Wendy had some yellow erasers and purple erasers in 2 packets. In Packet P, the ratio of the number of yellow erasers to purple erasers was 7 : 5. In Packet Q, the number of yellow erasers was 4 times the number of purple erasers. Wendy transferred ³₅ of the purple erasers from Packet P to Packet Q. The number of erasers in Packet P became 63 and the ratio of the number of yellow erasers to purple erasers in Packet Q became 8 : 9.

1. How many purple erasers were transferred from Packet P to Packet Q?
2. What was the number of erasers in Packet Q after the transfer?

	Packet P		Packet Q
	Yellow	Purple	Yellow	Purple
Comparing yellow erasers and purple erasers at first	7 u	5 u	4x2 = 8 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing yellow erasers and purple erasers in the end	7 u	2 u	8 p	9 p

(a)
Total number of erasers in the end for Packet P
= 7 u + 2 u
= 9 u

9 u = 63

1 u = 63 ÷ 9 = 7

Number of purple erasers that were transferred from Packet P to Packet Q
= 3 u
= 3 x 7
= 21

(b)
The number of yellow erasers in Packet Q remains unchanged.  Make the number of yellow erasers in Packet Q the same.  LCM of 4 and 8 is 8. 

Increase in the number of purple erasers in Packet Q
= 9 p - 2 p
= 7 p

7 p = 3 u
7 p = 21

1 p = 21 ÷ 7 = 3

Number of erasers in Packet Q in the end
= 8 p + 9 p
= 17 p
= 17 x 3
= 51

Answer(s): (a) 21; (b) 51