Jane had some yellow erasers and white erasers in 2 bags. In Bag Q, the ratio of the number of yellow erasers to white erasers was 9 : 7. In Bag R, the number of yellow erasers was 2 times the number of white erasers. Jane transferred ²₇ of the white erasers from Bag Q to Bag R. The number of erasers in Bag Q became 252 and the ratio of the number of yellow erasers to white erasers in Bag R became 6 : 7.

1. How many white erasers were transferred from Bag Q to Bag R?
2. What was the number of erasers in Bag R after the transfer?

	Bag Q		Bag R
	Yellow	White	Yellow	White
Comparing yellow erasers and white erasers at first	9 u	7 u	2x3 = 6 p	1x3 = 3 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing yellow erasers and white erasers in the end	9 u	5 u	6 p	7 p

(a)
Total number of erasers in the end for Bag Q
= 9 u + 5 u
= 14 u

14 u = 252

1 u = 252 ÷ 14 = 18

Number of white erasers that were transferred from Bag Q to Bag R
= 2 u
= 2 x 18
= 36

(b)
The number of yellow erasers in Bag R remains unchanged.  Make the number of yellow erasers in Bag R the same.  LCM of 2 and 6 is 6. 

Increase in the number of white erasers in Bag R
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 36

1 p = 36 ÷ 4 = 9

Number of erasers in Bag R in the end
= 6 p + 7 p
= 13 p
= 13 x 9
= 117

Answer(s): (a) 36; (b) 117