Daniel had 132 buttons. ³₄ were white and the rest were black and blue. The ratio of the number of black buttons to the number of blue buttons was 1 : 2. Daniel decided to give away some white buttons to decrease the number of white buttons to half of the total number of buttons.

1. How many more white buttons than black buttons did he have at first?
2. How many white buttons did he have to give away?

White buttons	Black buttons	Blue buttons	Total
3x3	1x3
	1x1	2x1
9 u	1 u	2 u	132

	White buttons	Black buttons	Blue buttons
Before	9 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing white, black and blue buttons in the end	1	1

(a)
The total number of black buttons and blue buttons is repeated. Make the total number of black buttons and blue buttons the same.  LCM of 1 and 3 is 3.

Total number of buttons at first
= 9 u + 1 u + 2 u
= 12 u

12 u = 132

1 u = 132 ÷ 12 = 11

Number of more white buttons than black buttons at first
= 9 u - 1 u
= 8 u
= 8 x 11
= 88

(b)
Number of more white buttons that Daniel had to give away
= 9 u - 3 u
= 6 u
= 6 x 11
= 66

Answer(s): (a) 88; (b) 66