Sean had 105 buttons. ⁴₅ were grey and the rest were brown and silver. The ratio of the number of brown buttons to the number of silver buttons was 1 : 2. Sean decided to give away some grey buttons to decrease the number of grey buttons to half of the total number of buttons.

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

Grey buttons	Brown buttons	Silver buttons	Total
4x3	1x3
	1x1	2x1
12 u	1 u	2 u	105

	Grey buttons	Brown buttons	Silver buttons
Before	12 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing grey, brown and silver buttons in the end	1	1

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

Total number of buttons at first
= 12 u + 1 u + 2 u
= 15 u

15 u = 105

1 u = 105 ÷ 15 = 7

Number of more grey buttons than brown buttons at first
= 12 u - 1 u
= 11 u
= 11 x 7
= 77

(b)
Number of more grey buttons that Sean had to give away
= 12 u - 3 u
= 9 u
= 9 x 7
= 63

Answer(s): (a) 77; (b) 63