Nicole had some white marbles and black marbles in 2 boxes. In Box H, the ratio of the number of white marbles to black marbles was 8 : 5. In Box J, the number of white marbles was 3 times the number of black marbles. Nicole transferred ⁴₅ of the black marbles from Box H to Box J. The number of marbles in Box H became 135 and the ratio of the number of white marbles to black marbles in Box J became 6 : 7.

1. How many black marbles were transferred from Box H to Box J?
2. What was the number of marbles in Box J after the transfer?

	Box H		Box J
	White	Black	White	Black
Comparing white marbles and black marbles at first	8 u	5 u	3x2 = 6 p	1x2 = 2 p
Before		5 u
Change		- 4 u		+ 4 u
After		1 u
Comparing white marbles and black marbles in the end	8 u	1 u	6 p	7 p

(a)
Total number of marbles in the end for Box H
= 8 u + 1 u
= 9 u

9 u = 135

1 u = 135 ÷ 9 = 15

Number of black marbles that were transferred from Box H to Box J
= 4 u
= 4 x 15
= 60

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

Increase in the number of black marbles in Box J
= 7 p - 2 p
= 5 p

5 p = 4 u
5 p = 60

1 p = 60 ÷ 5 = 12

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

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