Gwen had 462 coins. ²₇ were green and the rest were red and black. The ratio of the number of red coins to the number of black coins was 1 : 5. Gwen decided to buy some more green coins to increase the number of green coins to half of the total number of coins.

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

Green coins	Red coins	Black coins	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	462

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

(a)
The total number of red coins and black coins is repeated. Make the total number of red coins and black 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 = 462

1 u = 462 ÷ 42 = 11

Number of less red coins than green coins at first
= 12 u - 5 u
= 7 u
= 7 x 11
= 77

(b)
Number of more green coins that Gwen had to buy
= 30 u - 12 u
= 18 u
= 18 x 11
= 198

Answer(s): (a) 77; (b) 198