Jen had some grey coins and purple coins in 2 packets. In Packet Q, the ratio of the number of grey coins to purple coins was 8 : 7. In Packet R, the number of grey coins was 3 times the number of purple coins. Jen transferred ⁴₇ of the purple coins from Packet Q to Packet R. The number of coins in Packet Q became 110 and the ratio of the number of grey coins to purple coins in Packet R became 6 : 7.

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

	Packet Q		Packet R
	Grey	Purple	Grey	Purple
Comparing grey coins and purple coins at first	8 u	7 u	3x2 = 6 p	1x2 = 2 p
Before		7 u
Change		- 4 u		+ 4 u
After		3 u
Comparing grey coins and purple coins in the end	8 u	3 u	6 p	7 p

(a)
Total number of coins in the end for Packet Q
= 8 u + 3 u
= 11 u

11 u = 110

1 u = 110 ÷ 11 = 10

Number of purple coins that were transferred from Packet Q to Packet R
= 4 u
= 4 x 10
= 40

(b)
The number of grey coins in Packet R remains unchanged.  Make the number of grey coins in Packet R the same.  LCM of 3 and 6 is 6. 

Increase in the number of purple coins in Packet R
= 7 p - 2 p
= 5 p

5 p = 4 u
5 p = 40

1 p = 40 ÷ 5 = 8

Number of coins in Packet R in the end
= 6 p + 7 p
= 13 p
= 13 x 8
= 104

Answer(s): (a) 40; (b) 104