Emma had some yellow buttons and silver buttons in 2 bags. In Bag S, the ratio of the number of yellow buttons to silver buttons was 9 : 5. In Bag T, the number of yellow buttons was 5 times the number of silver buttons. Emma transferred ³₅ of the silver buttons from Bag S to Bag T. The number of buttons in Bag S became 165 and the ratio of the number of yellow buttons to silver buttons in Bag T became 10 : 11.

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

	Bag S		Bag T
	Yellow	Silver	Yellow	Silver
Comparing yellow buttons and silver buttons at first	9 u	5 u	5x2 = 10 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing yellow buttons and silver buttons in the end	9 u	2 u	10 p	11 p

(a)
Total number of buttons in the end for Bag S
= 9 u + 2 u
= 11 u

11 u = 165

1 u = 165 ÷ 11 = 15

Number of silver buttons that were transferred from Bag S to Bag T
= 3 u
= 3 x 15
= 45

(b)
The number of yellow buttons in Bag T remains unchanged.  Make the number of yellow buttons in Bag T the same.  LCM of 5 and 10 is 10. 

Increase in the number of silver buttons in Bag T
= 11 p - 2 p
= 9 p

9 p = 3 u
9 p = 45

1 p = 45 ÷ 9 = 5

Number of buttons in Bag T in the end
= 10 p + 11 p
= 21 p
= 21 x 5
= 105

Answer(s): (a) 45; (b) 105