Glen had 280 buttons. ⁵₇ were silver and the rest were yellow and gold. The ratio of the number of yellow buttons to the number of gold buttons was 1 : 4. Glen decided to give away some silver buttons to decrease the number of silver buttons to half of the total number of buttons.

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

Silver buttons	Yellow buttons	Gold buttons	Total
5x5	2x5
	1x2	4x2
25 u	2 u	8 u	280

	Silver buttons	Yellow buttons	Gold buttons
Before	25 u	2 u	8 u
Change	- ?
After	10 u	10 u
Comparing silver, yellow and gold buttons in the end	1	1

(a)
The total number of yellow buttons and gold buttons is repeated. Make the total number of yellow buttons and gold buttons the same.  LCM of 2 and 5 is 10.

Total number of buttons at first
= 25 u + 2 u + 8 u
= 35 u

35 u = 280

1 u = 280 ÷ 35 = 8

Number of more silver buttons than yellow buttons at first
= 25 u - 2 u
= 23 u
= 23 x 8
= 184

(b)
Number of more silver buttons that Glen had to give away
= 25 u - 10 u
= 15 u
= 15 x 8
= 120

Answer(s): (a) 184; (b) 120