Archie and Zane had 152 beads in total. Zane had 80 beads more than Archie at first. After Archie and Zane played a game with Natalie, Archie had ³₁₁ as many beads as Zane. If Archie lost as many beads as Zane to Natalie, find the number of beads that Archie lost to Natalie.

	Archie	Zane	Difference
Before	1 u	1 u + 80	80
Change	- ?	- ?
After	3 p	11 p	8 p

Total number of beads at first
= 1 u + 1 u + 80 
= 2 u + 80

2 u + 80 = 152
2 u = 152 - 80
2 u = 72

1 u = 72 ÷ 2 = 36

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

Difference in the number of beads in the end
= 11 p - 3 p
= 8 p

8 p = 80

1 p = 80 ÷ 8 = 10

Number of beads that Archie lost to Natalie
= 1 u - 3 p
= 36 - 3 x 10
= 36 - 30
= 6

Answer(s): 6