There were 321 silver, purple and red pens in a box. 21 red pens were removed from the box and the ratio of the number of silver pens to the number of purple pens to the number of red pens became 4 : 2 : 9. Then some yellow pens were added and the ratio of the number of red pens to the number of yellow pens was 9 : 9.

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

	Silver	Purple	Red	Yellow	Total
Before	4 u	2 u	9 u + 21	0	321
Change 1	No change	No change	- 21		- 21
After 1	4 u	2 u	9 u		300
Change 2	No change	No change	No change	+ 9 u
After 2	4 u	2 u	9 u	9 u

(a)
Total number of pens at first
= 4 u + 2 u + 9 u + 21
= 15 u + 21

15 u + 21 = 321
15 u = 321 - 21
15 u = 300

1 u = 300 ÷ 15 = 20

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

Number of purple pens at first
= 2 u
= 2 x 20
= 40

Number of red pens at first
= 9 u + 21
= 9 x 20 + 21
= 201 

At first
Silver pens : Purple pens : Red pens
80 : 40 : 201

(b)
Total number of pens in the box in the end
= 4 u + 2 u + 9 u + 9 u
= 24 u
= 480

Answer(s): (a) 80 : 40 : 201; (b) 480