There were 155 yellow, black and red markers in a box. 23 red markers were removed from the box and the ratio of the number of yellow markers to the number of black markers to the number of red markers became 5 : 4 : 3. Then some brown markers were added and the ratio of the number of red markers to the number of brown markers was 3 : 5.

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

	Yellow	Black	Red	Brown	Total
Before	5 u	4 u	3 u + 23	0	155
Change 1	No change	No change	- 23		- 23
After 1	5 u	4 u	3 u		132
Change 2	No change	No change	No change	+ 5 u
After 2	5 u	4 u	3 u	5 u

(a)
Total number of markers at first
= 5 u + 4 u + 3 u + 23
= 12 u + 23

12 u + 23 = 155
12 u = 155 - 23
12 u = 132

1 u = 132 ÷ 12 = 11

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

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

Number of red markers at first
= 3 u + 23
= 3 x 11 + 23
= 56 

At first
Yellow markers : Black markers : Red markers
55 : 44 : 56

(b)
Total number of markers in the box in the end
= 5 u + 4 u + 3 u + 5 u
= 17 u
= 187

Answer(s): (a) 55 : 44 : 56; (b) 187