Billy had 30 marbles. ³₅ were pink and the rest were blue and grey. The ratio of the number of blue marbles to the number of grey marbles was 1 : 5. Billy decided to give away some pink marbles to decrease the number of pink marbles to half of the total number of marbles.

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

Pink marbles	Blue marbles	Grey marbles	Total
3x3	2x3
	1x1	5x1
9 u	1 u	5 u	30

	Pink marbles	Blue marbles	Grey marbles
Before	9 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing pink, blue and grey marbles in the end	1	1

(a)
The total number of blue marbles and grey marbles is repeated. Make the total number of blue marbles and grey marbles the same.  LCM of 2 and 6 is 6.

Total number of marbles at first
= 9 u + 1 u + 5 u
= 15 u

15 u = 30

1 u = 30 ÷ 15 = 2

Number of more pink marbles than blue marbles at first
= 9 u - 1 u
= 8 u
= 8 x 2
= 16

(b)
Number of more pink marbles that Billy had to give away
= 9 u - 6 u
= 3 u
= 3 x 2
= 6

Answer(s): (a) 16; (b) 6