Carl and Ahmad had 118 beads in total. Carl had 48 beads less than Ahmad at first. After Carl and Ahmad played a game with Gwen, Carl had ¹₉ as many beads as Ahmad. If Carl lost as many beads as Ahmad to Gwen, find the number of beads that Ahmad lost to Gwen.

	Carl	Ahmad	Difference
Before	1 u	1 u + 48	48
Change	- ?	- ?
After	1 p	9 p	8 p

Total number of beads at first
= 1 u + 1 u + 48 
= 2 u + 48

2 u + 48 = 118
2 u = 118 - 48
2 u = 70

1 u = 70 ÷ 2 = 35

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

Difference in the number of beads in the end
= 9 p - 1 p
= 8 p

8 p = 48

1 p = 48 ÷ 8 = 6

Number of beads that Carl lost to Gwen
= 1 u - 1 p
= 35 - 1 x 6
= 35 - 6
= 29

Since Ahmad lost the same number of beads as Carl, the number of beads that each lost to Gwen is the same.

Number of beads that Ahmad lost = 29

Answer(s): 29