeremy lost to Irene
= 1 u - 3 p
= 31 - 3 x 7
= 31 - 21
= 10

Since Michael lost the same number of beads as Jeremy, the number of beads that each lost to Irene is the same.

Number of beads that Michael lost = 10

Answer(s): 10