There were 210 purple, blue and grey markers in a box. 12 grey markers were removed from the box and the ratio of the number of purple markers to the number of blue markers to the number of grey markers became 4 : 5 : 9. Then some brown markers were added and the ratio of the number of grey markers to the number of brown markers was 9 : 2.

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

	Purple	Blue	Grey	Brown	Total
Before	4 u	5 u	9 u + 12	0	210
Change 1	No change	No change	- 12		- 12
After 1	4 u	5 u	9 u		198
Change 2	No change	No change	No change	+ 2 u
After 2	4 u	5 u	9 u	2 u

(a)
Total number of markers at first
= 4 u + 5 u + 9 u + 12
= 18 u + 12

18 u + 12 = 210
18 u = 210 - 12
18 u = 198

1 u = 198 ÷ 18 = 11

Number of purple markers at first
= 4 u
= 4 x 11
= 44

Number of blue markers at first
= 5 u
= 5 x 11
= 55

Number of grey markers at first
= 9 u + 12
= 9 x 11 + 12
= 111 

At first
Purple markers : Blue markers : Grey markers
44 : 55 : 111

(b)
Total number of markers in the box in the end
= 4 u + 5 u + 9 u + 2 u
= 20 u
= 220

Answer(s): (a) 44 : 55 : 111; (b) 220