Fabian had 60 buttons. ⁴₅ were yellow and the rest were pink and purple. The ratio of the number of pink buttons to the number of purple buttons was 1 : 2. Fabian decided to give away some yellow buttons to decrease the number of yellow buttons to half of the total number of buttons.

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

Yellow buttons	Pink buttons	Purple buttons	Total
4x3	1x3
	1x1	2x1
12 u	1 u	2 u	60

	Yellow buttons	Pink buttons	Purple buttons
Before	12 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing yellow, pink and purple buttons in the end	1	1

(a)
The total number of pink buttons and purple buttons is repeated. Make the total number of pink buttons and purple buttons the same.  LCM of 1 and 3 is 3.

Total number of buttons at first
= 12 u + 1 u + 2 u
= 15 u

15 u = 60

1 u = 60 ÷ 15 = 4

Number of more yellow buttons than pink buttons at first
= 12 u - 1 u
= 11 u
= 11 x 4
= 44

(b)
Number of more yellow buttons that Fabian had to give away
= 12 u - 3 u
= 9 u
= 9 x 4
= 36

Answer(s): (a) 44; (b) 36