Michael had 240 coins. ⁴₅ were green and the rest were black and grey. The ratio of the number of black coins to the number of grey coins was 1 : 5. Michael decided to give away some green coins to decrease the number of green coins to half of the total number of coins.

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

Green coins	Black coins	Grey coins	Total
4x6	1x6
	1x1	5x1
24 u	1 u	5 u	240

	Green coins	Black coins	Grey coins
Before	24 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing green, black and grey coins in the end	1	1

(a)
The total number of black coins and grey coins is repeated. Make the total number of black coins and grey coins the same.  LCM of 1 and 6 is 6.

Total number of coins at first
= 24 u + 1 u + 5 u
= 30 u

30 u = 240

1 u = 240 ÷ 30 = 8

Number of more green coins than black coins at first
= 24 u - 1 u
= 23 u
= 23 x 8
= 184

(b)
Number of more green coins that Michael had to give away
= 24 u - 6 u
= 18 u
= 18 x 8
= 144

Answer(s): (a) 184; (b) 144