Albert and Warren had 90 beads in total. Warren had 16 beads more than Albert at first. After Albert and Warren played a game with Gillian, Albert had ¹₃ as many beads as Warren. If Albert lost as many beads as Warren to Gillian, find the number of beads that Albert lost to Gillian.

	Albert	Warren	Difference
Before	1 u	1 u + 16	16
Change	- ?	- ?
After	1 p	3 p	2 p

Total number of beads at first
= 1 u + 1 u + 16 
= 2 u + 16

2 u + 16 = 90
2 u = 90 - 16
2 u = 74

1 u = 74 ÷ 2 = 37

Since Albert lost the same number of beads as Warren, the difference in the number of beads between Albert and Warren 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 = 16

1 p = 16 ÷ 2 = 8

Number of beads that Albert lost to Gillian
= 1 u - 1 p
= 37 - 1 x 8
= 37 - 8
= 29

Answer(s): 29