Daniel had 132 cards. ³₄ were grey and the rest were red and white. The ratio of the number of red cards to the number of white cards was 1 : 2. Daniel 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 red cards did he have at first?
2. How many grey cards did he have to give away?

Grey cards	Red cards	White cards	Total
3x3	1x3
	1x1	2x1
9 u	1 u	2 u	132

	Grey cards	Red cards	White cards
Before	9 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing grey, red and white cards in the end	1	1

(a)
The total number of red cards and white cards is repeated. Make the total number of red cards and white cards the same.  LCM of 1 and 3 is 3.

Total number of cards at first
= 9 u + 1 u + 2 u
= 12 u

12 u = 132

1 u = 132 ÷ 12 = 11

Number of more grey cards than red cards at first
= 9 u - 1 u
= 8 u
= 8 x 11
= 88

(b)
Number of more grey cards that Daniel had to give away
= 9 u - 3 u
= 6 u
= 6 x 11
= 66

Answer(s): (a) 88; (b) 66