Jenson and Jack had 45 beads in total. Jack had 15 beads more than Jenson at first. After Jenson and Jack played a game with Vanessa, Jenson had ²₅ as many beads as Jack. If Jenson lost as many beads as Jack to Vanessa, find the number of beads that Jenson lost to Vanessa.

	Jenson	Jack	Difference
Before	1 u	1 u + 15	15
Change	- ?	- ?
After	2 p	5 p	3 p

Total number of beads at first
= 1 u + 1 u + 15 
= 2 u + 15

2 u + 15 = 45
2 u = 45 - 15
2 u = 30

1 u = 30 ÷ 2 = 15

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

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

3 p = 15

1 p = 15 ÷ 3 = 5

Number of beads that Jenson lost to Vanessa
= 1 u - 2 p
= 15 - 2 x 5
= 15 - 10
= 5

Answer(s): 5