Jaslyn had 63 marbles. ³₇ were red and the rest were silver and purple. The ratio of the number of silver marbles to the number of purple marbles was 1 : 2. Jaslyn decided to buy some more red marbles to increase the number of red marbles to half of the total number of marbles.

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

Red marbles	Silver marbles	Purple marbles	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	63

	Red marbles	Silver marbles	Purple marbles
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing red, silver and purple marbles in the end	1	1

(a)
The total number of silver marbles and purple marbles is repeated. Make the total number of silver marbles and purple 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 = 63

1 u = 63 ÷ 21 = 3

Number of less silver marbles than red marbles at first
= 9 u - 4 u
= 5 u
= 5 x 3
= 15

(b)
Number of more red marbles that Jaslyn had to buy
= 12 u - 9 u
= 3 u
= 3 x 3
= 9

Answer(s): (a) 15; (b) 9