Anna had 280 buttons. ²₇ were gold and the rest were yellow and silver. The ratio of the number of yellow buttons to the number of silver buttons was 1 : 3. Anna decided to buy some more gold buttons to increase the number of gold buttons to half of the total number of buttons.

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

Gold buttons	Yellow buttons	Silver buttons	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	280

	Gold buttons	Yellow buttons	Silver buttons
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing gold, yellow and silver buttons in the end	1	1

(a)
The total number of yellow buttons and silver buttons is repeated. Make the total number of yellow buttons and silver buttons the same.  LCM of 5 and 4 is 20.

Total number of buttons at first
= 8 u + 5 u + 15 u
= 28 u

28 u = 280

1 u = 280 ÷ 28 = 10

Number of less yellow buttons than gold buttons at first
= 8 u - 5 u
= 3 u
= 3 x 10
= 30

(b)
Number of more gold buttons that Anna had to buy
= 20 u - 8 u
= 12 u
= 12 x 10
= 120

Answer(s): (a) 30; (b) 120