Brandon had 150 stickers. ³₅ were gold and the rest were purple and blue. The ratio of the number of purple stickers to the number of blue stickers was 1 : 2. Brandon decided to give away some gold stickers to decrease the number of gold stickers to half of the total number of stickers.

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

Gold stickers	Purple stickers	Blue stickers	Total
3x3	2x3
	1x2	2x2
9 u	2 u	4 u	150

	Gold stickers	Purple stickers	Blue stickers
Before	9 u	2 u	4 u
Change	- ?
After	6 u	6 u
Comparing gold, purple and blue stickers in the end	1	1

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

Total number of stickers at first
= 9 u + 2 u + 4 u
= 15 u

15 u = 150

1 u = 150 ÷ 15 = 10

Number of more gold stickers than purple stickers at first
= 9 u - 2 u
= 7 u
= 7 x 10
= 70

(b)
Number of more gold stickers that Brandon had to give away
= 9 u - 6 u
= 3 u
= 3 x 10
= 30

Answer(s): (a) 70; (b) 30