Reggie had 180 buttons. ³₅ were brown and the rest were white and pink. The ratio of the number of white buttons to the number of pink buttons was 1 : 2. Reggie 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 white buttons did he have at first?
2. How many brown buttons did he have to give away?

Brown buttons	White buttons	Pink buttons	Total
3x3	2x3
	1x2	2x2
9 u	2 u	4 u	180

	Brown buttons	White buttons	Pink buttons
Before	9 u	2 u	4 u
Change	- ?
After	6 u	6 u
Comparing brown, white and pink buttons in the end	1	1

(a)
The total number of white buttons and pink buttons is repeated. Make the total number of white buttons and pink buttons the same.  LCM of 2 and 3 is 6.

Total number of buttons at first
= 9 u + 2 u + 4 u
= 15 u

15 u = 180

1 u = 180 ÷ 15 = 12

Number of more brown buttons than white buttons at first
= 9 u - 2 u
= 7 u
= 7 x 12
= 84

(b)
Number of more brown buttons that Reggie had to give away
= 9 u - 6 u
= 3 u
= 3 x 12
= 36

Answer(s): (a) 84; (b) 36