Natalie had some silver marbles and white marbles in 2 bags. In Bag M, the ratio of the number of silver marbles to white marbles was 8 : 5. In Bag N, the number of silver marbles was 2 times the number of white marbles. Natalie transferred ²₅ of the white marbles from Bag M to Bag N. The number of marbles in Bag M became 165 and the ratio of the number of silver marbles to white marbles in Bag N became 4 : 5.

1. How many white marbles were transferred from Bag M to Bag N?
2. What was the number of marbles in Bag N after the transfer?

	Bag M		Bag N
	Silver	White	Silver	White
Comparing silver marbles and white marbles at first	8 u	5 u	2x2 = 4 p	1x2 = 2 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing silver marbles and white marbles in the end	8 u	3 u	4 p	5 p

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

11 u = 165

1 u = 165 ÷ 11 = 15

Number of white marbles that were transferred from Bag M to Bag N
= 2 u
= 2 x 15
= 30

(b)
The number of silver marbles in Bag N remains unchanged.  Make the number of silver marbles in Bag N the same.  LCM of 2 and 4 is 4. 

Increase in the number of white marbles in Bag N
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 30

1 p = 30 ÷ 3 = 10

Number of marbles in Bag N in the end
= 4 p + 5 p
= 9 p
= 9 x 10
= 90

Answer(s): (a) 30; (b) 90