Emily had 225 marbles. ²₅ were grey and the rest were purple and white. The ratio of the number of purple marbles to the number of white marbles was 1 : 4. Emily 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 purple marbles than grey marbles did he have at first?
2. How many more grey marbles did he have to buy?

Grey marbles	Purple marbles	White marbles	Total
2x5	3x5
	1x3	4x3
10 u	3 u	12 u	225

	Grey marbles	Purple marbles	White marbles
Before	10 u	3 u	12 u
Change	+ ?
After	15 u	15 u
Comparing grey, purple and white marbles in the end	1	1

(a)
The total number of purple marbles and white marbles is repeated. Make the total number of purple marbles and white marbles the same.  LCM of 3 and 5 is 15.

Total number of marbles at first
= 10 u + 3 u + 12 u
= 25 u

25 u = 225

1 u = 225 ÷ 25 = 9

Number of less purple marbles than grey marbles at first
= 10 u - 3 u
= 7 u
= 7 x 9
= 63

(b)
Number of more grey marbles that Emily had to buy
= 15 u - 10 u
= 5 u
= 5 x 9
= 45

Answer(s): (a) 63; (b) 45