Pamela had some brown marbles and green marbles in 2 boxes. In Box F, the ratio of the number of brown marbles to green marbles was 9 : 7. In Box G, the number of brown marbles was 5 times the number of green marbles. Pamela transferred ⁴₇ of the green marbles from Box F to Box G. The number of marbles in Box F became 216 and the ratio of the number of brown marbles to green marbles in Box G became 10 : 11.

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

	Box F		Box G
	Brown	Green	Brown	Green
Comparing brown marbles and green marbles at first	9 u	7 u	5x2 = 10 p	1x2 = 2 p
Before		7 u
Change		- 4 u		+ 4 u
After		3 u
Comparing brown marbles and green marbles in the end	9 u	3 u	10 p	11 p

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

12 u = 216

1 u = 216 ÷ 12 = 18

Number of green marbles that were transferred from Box F to Box G
= 4 u
= 4 x 18
= 72

(b)
The number of brown marbles in Box G remains unchanged.  Make the number of brown marbles in Box G the same.  LCM of 5 and 10 is 10. 

Increase in the number of green marbles in Box G
= 11 p - 2 p
= 9 p

9 p = 4 u
9 p = 72

1 p = 72 ÷ 9 = 8

Number of marbles in Box G in the end
= 10 p + 11 p
= 21 p
= 21 x 8
= 168

Answer(s): (a) 72; (b) 168