Gillian had 200 coins. ²₅ were gold and the rest were red and silver. The ratio of the number of red coins to the number of silver coins was 1 : 4. Gillian decided to buy some more gold coins to increase the number of gold coins to half of the total number of coins.

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

Gold coins	Red coins	Silver coins	Total
2x5	3x5
	1x3	4x3
10 u	3 u	12 u	200

	Gold coins	Red coins	Silver coins
Before	10 u	3 u	12 u
Change	+ ?
After	15 u	15 u
Comparing gold, red and silver coins in the end	1	1

(a)
The total number of red coins and silver coins is repeated. Make the total number of red coins and silver coins the same.  LCM of 3 and 5 is 15.

Total number of coins at first
= 10 u + 3 u + 12 u
= 25 u

25 u = 200

1 u = 200 ÷ 25 = 8

Number of less red coins than gold coins at first
= 10 u - 3 u
= 7 u
= 7 x 8
= 56

(b)
Number of more gold coins that Gillian had to buy
= 15 u - 10 u
= 5 u
= 5 x 8
= 40

Answer(s): (a) 56; (b) 40