Elijah had 48 buttons. ³₄ were pink and the rest were red and white. The ratio of the number of red buttons to the number of white buttons was 1 : 5. Elijah decided to give away some pink buttons to decrease the number of pink buttons to half of the total number of buttons.

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

Pink buttons	Red buttons	White buttons	Total
3x6	1x6
	1x1	5x1
18 u	1 u	5 u	48

	Pink buttons	Red buttons	White buttons
Before	18 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing pink, red and white buttons in the end	1	1

(a)
The total number of red buttons and white buttons is repeated. Make the total number of red buttons and white buttons the same.  LCM of 1 and 6 is 6.

Total number of buttons at first
= 18 u + 1 u + 5 u
= 24 u

24 u = 48

1 u = 48 ÷ 24 = 2

Number of more pink buttons than red buttons at first
= 18 u - 1 u
= 17 u
= 17 x 2
= 34

(b)
Number of more pink buttons that Elijah had to give away
= 18 u - 6 u
= 12 u
= 12 x 2
= 24

Answer(s): (a) 34; (b) 24