Jaslyn had some white marbles and pink marbles in 2 packets. In Packet L, the ratio of the number of white marbles to pink marbles was 8 : 7. In Packet M, the number of white marbles was 2 times the number of pink marbles. Jaslyn transferred ²₇ of the pink marbles from Packet L to Packet M. The number of marbles in Packet L became 234 and the ratio of the number of white marbles to pink marbles in Packet M became 4 : 5.

1. How many pink marbles were transferred from Packet L to Packet M?
2. What was the number of marbles in Packet M after the transfer?

	Packet L		Packet M
	White	Pink	White	Pink
Comparing white marbles and pink marbles at first	8 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing white marbles and pink marbles in the end	8 u	5 u	4 p	5 p

(a)
Total number of marbles in the end for Packet L
= 8 u + 5 u
= 13 u

13 u = 234

1 u = 234 ÷ 13 = 18

Number of pink marbles that were transferred from Packet L to Packet M
= 2 u
= 2 x 18
= 36

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

Increase in the number of pink marbles in Packet M
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

Number of marbles in Packet M in the end
= 4 p + 5 p
= 9 p
= 9 x 12
= 108

Answer(s): (a) 36; (b) 108