Eva had 180 buttons. ²₅ were white and the rest were yellow and brown. The ratio of the number of yellow buttons to the number of brown buttons was 1 : 3. Eva 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 yellow buttons than white buttons did he have at first?
2. How many more white buttons did he have to buy?

White buttons	Yellow buttons	Brown buttons	Total
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	180

	White buttons	Yellow buttons	Brown buttons
Before	8 u	3 u	9 u
Change	+ ?
After	12 u	12 u
Comparing white, yellow and brown buttons in the end	1	1

(a)
The total number of yellow buttons and brown buttons is repeated. Make the total number of yellow buttons and brown 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 = 180

1 u = 180 ÷ 20 = 9

Number of less yellow buttons than white buttons at first
= 8 u - 3 u
= 5 u
= 5 x 9
= 45

(b)
Number of more white buttons that Eva had to buy
= 12 u - 8 u
= 4 u
= 4 x 9
= 36

Answer(s): (a) 45; (b) 36