Glen had 150 cards. ³₅ were purple and the rest were red and grey. The ratio of the number of red cards to the number of grey cards was 1 : 2. Glen decided to give away some purple cards to decrease the number of purple cards to half of the total number of cards.

1. How many more purple cards than red cards did he have at first?
2. How many purple cards did he have to give away?

Purple cards	Red cards	Grey cards	Total
3x3	2x3
	1x2	2x2
9 u	2 u	4 u	150

	Purple cards	Red cards	Grey cards
Before	9 u	2 u	4 u
Change	- ?
After	6 u	6 u
Comparing purple, red and grey cards in the end	1	1

(a)
The total number of red cards and grey cards is repeated. Make the total number of red cards and grey cards the same.  LCM of 2 and 3 is 6.

Total number of cards at first
= 9 u + 2 u + 4 u
= 15 u

15 u = 150

1 u = 150 ÷ 15 = 10

Number of more purple cards than red cards at first
= 9 u - 2 u
= 7 u
= 7 x 10
= 70

(b)
Number of more purple cards that Glen had to give away
= 9 u - 6 u
= 3 u
= 3 x 10
= 30

Answer(s): (a) 70; (b) 30