There were 139 purple, brown and red markers in a box. 11 red markers were removed from the box and the ratio of the number of purple markers to the number of brown markers to the number of red markers became 3 : 4 : 9. Then some gold markers were added and the ratio of the number of red markers to the number of gold markers was 9 : 3.

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

	Purple	Brown	Red	Gold	Total
Before	3 u	4 u	9 u + 11	0	139
Change 1	No change	No change	- 11		- 11
After 1	3 u	4 u	9 u		128
Change 2	No change	No change	No change	+ 3 u
After 2	3 u	4 u	9 u	3 u

(a)
Total number of markers at first
= 3 u + 4 u + 9 u + 11
= 16 u + 11

16 u + 11 = 139
16 u = 139 - 11
16 u = 128

1 u = 128 ÷ 16 = 8

Number of purple markers at first
= 3 u
= 3 x 8
= 24

Number of brown markers at first
= 4 u
= 4 x 8
= 32

Number of red markers at first
= 9 u + 11
= 9 x 8 + 11
= 83 

At first
Purple markers : Brown markers : Red markers
24 : 32 : 83

(b)
Total number of markers in the box in the end
= 3 u + 4 u + 9 u + 3 u
= 19 u
= 152

Answer(s): (a) 24 : 32 : 83; (b) 152