There were 229 green, pink and grey markers in a box. 25 grey markers were removed from the box and the ratio of the number of green markers to the number of pink markers to the number of grey markers became 5 : 4 : 3. Then some purple markers were added and the ratio of the number of grey markers to the number of purple markers was 3 : 6.

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

	Green	Pink	Grey	Purple	Total
Before	5 u	4 u	3 u + 25	0	229
Change 1	No change	No change	- 25		- 25
After 1	5 u	4 u	3 u		204
Change 2	No change	No change	No change	+ 6 u
After 2	5 u	4 u	3 u	6 u

(a)
Total number of markers at first
= 5 u + 4 u + 3 u + 25
= 12 u + 25

12 u + 25 = 229
12 u = 229 - 25
12 u = 204

1 u = 204 ÷ 12 = 17

Number of green markers at first
= 5 u
= 5 x 17
= 85

Number of pink markers at first
= 4 u
= 4 x 17
= 68

Number of grey markers at first
= 3 u + 25
= 3 x 17 + 25
= 76 

At first
Green markers : Pink markers : Grey markers
85 : 68 : 76

(b)
Total number of markers in the box in the end
= 5 u + 4 u + 3 u + 6 u
= 18 u
= 306

Answer(s): (a) 85 : 68 : 76; (b) 306