There were 183 purple, white and green markers in a box. 14 green markers were removed from the box and the ratio of the number of purple markers to the number of white markers to the number of green markers became 4 : 2 : 7. Then some grey markers were added and the ratio of the number of green markers to the number of grey markers was 7 : 2.

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

	Purple	White	Green	Grey	Total
Before	4 u	2 u	7 u + 14	0	183
Change 1	No change	No change	- 14		- 14
After 1	4 u	2 u	7 u		169
Change 2	No change	No change	No change	+ 2 u
After 2	4 u	2 u	7 u	2 u

(a)
Total number of markers at first
= 4 u + 2 u + 7 u + 14
= 13 u + 14

13 u + 14 = 183
13 u = 183 - 14
13 u = 169

1 u = 169 ÷ 13 = 13

Number of purple markers at first
= 4 u
= 4 x 13
= 52

Number of white markers at first
= 2 u
= 2 x 13
= 26

Number of green markers at first
= 7 u + 14
= 7 x 13 + 14
= 105 

At first
Purple markers : White markers : Green markers
52 : 26 : 105

(b)
Total number of markers in the box in the end
= 4 u + 2 u + 7 u + 2 u
= 15 u
= 195

Answer(s): (a) 52 : 26 : 105; (b) 195