Cole had 280 cards. ⁵₇ were white and the rest were brown and grey. The ratio of the number of brown cards to the number of grey cards was 1 : 4. Cole decided to give away some white cards to decrease the number of white cards to half of the total number of cards.

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

White cards	Brown cards	Grey cards	Total
5x5	2x5
	1x2	4x2
25 u	2 u	8 u	280

	White cards	Brown cards	Grey cards
Before	25 u	2 u	8 u
Change	- ?
After	10 u	10 u
Comparing white, 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 2 and 5 is 10.

Total number of cards at first
= 25 u + 2 u + 8 u
= 35 u

35 u = 280

1 u = 280 ÷ 35 = 8

Number of more white cards than brown cards at first
= 25 u - 2 u
= 23 u
= 23 x 8
= 184

(b)
Number of more white cards that Cole had to give away
= 25 u - 10 u
= 15 u
= 15 x 8
= 120

Answer(s): (a) 184; (b) 120