Ivory had some brown buttons and grey buttons in 2 boxes. In Box Q, the ratio of the number of brown buttons to grey buttons was 10 : 3. In Box R, the number of brown buttons was 2 times the number of grey buttons. Ivory transferred ²₃ of the grey buttons from Box Q to Box R. The number of buttons in Box Q became 132 and the ratio of the number of brown buttons to grey buttons in Box R became 4 : 5.

1. How many grey buttons were transferred from Box Q to Box R?
2. What was the number of buttons in Box R after the transfer?

	Box Q		Box R
	Brown	Grey	Brown	Grey
Comparing brown buttons and grey buttons at first	10 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing brown buttons and grey buttons in the end	10 u	1 u	4 p	5 p

(a)
Total number of buttons in the end for Box Q
= 10 u + 1 u
= 11 u

11 u = 132

1 u = 132 ÷ 11 = 12

Number of grey buttons that were transferred from Box Q to Box R
= 2 u
= 2 x 12
= 24

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

Increase in the number of grey buttons in Box R
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 24

1 p = 24 ÷ 3 = 8

Number of buttons in Box R in the end
= 4 p + 5 p
= 9 p
= 9 x 8
= 72

Answer(s): (a) 24; (b) 72