Zeph had 216 coins. ⁵₆ were black and the rest were silver and purple. The ratio of the number of silver coins to the number of purple coins was 1 : 5. Zeph decided to give away some black coins to decrease the number of black coins to half of the total number of coins.

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

Black coins	Silver coins	Purple coins	Total
5x6	1x6
	1x1	5x1
30 u	1 u	5 u	216

	Black coins	Silver coins	Purple coins
Before	30 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing black, silver and purple coins in the end	1	1

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

Total number of coins at first
= 30 u + 1 u + 5 u
= 36 u

36 u = 216

1 u = 216 ÷ 36 = 6

Number of more black coins than silver coins at first
= 30 u - 1 u
= 29 u
= 29 x 6
= 174

(b)
Number of more black coins that Zeph had to give away
= 30 u - 6 u
= 24 u
= 24 x 6
= 144

Answer(s): (a) 174; (b) 144