There were 104 brown, black and gold markers in a box. 6 gold markers were removed from the box and the ratio of the number of brown markers to the number of black markers to the number of gold markers became 4 : 3 : 7. Then some purple markers were added and the ratio of the number of gold markers to the number of purple markers was 7 : 3.

1. What was the ratio of the number of brown markers to the number of black markers to the number of gold markers at first?
2. How many markers were in the box in the end?

	Brown	Black	Gold	Purple	Total
Before	4 u	3 u	7 u + 6	0	104
Change 1	No change	No change	- 6		- 6
After 1	4 u	3 u	7 u		98
Change 2	No change	No change	No change	+ 3 u
After 2	4 u	3 u	7 u	3 u

(a)
Total number of markers at first
= 4 u + 3 u + 7 u + 6
= 14 u + 6

14 u + 6 = 104
14 u = 104 - 6
14 u = 98

1 u = 98 ÷ 14 = 7

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

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

Number of gold markers at first
= 7 u + 6
= 7 x 7 + 6
= 55 

At first
Brown markers : Black markers : Gold markers
28 : 21 : 55

(b)
Total number of markers in the box in the end
= 4 u + 3 u + 7 u + 3 u
= 17 u
= 119

Answer(s): (a) 28 : 21 : 55; (b) 119