Tammy had 168 marbles. ²₇ were purple and the rest were red and blue. The ratio of the number of red marbles to the number of blue marbles was 1 : 3. Tammy decided to buy some more purple marbles to increase the number of purple marbles to half of the total number of marbles.

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

Purple marbles	Red marbles	Blue marbles	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	168

	Purple marbles	Red marbles	Blue marbles
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing purple, red and blue marbles in the end	1	1

(a)
The total number of red marbles and blue marbles is repeated. Make the total number of red marbles and blue marbles the same.  LCM of 5 and 4 is 20.

Total number of marbles at first
= 8 u + 5 u + 15 u
= 28 u

28 u = 168

1 u = 168 ÷ 28 = 6

Number of less red marbles than purple marbles at first
= 8 u - 5 u
= 3 u
= 3 x 6
= 18

(b)
Number of more purple marbles that Tammy had to buy
= 20 u - 8 u
= 12 u
= 12 x 6
= 72

Answer(s): (a) 18; (b) 72