Jade had 252 marbles. ³₇ were grey and the rest were blue and brown. The ratio of the number of blue marbles to the number of brown marbles was 1 : 2. Jade decided to buy some more grey marbles to increase the number of grey marbles to half of the total number of marbles.

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

Grey marbles	Blue marbles	Brown marbles	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	252

	Grey marbles	Blue marbles	Brown marbles
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing grey, blue and brown marbles in the end	1	1

(a)
The total number of blue marbles and brown marbles is repeated. Make the total number of blue marbles and brown marbles the same.  LCM of 4 and 3 is 12.

Total number of marbles at first
= 9 u + 4 u + 8 u
= 21 u

21 u = 252

1 u = 252 ÷ 21 = 12

Number of less blue marbles than grey marbles at first
= 9 u - 4 u
= 5 u
= 5 x 12
= 60

(b)
Number of more grey marbles that Jade had to buy
= 12 u - 9 u
= 3 u
= 3 x 12
= 36

Answer(s): (a) 60; (b) 36