Gillian had 420 marbles. ²₇ were pink and the rest were white and blue. The ratio of the number of white marbles to the number of blue marbles was 1 : 5. Gillian decided to buy some more pink marbles to increase the number of pink marbles to half of the total number of marbles.

1. How many less white marbles than pink marbles did he have at first?
2. How many more pink marbles did he have to buy?

Pink marbles	White marbles	Blue marbles	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	420

	Pink marbles	White marbles	Blue marbles
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing pink, white and blue marbles in the end	1	1

(a)
The total number of white marbles and blue marbles is repeated. Make the total number of white marbles and blue marbles the same.  LCM of 5 and 6 is 30.

Total number of marbles at first
= 12 u + 5 u + 25 u
= 42 u

42 u = 420

1 u = 420 ÷ 42 = 10

Number of less white marbles than pink marbles at first
= 12 u - 5 u
= 7 u
= 7 x 10
= 70

(b)
Number of more pink marbles that Gillian had to buy
= 30 u - 12 u
= 18 u
= 18 x 10
= 180

Answer(s): (a) 70; (b) 180