Xuan had 60 buttons. ²₅ were silver and the rest were white and purple. The ratio of the number of white buttons to the number of purple buttons was 1 : 3. Xuan decided to buy some more silver buttons to increase the number of silver buttons to half of the total number of buttons.

1. How many less white buttons than silver buttons did he have at first?
2. How many more silver buttons did he have to buy?

Silver buttons	White buttons	Purple buttons	Total
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	60

	Silver buttons	White buttons	Purple buttons
Before	8 u	3 u	9 u
Change	+ ?
After	12 u	12 u
Comparing silver, white and purple buttons in the end	1	1

(a)
The total number of white buttons and purple buttons is repeated. Make the total number of white buttons and purple buttons the same.  LCM of 3 and 4 is 12.

Total number of buttons at first
= 8 u + 3 u + 9 u
= 20 u

20 u = 60

1 u = 60 ÷ 20 = 3

Number of less white buttons than silver buttons at first
= 8 u - 3 u
= 5 u
= 5 x 3
= 15

(b)
Number of more silver buttons that Xuan had to buy
= 12 u - 8 u
= 4 u
= 4 x 3
= 12

Answer(s): (a) 15; (b) 12