There were 92 green, grey and white markers in a box. 8 white markers were removed from the box and the ratio of the number of green markers to the number of grey markers to the number of white markers became 4 : 3 : 5. Then some gold markers were added and the ratio of the number of white markers to the number of gold markers was 5 : 4.

1. What was the ratio of the number of green markers to the number of grey markers to the number of white markers at first?
2. How many markers were in the box in the end?

	Green	Grey	White	Gold	Total
Before	4 u	3 u	5 u + 8	0	92
Change 1	No change	No change	- 8		- 8
After 1	4 u	3 u	5 u		84
Change 2	No change	No change	No change	+ 4 u
After 2	4 u	3 u	5 u	4 u

(a)
Total number of markers at first
= 4 u + 3 u + 5 u + 8
= 12 u + 8

12 u + 8 = 92
12 u = 92 - 8
12 u = 84

1 u = 84 ÷ 12 = 7

Number of green markers at first
= 4 u
= 4 x 7
= 28

Number of grey markers at first
= 3 u
= 3 x 7
= 21

Number of white markers at first
= 5 u + 8
= 5 x 7 + 8
= 43 

At first
Green markers : Grey markers : White markers
28 : 21 : 43

(b)
Total number of markers in the box in the end
= 4 u + 3 u + 5 u + 4 u
= 16 u
= 112

Answer(s): (a) 28 : 21 : 43; (b) 112