Rael had 180 cards. ⁵₆ were yellow and the rest were brown and black. The ratio of the number of brown cards to the number of black cards was 1 : 2. Rael decided to give away some yellow cards to decrease the number of yellow cards to half of the total number of cards.

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

Yellow cards	Brown cards	Black cards	Total
5x3	1x3
	1x1	2x1
15 u	1 u	2 u	180

	Yellow cards	Brown cards	Black cards
Before	15 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing yellow, brown and black cards in the end	1	1

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

Total number of cards at first
= 15 u + 1 u + 2 u
= 18 u

18 u = 180

1 u = 180 ÷ 18 = 10

Number of more yellow cards than brown cards at first
= 15 u - 1 u
= 14 u
= 14 x 10
= 140

(b)
Number of more yellow cards that Rael had to give away
= 15 u - 3 u
= 12 u
= 12 x 10
= 120

Answer(s): (a) 140; (b) 120