Pamela had some grey beads and yellow beads in 2 packets. In Packet D, the ratio of the number of grey beads to yellow beads was 8 : 7. In Packet E, the number of grey beads was 4 times the number of yellow beads. Pamela transferred ²₇ of the yellow beads from Packet D to Packet E. The number of beads in Packet D became 182 and the ratio of the number of grey beads to yellow beads in Packet E became 8 : 9.

1. How many yellow beads were transferred from Packet D to Packet E?
2. What was the number of beads in Packet E after the transfer?

	Packet D		Packet E
	Grey	Yellow	Grey	Yellow
Comparing grey beads and yellow beads at first	8 u	7 u	4x2 = 8 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing grey beads and yellow beads in the end	8 u	5 u	8 p	9 p

(a)
Total number of beads in the end for Packet D
= 8 u + 5 u
= 13 u

13 u = 182

1 u = 182 ÷ 13 = 14

Number of yellow beads that were transferred from Packet D to Packet E
= 2 u
= 2 x 14
= 28

(b)
The number of grey beads in Packet E remains unchanged.  Make the number of grey beads in Packet E the same.  LCM of 4 and 8 is 8. 

Increase in the number of yellow beads in Packet E
= 9 p - 2 p
= 7 p

7 p = 2 u
7 p = 28

1 p = 28 ÷ 7 = 4

Number of beads in Packet E in the end
= 8 p + 9 p
= 17 p
= 17 x 4
= 68

Answer(s): (a) 28; (b) 68