John and Oliver had 85 beads in total. John had 21 beads less than Oliver at first. After John and Oliver played a game with Esther, John had ¹₄ as many beads as Oliver. If John lost as many beads as Oliver to Esther, find the number of beads that Oliver lost to Esther.

	John	Oliver	Difference
Before	1 u	1 u + 21	21
Change	- ?	- ?
After	1 p	4 p	3 p

Total number of beads at first
= 1 u + 1 u + 21 
= 2 u + 21

2 u + 21 = 85
2 u = 85 - 21
2 u = 64

1 u = 64 ÷ 2 = 32

Since John lost the same number of beads as Oliver, the difference in the number of beads between John and Oliver 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 = 21

1 p = 21 ÷ 3 = 7

Number of beads that John lost to Esther
= 1 u - 1 p
= 32 - 1 x 7
= 32 - 7
= 25

Since Oliver lost the same number of beads as John, the number of beads that each lost to Esther is the same.

Number of beads that Oliver lost = 25

Answer(s): 25