Jack had 168 cards. ⁵₇ were grey and the rest were black and gold. The ratio of the number of black cards to the number of gold cards was 1 : 2. Jack decided to give away some grey cards to decrease the number of grey cards to half of the total number of cards.

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

Grey cards	Black cards	Gold cards	Total
5x3	2x3
	1x2	2x2
15 u	2 u	4 u	168

	Grey cards	Black cards	Gold cards
Before	15 u	2 u	4 u
Change	- ?
After	6 u	6 u
Comparing grey, black and gold cards in the end	1	1

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

Total number of cards at first
= 15 u + 2 u + 4 u
= 21 u

21 u = 168

1 u = 168 ÷ 21 = 8

Number of more grey cards than black cards at first
= 15 u - 2 u
= 13 u
= 13 x 8
= 104

(b)
Number of more grey cards that Jack had to give away
= 15 u - 6 u
= 9 u
= 9 x 8
= 72

Answer(s): (a) 104; (b) 72