There were 109 pink, blue and red markers in a box. 19 red markers were removed from the box and the ratio of the number of pink markers to the number of blue markers to the number of red markers became 2 : 5 : 3. Then some green markers were added and the ratio of the number of red markers to the number of green markers was 3 : 5.

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

	Pink	Blue	Red	Green	Total
Before	2 u	5 u	3 u + 19	0	109
Change 1	No change	No change	- 19		- 19
After 1	2 u	5 u	3 u		90
Change 2	No change	No change	No change	+ 5 u
After 2	2 u	5 u	3 u	5 u

(a)
Total number of markers at first
= 2 u + 5 u + 3 u + 19
= 10 u + 19

10 u + 19 = 109
10 u = 109 - 19
10 u = 90

1 u = 90 ÷ 10 = 9

Number of pink markers at first
= 2 u
= 2 x 9
= 18

Number of blue markers at first
= 5 u
= 5 x 9
= 45

Number of red markers at first
= 3 u + 19
= 3 x 9 + 19
= 46 

At first
Pink markers : Blue markers : Red markers
18 : 45 : 46

(b)
Total number of markers in the box in the end
= 2 u + 5 u + 3 u + 5 u
= 15 u
= 135

Answer(s): (a) 18 : 45 : 46; (b) 135