Elyse had 420 buttons. ²₇ were pink and the rest were white and brown. The ratio of the number of white buttons to the number of brown buttons was 1 : 5. Elyse decided to buy some more pink buttons to increase the number of pink buttons to half of the total number of buttons.

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

Pink buttons	White buttons	Brown buttons	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	420

	Pink buttons	White buttons	Brown buttons
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing pink, white and brown buttons in the end	1	1

(a)
The total number of white buttons and brown buttons is repeated. Make the total number of white buttons and brown buttons the same.  LCM of 5 and 6 is 30.

Total number of buttons at first
= 12 u + 5 u + 25 u
= 42 u

42 u = 420

1 u = 420 ÷ 42 = 10

Number of less white buttons than pink buttons at first
= 12 u - 5 u
= 7 u
= 7 x 10
= 70

(b)
Number of more pink buttons that Elyse had to buy
= 30 u - 12 u
= 18 u
= 18 x 10
= 180

Answer(s): (a) 70; (b) 180