Cindy had some white marbles and brown marbles in 2 bags. In Bag Y, the ratio of the number of white marbles to brown marbles was 8 : 5. In Bag Z, the number of white marbles was 5 times the number of brown marbles. Cindy transferred ²₅ of the brown marbles from Bag Y to Bag Z. The number of marbles in Bag Y became 99 and the ratio of the number of white marbles to brown marbles in Bag Z became 10 : 11.

1. How many brown marbles were transferred from Bag Y to Bag Z?
2. What was the number of marbles in Bag Z after the transfer?

	Bag Y		Bag Z
	White	Brown	White	Brown
Comparing white marbles and brown marbles at first	8 u	5 u	5x2 = 10 p	1x2 = 2 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing white marbles and brown marbles in the end	8 u	3 u	10 p	11 p

(a)
Total number of marbles in the end for Bag Y
= 8 u + 3 u
= 11 u

11 u = 99

1 u = 99 ÷ 11 = 9

Number of brown marbles that were transferred from Bag Y to Bag Z
= 2 u
= 2 x 9
= 18

(b)
The number of white marbles in Bag Z remains unchanged.  Make the number of white marbles in Bag Z the same.  LCM of 5 and 10 is 10. 

Increase in the number of brown marbles in Bag Z
= 11 p - 2 p
= 9 p

9 p = 2 u
9 p = 18

1 p = 18 ÷ 9 = 2

Number of marbles in Bag Z in the end
= 10 p + 11 p
= 21 p
= 21 x 2
= 42

Answer(s): (a) 18; (b) 42