Linda had 80 buttons. ²₅ were purple and the rest were yellow and brown. The ratio of the number of yellow buttons to the number of brown buttons was 1 : 3. Linda decided to buy some more purple buttons to increase the number of purple buttons to half of the total number of buttons.

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

Purple buttons	Yellow buttons	Brown buttons	Total
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	80

	Purple buttons	Yellow buttons	Brown buttons
Before	8 u	3 u	9 u
Change	+ ?
After	12 u	12 u
Comparing purple, 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 = 80

1 u = 80 ÷ 20 = 4

Number of less yellow buttons than purple buttons at first
= 8 u - 3 u
= 5 u
= 5 x 4
= 20

(b)
Number of more purple buttons that Linda had to buy
= 12 u - 8 u
= 4 u
= 4 x 4
= 16

Answer(s): (a) 20; (b) 16