Hazel had some silver buttons and white buttons in 2 boxes. In Box T, the ratio of the number of silver buttons to white buttons was 9 : 7. In Box U, the number of silver buttons was 3 times the number of white buttons. Hazel transferred ²₇ of the white buttons from Box T to Box U. The number of buttons in Box T became 210 and the ratio of the number of silver buttons to white buttons in Box U became 6 : 7.

1. How many white buttons were transferred from Box T to Box U?
2. What was the number of buttons in Box U after the transfer?

	Box T		Box U
	Silver	White	Silver	White
Comparing silver buttons and white buttons at first	9 u	7 u	3x2 = 6 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing silver buttons and white buttons in the end	9 u	5 u	6 p	7 p

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

14 u = 210

1 u = 210 ÷ 14 = 15

Number of white buttons that were transferred from Box T to Box U
= 2 u
= 2 x 15
= 30

(b)
The number of silver buttons in Box U remains unchanged.  Make the number of silver buttons in Box U the same.  LCM of 3 and 6 is 6. 

Increase in the number of white buttons in Box U
= 7 p - 2 p
= 5 p

5 p = 2 u
5 p = 30

1 p = 30 ÷ 5 = 6

Number of buttons in Box U in the end
= 6 p + 7 p
= 13 p
= 13 x 6
= 78

Answer(s): (a) 30; (b) 78