Mary had 462 marbles. ²₇ were gold and the rest were white and blue. The ratio of the number of white marbles to the number of blue marbles was 1 : 5. Mary decided to buy some more gold marbles to increase the number of gold marbles to half of the total number of marbles.

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

Gold marbles	White marbles	Blue marbles	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	462

	Gold marbles	White marbles	Blue marbles
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing gold, 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 = 462

1 u = 462 ÷ 42 = 11

Number of less white marbles than gold marbles at first
= 12 u - 5 u
= 7 u
= 7 x 11
= 77

(b)
Number of more gold marbles that Mary had to buy
= 30 u - 12 u
= 18 u
= 18 x 11
= 198

Answer(s): (a) 77; (b) 198