Gwen had some gold buttons and yellow buttons in 2 bags. In Bag N, the ratio of the number of gold buttons to yellow buttons was 8 : 5. In Bag P, the number of gold buttons was 3 times the number of yellow buttons. Gwen transferred ³₅ of the yellow buttons from Bag N to Bag P. The number of buttons in Bag N became 150 and the ratio of the number of gold buttons to yellow buttons in Bag P became 6 : 7.

1. How many yellow buttons were transferred from Bag N to Bag P?
2. What was the number of buttons in Bag P after the transfer?

	Bag N		Bag P
	Gold	Yellow	Gold	Yellow
Comparing gold buttons and yellow buttons at first	8 u	5 u	3x2 = 6 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing gold buttons and yellow buttons in the end	8 u	2 u	6 p	7 p

(a)
Total number of buttons in the end for Bag N
= 8 u + 2 u
= 10 u

10 u = 150

1 u = 150 ÷ 10 = 15

Number of yellow buttons that were transferred from Bag N to Bag P
= 3 u
= 3 x 15
= 45

(b)
The number of gold buttons in Bag P remains unchanged.  Make the number of gold buttons in Bag P the same.  LCM of 3 and 6 is 6. 

Increase in the number of yellow buttons in Bag P
= 7 p - 2 p
= 5 p

5 p = 3 u
5 p = 45

1 p = 45 ÷ 5 = 9

Number of buttons in Bag P in the end
= 6 p + 7 p
= 13 p
= 13 x 9
= 117

Answer(s): (a) 45; (b) 117