Wendy had some grey marbles and green marbles in 2 boxes. In Box A, the ratio of the number of grey marbles to green marbles was 7 : 3. In Box B, the number of grey marbles was 2 times the number of green marbles. Wendy transferred ²₃ of the green marbles from Box A to Box B. The number of marbles in Box A became 120 and the ratio of the number of grey marbles to green marbles in Box B became 4 : 5.

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

	Box A		Box B
	Grey	Green	Grey	Green
Comparing grey marbles and green marbles at first	7 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing grey marbles and green marbles in the end	7 u	1 u	4 p	5 p

(a)
Total number of marbles in the end for Box A
= 7 u + 1 u
= 8 u

8 u = 120

1 u = 120 ÷ 8 = 15

Number of green marbles that were transferred from Box A to Box B
= 2 u
= 2 x 15
= 30

(b)
The number of grey marbles in Box B remains unchanged.  Make the number of grey marbles in Box B the same.  LCM of 2 and 4 is 4. 

Increase in the number of green marbles in Box B
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 30

1 p = 30 ÷ 3 = 10

Number of marbles in Box B in the end
= 4 p + 5 p
= 9 p
= 9 x 10
= 90

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