Pierre had 96 buttons. ³₄ were brown and the rest were black and silver. The ratio of the number of black buttons to the number of silver buttons was 1 : 3. Pierre decided to give away some brown buttons to decrease the number of brown buttons to half of the total number of buttons.

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

Brown buttons	Black buttons	Silver buttons	Total
3x4	1x4
	1x1	3x1
12 u	1 u	3 u	96

	Brown buttons	Black buttons	Silver buttons
Before	12 u	1 u	3 u
Change	- ?
After	4 u	4 u
Comparing brown, black and silver buttons in the end	1	1

(a)
The total number of black buttons and silver buttons is repeated. Make the total number of black buttons and silver buttons the same.  LCM of 1 and 4 is 4.

Total number of buttons at first
= 12 u + 1 u + 3 u
= 16 u

16 u = 96

1 u = 96 ÷ 16 = 6

Number of more brown buttons than black buttons at first
= 12 u - 1 u
= 11 u
= 11 x 6
= 66

(b)
Number of more brown buttons that Pierre had to give away
= 12 u - 4 u
= 8 u
= 8 x 6
= 48

Answer(s): (a) 66; (b) 48