Lynn had 84 coins. ²₇ were black and the rest were green and gold. The ratio of the number of green coins to the number of gold coins was 1 : 5. Lynn decided to buy some more black coins to increase the number of black coins to half of the total number of coins.

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

Black coins	Green coins	Gold coins	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	84

	Black coins	Green coins	Gold coins
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing black, green and gold coins in the end	1	1

(a)
The total number of green coins and gold coins is repeated. Make the total number of green coins and gold coins the same.  LCM of 5 and 6 is 30.

Total number of coins at first
= 12 u + 5 u + 25 u
= 42 u

42 u = 84

1 u = 84 ÷ 42 = 2

Number of less green coins than black coins at first
= 12 u - 5 u
= 7 u
= 7 x 2
= 14

(b)
Number of more black coins that Lynn had to buy
= 30 u - 12 u
= 18 u
= 18 x 2
= 36

Answer(s): (a) 14; (b) 36