There were 98 grey, green and brown markers in a box. 8 brown markers were removed from the box and the ratio of the number of grey markers to the number of green markers to the number of brown markers became 3 : 2 : 5. Then some yellow markers were added and the ratio of the number of brown markers to the number of yellow markers was 5 : 9.

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

	Grey	Green	Brown	Yellow	Total
Before	3 u	2 u	5 u + 8	0	98
Change 1	No change	No change	- 8		- 8
After 1	3 u	2 u	5 u		90
Change 2	No change	No change	No change	+ 9 u
After 2	3 u	2 u	5 u	9 u

(a)
Total number of markers at first
= 3 u + 2 u + 5 u + 8
= 10 u + 8

10 u + 8 = 98
10 u = 98 - 8
10 u = 90

1 u = 90 ÷ 10 = 9

Number of grey markers at first
= 3 u
= 3 x 9
= 27

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

Number of brown markers at first
= 5 u + 8
= 5 x 9 + 8
= 53 

At first
Grey markers : Green markers : Brown markers
27 : 18 : 53

(b)
Total number of markers in the box in the end
= 3 u + 2 u + 5 u + 9 u
= 19 u
= 171

Answer(s): (a) 27 : 18 : 53; (b) 171