Nicole had some brown marbles and silver marbles in 2 packets. In Packet N, the ratio of the number of brown marbles to silver marbles was 10 : 7. In Packet P, the number of brown marbles was 2 times the number of silver marbles. Nicole transferred ²₇ of the silver marbles from Packet N to Packet P. The number of marbles in Packet N became 135 and the ratio of the number of brown marbles to silver marbles in Packet P became 4 : 5.

1. How many silver marbles were transferred from Packet N to Packet P?
2. What was the number of marbles in Packet P after the transfer?

	Packet N		Packet P
	Brown	Silver	Brown	Silver
Comparing brown marbles and silver marbles at first	10 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing brown marbles and silver marbles in the end	10 u	5 u	4 p	5 p

(a)
Total number of marbles in the end for Packet N
= 10 u + 5 u
= 15 u

15 u = 135

1 u = 135 ÷ 15 = 9

Number of silver marbles that were transferred from Packet N to Packet P
= 2 u
= 2 x 9
= 18

(b)
The number of brown marbles in Packet P remains unchanged.  Make the number of brown marbles in Packet P the same.  LCM of 2 and 4 is 4. 

Increase in the number of silver marbles in Packet P
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 18

1 p = 18 ÷ 3 = 6

Number of marbles in Packet P in the end
= 4 p + 5 p
= 9 p
= 9 x 6
= 54

Answer(s): (a) 18; (b) 54