Victoria had some yellow buttons and red buttons in 2 packets. In Packet F, the ratio of the number of yellow buttons to red buttons was 8 : 3. In Packet G, the number of yellow buttons was 2 times the number of red buttons. Victoria transferred ²₃ of the red buttons from Packet F to Packet G. The number of buttons in Packet F became 54 and the ratio of the number of yellow buttons to red buttons in Packet G became 4 : 5.

1. How many red buttons were transferred from Packet F to Packet G?
2. What was the number of buttons in Packet G after the transfer?

	Packet F		Packet G
	Yellow	Red	Yellow	Red
Comparing yellow buttons and red buttons at first	8 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing yellow buttons and red buttons in the end	8 u	1 u	4 p	5 p

(a)
Total number of buttons in the end for Packet F
= 8 u + 1 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of red buttons that were transferred from Packet F to Packet G
= 2 u
= 2 x 6
= 12

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

Increase in the number of red buttons in Packet G
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 12

1 p = 12 ÷ 3 = 4

Number of buttons in Packet G in the end
= 4 p + 5 p
= 9 p
= 9 x 4
= 36

Answer(s): (a) 12; (b) 36