Fanny had some yellow marbles and purple marbles in 2 packets. In Packet D, the ratio of the number of yellow marbles to purple marbles was 9 : 7. In Packet E, the number of yellow marbles was 2 times the number of purple marbles. Fanny transferred ²₇ of the purple marbles from Packet D to Packet E. The number of marbles in Packet D became 126 and the ratio of the number of yellow marbles to purple marbles in Packet E became 4 : 5.

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

	Packet D		Packet E
	Yellow	Purple	Yellow	Purple
Comparing yellow marbles and purple marbles at first	9 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing yellow marbles and purple marbles in the end	9 u	5 u	4 p	5 p

(a)
Total number of marbles in the end for Packet D
= 9 u + 5 u
= 14 u

14 u = 126

1 u = 126 ÷ 14 = 9

Number of purple marbles that were transferred from Packet D to Packet E
= 2 u
= 2 x 9
= 18

(b)
The number of yellow marbles in Packet E remains unchanged.  Make the number of yellow marbles in Packet E the same.  LCM of 2 and 4 is 4. 

Increase in the number of purple marbles in Packet E
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 18

1 p = 18 ÷ 3 = 6

Number of marbles in Packet E in the end
= 4 p + 5 p
= 9 p
= 9 x 6
= 54

Answer(s): (a) 18; (b) 54