There were 195 silver, red and purple staplers in a box. 8 purple staplers were removed from the box and the ratio of the number of silver staplers to the number of red staplers to the number of purple staplers became 5 : 3 : 9. Then some grey staplers were added and the ratio of the number of purple staplers to the number of grey staplers was 9 : 5.

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

	Silver	Red	Purple	Grey	Total
Before	5 u	3 u	9 u + 8	0	195
Change 1	No change	No change	- 8		- 8
After 1	5 u	3 u	9 u		187
Change 2	No change	No change	No change	+ 5 u
After 2	5 u	3 u	9 u	5 u

(a)
Total number of staplers at first
= 5 u + 3 u + 9 u + 8
= 17 u + 8

17 u + 8 = 195
17 u = 195 - 8
17 u = 187

1 u = 187 ÷ 17 = 11

Number of silver staplers at first
= 5 u
= 5 x 11
= 55

Number of red staplers at first
= 3 u
= 3 x 11
= 33

Number of purple staplers at first
= 9 u + 8
= 9 x 11 + 8
= 107 

At first
Silver staplers : Red staplers : Purple staplers
55 : 33 : 107

(b)
Total number of staplers in the box in the end
= 5 u + 3 u + 9 u + 5 u
= 22 u
= 242

Answer(s): (a) 55 : 33 : 107; (b) 242