Seth and Howard had 120 beads in total. Seth had 60 beads less than Howard at first. After Seth and Howard played a game with Emily, Seth had ¹₇ as many beads as Howard. If Seth lost as many beads as Howard to Emily, find the number of beads that Howard lost to Emily.

	Seth	Howard	Difference
Before	1 u	1 u + 60	60
Change	- ?	- ?
After	1 p	7 p	6 p

Total number of beads at first
= 1 u + 1 u + 60 
= 2 u + 60

2 u + 60 = 120
2 u = 120 - 60
2 u = 60

1 u = 60 ÷ 2 = 30

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

Difference in the number of beads in the end
= 7 p - 1 p
= 6 p

6 p = 60

1 p = 60 ÷ 6 = 10

Number of beads that Seth lost to Emily
= 1 u - 1 p
= 30 - 1 x 10
= 30 - 10
= 20

Since Howard lost the same number of beads as Seth, the number of beads that each lost to Emily is the same.

Number of beads that Howard lost = 20

Answer(s): 20