Zeph had 120 coins. ³₄ were blue and the rest were gold and white. The ratio of the number of gold coins to the number of white coins was 1 : 4. Zeph decided to give away some blue coins to decrease the number of blue coins to half of the total number of coins.

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

Blue coins	Gold coins	White coins	Total
3x5	1x5
	1x1	4x1
15 u	1 u	4 u	120

	Blue coins	Gold coins	White coins
Before	15 u	1 u	4 u
Change	- ?
After	5 u	5 u
Comparing blue, gold and white coins in the end	1	1

(a)
The total number of gold coins and white coins is repeated. Make the total number of gold coins and white coins the same.  LCM of 1 and 5 is 5.

Total number of coins at first
= 15 u + 1 u + 4 u
= 20 u

20 u = 120

1 u = 120 ÷ 20 = 6

Number of more blue coins than gold coins at first
= 15 u - 1 u
= 14 u
= 14 x 6
= 84

(b)
Number of more blue coins that Zeph had to give away
= 15 u - 5 u
= 10 u
= 10 x 6
= 60

Answer(s): (a) 84; (b) 60