Asher had 24 marbles. ³₄ were black and the rest were white and green. The ratio of the number of white marbles to the number of green marbles was 1 : 2. Asher decided to give away some black marbles to decrease the number of black marbles to half of the total number of marbles.

1. How many more black marbles than white marbles did he have at first?
2. How many black marbles did he have to give away?

Black marbles	White marbles	Green marbles	Total
3x3	1x3
	1x1	2x1
9 u	1 u	2 u	24

	Black marbles	White marbles	Green marbles
Before	9 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing black, white and green marbles in the end	1	1

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

Total number of marbles at first
= 9 u + 1 u + 2 u
= 12 u

12 u = 24

1 u = 24 ÷ 12 = 2

Number of more black marbles than white marbles at first
= 9 u - 1 u
= 8 u
= 8 x 2
= 16

(b)
Number of more black marbles that Asher had to give away
= 9 u - 3 u
= 6 u
= 6 x 2
= 12

Answer(s): (a) 16; (b) 12