Nicole had 420 cards. ²₇ were green and the rest were white and pink. The ratio of the number of white cards to the number of pink cards was 1 : 5. Nicole decided to buy some more green cards to increase the number of green cards to half of the total number of cards.

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

Green cards	White cards	Pink cards	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	420

	Green cards	White cards	Pink cards
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing green, white and pink cards in the end	1	1

(a)
The total number of white cards and pink cards is repeated. Make the total number of white cards and pink cards the same.  LCM of 5 and 6 is 30.

Total number of cards at first
= 12 u + 5 u + 25 u
= 42 u

42 u = 420

1 u = 420 ÷ 42 = 10

Number of less white cards than green cards at first
= 12 u - 5 u
= 7 u
= 7 x 10
= 70

(b)
Number of more green cards that Nicole had to buy
= 30 u - 12 u
= 18 u
= 18 x 10
= 180

Answer(s): (a) 70; (b) 180