Kimberly had 280 coins. ³₇ were purple and the rest were red and white. The ratio of the number of red coins to the number of white coins was 1 : 4. Kimberly decided to buy some more purple coins to increase the number of purple coins to half of the total number of coins.

1. How many less red coins than purple coins did he have at first?
2. How many more purple coins did he have to buy?

Purple coins	Red coins	White coins	Total
3x5	4x5
	1x4	4x4
15 u	4 u	16 u	280

	Purple coins	Red coins	White coins
Before	15 u	4 u	16 u
Change	+ ?
After	20 u	20 u
Comparing purple, red and white coins in the end	1	1

(a)
The total number of red coins and white coins is repeated. Make the total number of red coins and white coins the same.  LCM of 4 and 5 is 20.

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

35 u = 280

1 u = 280 ÷ 35 = 8

Number of less red coins than purple coins at first
= 15 u - 4 u
= 11 u
= 11 x 8
= 88

(b)
Number of more purple coins that Kimberly had to buy
= 20 u - 15 u
= 5 u
= 5 x 8
= 40

Answer(s): (a) 88; (b) 40