Risa had 378 marbles. ²₇ were blue and the rest were white and silver. The ratio of the number of white marbles to the number of silver marbles was 1 : 5. Risa decided to buy some more blue marbles to increase the number of blue marbles to half of the total number of marbles.

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

Blue marbles	White marbles	Silver marbles	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	378

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

(a)
The total number of white marbles and silver marbles is repeated. Make the total number of white marbles and silver 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 = 378

1 u = 378 ÷ 42 = 9

Number of less white marbles than blue marbles at first
= 12 u - 5 u
= 7 u
= 7 x 9
= 63

(b)
Number of more blue marbles that Risa had to buy
= 30 u - 12 u
= 18 u
= 18 x 9
= 162

Answer(s): (a) 63; (b) 162