Gem had 168 cards. ²₇ were gold and the rest were green and grey. The ratio of the number of green cards to the number of grey cards was 1 : 5. Gem decided to buy some more gold cards to increase the number of gold cards to half of the total number of cards.

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

Gold cards	Green cards	Grey cards	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	168

	Gold cards	Green cards	Grey cards
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing gold, green and grey cards in the end	1	1

(a)
The total number of green cards and grey cards is repeated. Make the total number of green cards and grey 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 = 168

1 u = 168 ÷ 42 = 4

Number of less green cards than gold cards at first
= 12 u - 5 u
= 7 u
= 7 x 4
= 28

(b)
Number of more gold cards that Gem had to buy
= 30 u - 12 u
= 18 u
= 18 x 4
= 72

Answer(s): (a) 28; (b) 72