Jade had 20 buttons. ²₅ were white and the rest were purple and grey. The ratio of the number of purple buttons to the number of grey buttons was 1 : 5. Jade decided to buy some more white buttons to increase the number of white buttons to half of the total number of buttons.

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

White buttons	Purple buttons	Grey buttons	Total
2x2	3x2
	1x1	5x1
4 u	1 u	5 u	20

	White buttons	Purple buttons	Grey buttons
Before	4 u	1 u	5 u
Change	+ ?
After	6 u	6 u
Comparing white, purple and grey buttons in the end	1	1

(a)
The total number of purple buttons and grey buttons is repeated. Make the total number of purple buttons and grey buttons the same.  LCM of 3 and 6 is 6.

Total number of buttons at first
= 4 u + 1 u + 5 u
= 10 u

10 u = 20

1 u = 20 ÷ 10 = 2

Number of less purple buttons than white buttons at first
= 4 u - 1 u
= 3 u
= 3 x 2
= 6

(b)
Number of more white buttons that Jade had to buy
= 6 u - 4 u
= 2 u
= 2 x 2
= 4

Answer(s): (a) 6; (b) 4