There were 206 gold, grey and red markers in a box. 24 red markers were removed from the box and the ratio of the number of gold markers to the number of grey markers to the number of red markers became 2 : 5 : 7. Then some black markers were added and the ratio of the number of red markers to the number of black markers was 7 : 3.

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

	Gold	Grey	Red	Black	Total
Before	2 u	5 u	7 u + 24	0	206
Change 1	No change	No change	- 24		- 24
After 1	2 u	5 u	7 u		182
Change 2	No change	No change	No change	+ 3 u
After 2	2 u	5 u	7 u	3 u

(a)
Total number of markers at first
= 2 u + 5 u + 7 u + 24
= 14 u + 24

14 u + 24 = 206
14 u = 206 - 24
14 u = 182

1 u = 182 ÷ 14 = 13

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

Number of grey markers at first
= 5 u
= 5 x 13
= 65

Number of red markers at first
= 7 u + 24
= 7 x 13 + 24
= 115 

At first
Gold markers : Grey markers : Red markers
26 : 65 : 115

(b)
Total number of markers in the box in the end
= 2 u + 5 u + 7 u + 3 u
= 17 u
= 221

Answer(s): (a) 26 : 65 : 115; (b) 221