There were 167 blue, red and gold markers in a box. 17 gold markers were removed from the box and the ratio of the number of blue markers to the number of red markers to the number of gold markers became 5 : 2 : 3. Then some white markers were added and the ratio of the number of gold markers to the number of white markers was 3 : 9.

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

	Blue	Red	Gold	White	Total
Before	5 u	2 u	3 u + 17	0	167
Change 1	No change	No change	- 17		- 17
After 1	5 u	2 u	3 u		150
Change 2	No change	No change	No change	+ 9 u
After 2	5 u	2 u	3 u	9 u

(a)
Total number of markers at first
= 5 u + 2 u + 3 u + 17
= 10 u + 17

10 u + 17 = 167
10 u = 167 - 17
10 u = 150

1 u = 150 ÷ 10 = 15

Number of blue markers at first
= 5 u
= 5 x 15
= 75

Number of red markers at first
= 2 u
= 2 x 15
= 30

Number of gold markers at first
= 3 u + 17
= 3 x 15 + 17
= 62 

At first
Blue markers : Red markers : Gold markers
75 : 30 : 62

(b)
Total number of markers in the box in the end
= 5 u + 2 u + 3 u + 9 u
= 19 u
= 285

Answer(s): (a) 75 : 30 : 62; (b) 285