Mark had 168 stickers. ⁴₇ were black and the rest were blue and green. The ratio of the number of blue stickers to the number of green stickers was 1 : 5. Mark decided to give away some black stickers to decrease the number of black stickers to half of the total number of stickers.

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

Black stickers	Blue stickers	Green stickers	Total
4x2	3x2
	1x1	5x1
8 u	1 u	5 u	168

	Black stickers	Blue stickers	Green stickers
Before	8 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing black, blue and green stickers in the end	1	1

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

Total number of stickers at first
= 8 u + 1 u + 5 u
= 14 u

14 u = 168

1 u = 168 ÷ 14 = 12

Number of more black stickers than blue stickers at first
= 8 u - 1 u
= 7 u
= 7 x 12
= 84

(b)
Number of more black stickers that Mark had to give away
= 8 u - 6 u
= 2 u
= 2 x 12
= 24

Answer(s): (a) 84; (b) 24