George and Michael had 111 beads in total. George had 33 beads less than Michael at first. After George and Michael played a game with Usha, George had ¹₄ as many beads as Michael. If George lost as many beads as Michael to Usha, find the number of beads that Michael lost to Usha.

	George	Michael	Difference
Before	1 u	1 u + 33	33
Change	- ?	- ?
After	1 p	4 p	3 p

Total number of beads at first
= 1 u + 1 u + 33 
= 2 u + 33

2 u + 33 = 111
2 u = 111 - 33
2 u = 78

1 u = 78 ÷ 2 = 39

Since George lost the same number of beads as Michael, the difference in the number of beads between George and Michael 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 = 33

1 p = 33 ÷ 3 = 11

Number of beads that George lost to Usha
= 1 u - 1 p
= 39 - 1 x 11
= 39 - 11
= 28

Since Michael lost the same number of beads as George, the number of beads that each lost to Usha is the same.

Number of beads that Michael lost = 28

Answer(s): 28