There were 367 silver, red and blue pens in a box. 7 blue pens were removed from the box and the ratio of the number of silver pens to the number of red pens to the number of blue pens became 4 : 5 : 9. Then some brown pens were added and the ratio of the number of blue pens to the number of brown pens was 9 : 4.

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

	Silver	Red	Blue	Brown	Total
Before	4 u	5 u	9 u + 7	0	367
Change 1	No change	No change	- 7		- 7
After 1	4 u	5 u	9 u		360
Change 2	No change	No change	No change	+ 4 u
After 2	4 u	5 u	9 u	4 u

(a)
Total number of pens at first
= 4 u + 5 u + 9 u + 7
= 18 u + 7

18 u + 7 = 367
18 u = 367 - 7
18 u = 360

1 u = 360 ÷ 18 = 20

Number of silver pens at first
= 4 u
= 4 x 20
= 80

Number of red pens at first
= 5 u
= 5 x 20
= 100

Number of blue pens at first
= 9 u + 7
= 9 x 20 + 7
= 187 

At first
Silver pens : Red pens : Blue pens
80 : 100 : 187

(b)
Total number of pens in the box in the end
= 4 u + 5 u + 9 u + 4 u
= 22 u
= 440

Answer(s): (a) 80 : 100 : 187; (b) 440