Nora had some grey marbles and green marbles in 2 boxes. In Box K, the ratio of the number of grey marbles to green marbles was 9 : 7. In Box L, the number of grey marbles was 3 times the number of green marbles. Nora transferred ⁴₇ of the green marbles from Box K to Box L. The number of marbles in Box K became 180 and the ratio of the number of grey marbles to green marbles in Box L became 6 : 7.

1. How many green marbles were transferred from Box K to Box L?
2. What was the number of marbles in Box L after the transfer?

	Box K		Box L
	Grey	Green	Grey	Green
Comparing grey marbles and green marbles at first	9 u	7 u	3x2 = 6 p	1x2 = 2 p
Before		7 u
Change		- 4 u		+ 4 u
After		3 u
Comparing grey marbles and green marbles in the end	9 u	3 u	6 p	7 p

(a)
Total number of marbles in the end for Box K
= 9 u + 3 u
= 12 u

12 u = 180

1 u = 180 ÷ 12 = 15

Number of green marbles that were transferred from Box K to Box L
= 4 u
= 4 x 15
= 60

(b)
The number of grey marbles in Box L remains unchanged.  Make the number of grey marbles in Box L the same.  LCM of 3 and 6 is 6. 

Increase in the number of green marbles in Box L
= 7 p - 2 p
= 5 p

5 p = 4 u
5 p = 60

1 p = 60 ÷ 5 = 12

Number of marbles in Box L in the end
= 6 p + 7 p
= 13 p
= 13 x 12
= 156

Answer(s): (a) 60; (b) 156