Xylia had some brown marbles and blue marbles in 2 boxes. In Box D, the ratio of the number of brown marbles to blue marbles was 8 : 7. In Box E, the number of brown marbles was 2 times the number of blue marbles. Xylia transferred ²₇ of the blue marbles from Box D to Box E. The number of marbles in Box D became 234 and the ratio of the number of brown marbles to blue marbles in Box E became 4 : 5.

1. How many blue marbles were transferred from Box D to Box E?
2. What was the number of marbles in Box E after the transfer?

	Box D		Box E
	Brown	Blue	Brown	Blue
Comparing brown marbles and blue 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 brown marbles and blue marbles in the end	8 u	5 u	4 p	5 p

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

13 u = 234

1 u = 234 ÷ 13 = 18

Number of blue marbles that were transferred from Box D to Box E
= 2 u
= 2 x 18
= 36

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

Increase in the number of blue marbles in Box E
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

Number of marbles in Box E in the end
= 4 p + 5 p
= 9 p
= 9 x 12
= 108

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