Pamela had 40 buttons. ²₅ were brown and the rest were yellow and red. The ratio of the number of yellow buttons to the number of red buttons was 1 : 3. Pamela decided to buy some more brown buttons to increase the number of brown buttons to half of the total number of buttons.

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

Brown buttons	Yellow buttons	Red buttons	Total
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	40

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

(a)
The total number of yellow buttons and red buttons is repeated. Make the total number of yellow buttons and red 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 = 40

1 u = 40 ÷ 20 = 2

Number of less yellow buttons than brown buttons at first
= 8 u - 3 u
= 5 u
= 5 x 2
= 10

(b)
Number of more brown buttons that Pamela had to buy
= 12 u - 8 u
= 4 u
= 4 x 2
= 8

Answer(s): (a) 10; (b) 8