Fred had 90 cards. ⁵₆ were white and the rest were yellow and purple. The ratio of the number of yellow cards to the number of purple cards was 1 : 4. Fred 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 yellow cards did he have at first?
2. How many white cards did he have to give away?

White cards	Yellow cards	Purple cards	Total
5x5	1x5
	1x1	4x1
25 u	1 u	4 u	90

	White cards	Yellow cards	Purple cards
Before	25 u	1 u	4 u
Change	- ?
After	5 u	5 u
Comparing white, yellow and purple cards in the end	1	1

(a)
The total number of yellow cards and purple cards is repeated. Make the total number of yellow cards and purple cards the same.  LCM of 1 and 5 is 5.

Total number of cards at first
= 25 u + 1 u + 4 u
= 30 u

30 u = 90

1 u = 90 ÷ 30 = 3

Number of more white cards than yellow cards at first
= 25 u - 1 u
= 24 u
= 24 x 3
= 72

(b)
Number of more white cards that Fred had to give away
= 25 u - 5 u
= 20 u
= 20 x 3
= 60

Answer(s): (a) 72; (b) 60