Hazel had some brown buttons and blue buttons in 2 boxes. In Box J, the ratio of the number of brown buttons to blue buttons was 9 : 7. In Box K, the number of brown buttons was 2 times the number of blue buttons. Hazel transferred ²₇ of the blue buttons from Box J to Box K. The number of buttons in Box J became 140 and the ratio of the number of brown buttons to blue buttons in Box K became 6 : 7.

1. How many blue buttons were transferred from Box J to Box K?
2. What was the number of buttons in Box K after the transfer?

	Box J		Box K
	Brown	Blue	Brown	Blue
Comparing brown buttons and blue buttons at first	9 u	7 u	2x3 = 6 p	1x3 = 3 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing brown buttons and blue buttons in the end	9 u	5 u	6 p	7 p

(a)
Total number of buttons in the end for Box J
= 9 u + 5 u
= 14 u

14 u = 140

1 u = 140 ÷ 14 = 10

Number of blue buttons that were transferred from Box J to Box K
= 2 u
= 2 x 10
= 20

(b)
The number of brown buttons in Box K remains unchanged.  Make the number of brown buttons in Box K the same.  LCM of 2 and 6 is 6. 

Increase in the number of blue buttons in Box K
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 20

1 p = 20 ÷ 4 = 5

Number of buttons in Box K in the end
= 6 p + 7 p
= 13 p
= 13 x 5
= 65

Answer(s): (a) 20; (b) 65