Kimberly had 315 cards. ³₇ were brown and the rest were blue and green. The ratio of the number of blue cards to the number of green cards was 1 : 4. Kimberly decided to buy some more brown cards to increase the number of brown cards to half of the total number of cards.

1. How many less blue cards than brown cards did he have at first?
2. How many more brown cards did he have to buy?

Brown cards	Blue cards	Green cards	Total
3x5	4x5
	1x4	4x4
15 u	4 u	16 u	315

	Brown cards	Blue cards	Green cards
Before	15 u	4 u	16 u
Change	+ ?
After	20 u	20 u
Comparing brown, blue and green cards in the end	1	1

(a)
The total number of blue cards and green cards is repeated. Make the total number of blue cards and green cards the same.  LCM of 4 and 5 is 20.

Total number of cards at first
= 15 u + 4 u + 16 u
= 35 u

35 u = 315

1 u = 315 ÷ 35 = 9

Number of less blue cards than brown cards at first
= 15 u - 4 u
= 11 u
= 11 x 9
= 99

(b)
Number of more brown cards that Kimberly had to buy
= 20 u - 15 u
= 5 u
= 5 x 9
= 45

Answer(s): (a) 99; (b) 45