Jack had 40 buttons. ³₅ were brown and the rest were black and blue. The ratio of the number of black buttons to the number of blue buttons was 1 : 3. Jack 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	Blue buttons	Total
3x2	2x2
	1x1	3x1
6 u	1 u	3 u	40

	Brown buttons	Black buttons	Blue buttons
Before	6 u	1 u	3 u
Change	- ?
After	4 u	4 u
Comparing brown, 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 2 and 4 is 4.

Total number of buttons at first
= 6 u + 1 u + 3 u
= 10 u

10 u = 40

1 u = 40 ÷ 10 = 4

Number of more brown buttons than black buttons at first
= 6 u - 1 u
= 5 u
= 5 x 4
= 20

(b)
Number of more brown buttons that Jack had to give away
= 6 u - 4 u
= 2 u
= 2 x 4
= 8

Answer(s): (a) 20; (b) 8