Sarah had 504 marbles. ²₇ were silver and the rest were purple and red. The ratio of the number of purple marbles to the number of red marbles was 1 : 5. Sarah decided to buy some more silver marbles to increase the number of silver marbles to half of the total number of marbles.

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

Silver marbles	Purple marbles	Red marbles	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	504

	Silver marbles	Purple marbles	Red marbles
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing silver, purple and red marbles in the end	1	1

(a)
The total number of purple marbles and red marbles is repeated. Make the total number of purple marbles and red 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 = 504

1 u = 504 ÷ 42 = 12

Number of less purple marbles than silver marbles at first
= 12 u - 5 u
= 7 u
= 7 x 12
= 84

(b)
Number of more silver marbles that Sarah had to buy
= 30 u - 12 u
= 18 u
= 18 x 12
= 216

Answer(s): (a) 84; (b) 216