Ahmad had 270 cards. ⁴₅ were green and the rest were brown and grey. The ratio of the number of brown cards to the number of grey cards was 1 : 5. Ahmad decided to give away some green cards to decrease the number of green cards to half of the total number of cards.

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

Green cards	Brown cards	Grey cards	Total
4x6	1x6
	1x1	5x1
24 u	1 u	5 u	270

	Green cards	Brown cards	Grey cards
Before	24 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing green, brown and grey cards in the end	1	1

(a)
The total number of brown cards and grey cards is repeated. Make the total number of brown cards and grey cards the same.  LCM of 1 and 6 is 6.

Total number of cards at first
= 24 u + 1 u + 5 u
= 30 u

30 u = 270

1 u = 270 ÷ 30 = 9

Number of more green cards than brown cards at first
= 24 u - 1 u
= 23 u
= 23 x 9
= 207

(b)
Number of more green cards that Ahmad had to give away
= 24 u - 6 u
= 18 u
= 18 x 9
= 162

Answer(s): (a) 207; (b) 162