Charlie had 168 stickers. ⁵₇ were purple and the rest were grey and yellow. The ratio of the number of grey stickers to the number of yellow stickers was 1 : 2. Charlie decided to give away some purple stickers to decrease the number of purple stickers to half of the total number of stickers.

1. How many more purple stickers than grey stickers did he have at first?
2. How many purple stickers did he have to give away?

Purple stickers	Grey stickers	Yellow stickers	Total
5x3	2x3
	1x2	2x2
15 u	2 u	4 u	168

	Purple stickers	Grey stickers	Yellow stickers
Before	15 u	2 u	4 u
Change	- ?
After	6 u	6 u
Comparing purple, grey and yellow stickers in the end	1	1

(a)
The total number of grey stickers and yellow stickers is repeated. Make the total number of grey stickers and yellow stickers the same.  LCM of 2 and 3 is 6.

Total number of stickers at first
= 15 u + 2 u + 4 u
= 21 u

21 u = 168

1 u = 168 ÷ 21 = 8

Number of more purple stickers than grey stickers at first
= 15 u - 2 u
= 13 u
= 13 x 8
= 104

(b)
Number of more purple stickers that Charlie had to give away
= 15 u - 6 u
= 9 u
= 9 x 8
= 72

Answer(s): (a) 104; (b) 72