Sam had 126 coins. ⁵₆ were black and the rest were green and white. The ratio of the number of green coins to the number of white coins was 1 : 2. Sam 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 green coins did he have at first?
2. How many black coins did he have to give away?

Black coins	Green coins	White coins	Total
5x3	1x3
	1x1	2x1
15 u	1 u	2 u	126

	Black coins	Green coins	White coins
Before	15 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing black, green and white coins in the end	1	1

(a)
The total number of green coins and white coins is repeated. Make the total number of green coins and white coins the same.  LCM of 1 and 3 is 3.

Total number of coins at first
= 15 u + 1 u + 2 u
= 18 u

18 u = 126

1 u = 126 ÷ 18 = 7

Number of more black coins than green coins at first
= 15 u - 1 u
= 14 u
= 14 x 7
= 98

(b)
Number of more black coins that Sam had to give away
= 15 u - 3 u
= 12 u
= 12 x 7
= 84

Answer(s): (a) 98; (b) 84