Xuan had some yellow buttons and pink buttons in 2 packets. In Packet S, the ratio of the number of yellow buttons to pink buttons was 10 : 7. In Packet T, the number of yellow buttons was 2 times the number of pink buttons. Xuan transferred ³₇ of the pink buttons from Packet S to Packet T. The number of buttons in Packet S became 56 and the ratio of the number of yellow buttons to pink buttons in Packet T became 6 : 7.

1. How many pink buttons were transferred from Packet S to Packet T?
2. What was the number of buttons in Packet T after the transfer?

	Packet S		Packet T
	Yellow	Pink	Yellow	Pink
Comparing yellow buttons and pink buttons at first	10 u	7 u	2x3 = 6 p	1x3 = 3 p
Before		7 u
Change		- 3 u		+ 3 u
After		4 u
Comparing yellow buttons and pink buttons in the end	10 u	4 u	6 p	7 p

(a)
Total number of buttons in the end for Packet S
= 10 u + 4 u
= 14 u

14 u = 56

1 u = 56 ÷ 14 = 4

Number of pink buttons that were transferred from Packet S to Packet T
= 3 u
= 3 x 4
= 12

(b)
The number of yellow buttons in Packet T remains unchanged.  Make the number of yellow buttons in Packet T the same.  LCM of 2 and 6 is 6. 

Increase in the number of pink buttons in Packet T
= 7 p - 3 p
= 4 p

4 p = 3 u
4 p = 12

1 p = 12 ÷ 4 = 3

Number of buttons in Packet T in the end
= 6 p + 7 p
= 13 p
= 13 x 3
= 39

Answer(s): (a) 12; (b) 39