Barbara had some black coins and gold coins in 2 packets. In Packet C, the ratio of the number of black coins to gold coins was 8 : 5. In Packet D, the number of black coins was 2 times the number of gold coins. Barbara transferred ²₅ of the gold coins from Packet C to Packet D. The number of coins in Packet C became 44 and the ratio of the number of black coins to gold coins in Packet D became 6 : 7.

1. How many gold coins were transferred from Packet C to Packet D?
2. What was the number of coins in Packet D after the transfer?

	Packet C		Packet D
	Black	Gold	Black	Gold
Comparing black coins and gold coins at first	8 u	5 u	2x3 = 6 p	1x3 = 3 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing black coins and gold coins in the end	8 u	3 u	6 p	7 p

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

11 u = 44

1 u = 44 ÷ 11 = 4

Number of gold coins that were transferred from Packet C to Packet D
= 2 u
= 2 x 4
= 8

(b)
The number of black coins in Packet D remains unchanged.  Make the number of black coins in Packet D the same.  LCM of 2 and 6 is 6. 

Increase in the number of gold coins in Packet D
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 8

1 p = 8 ÷ 4 = 2

Number of coins in Packet D in the end
= 6 p + 7 p
= 13 p
= 13 x 2
= 26

Answer(s): (a) 8; (b) 26