Riordan had 275 coins. ⁴₅ were purple and the rest were black and blue. The ratio of the number of black coins to the number of blue coins was 1 : 4. Riordan decided to give away some purple coins to decrease the number of purple coins to half of the total number of coins.

1. How many more purple coins than black coins did he have at first?
2. How many purple coins did he have to give away?

Purple coins	Black coins	Blue coins	Total
4x5	1x5
	1x1	4x1
20 u	1 u	4 u	275

	Purple coins	Black coins	Blue coins
Before	20 u	1 u	4 u
Change	- ?
After	5 u	5 u
Comparing purple, black and blue coins in the end	1	1

(a)
The total number of black coins and blue coins is repeated. Make the total number of black coins and blue coins the same.  LCM of 1 and 5 is 5.

Total number of coins at first
= 20 u + 1 u + 4 u
= 25 u

25 u = 275

1 u = 275 ÷ 25 = 11

Number of more purple coins than black coins at first
= 20 u - 1 u
= 19 u
= 19 x 11
= 209

(b)
Number of more purple coins that Riordan had to give away
= 20 u - 5 u
= 15 u
= 15 x 11
= 165

Answer(s): (a) 209; (b) 165