There were 117 green, yellow and black staplers in a box. 19 black staplers were removed from the box and the ratio of the number of green staplers to the number of yellow staplers to the number of black staplers became 3 : 2 : 9. Then some blue staplers were added and the ratio of the number of black staplers to the number of blue staplers was 9 : 2.

1. What was the ratio of the number of green staplers to the number of yellow staplers to the number of black staplers at first?
2. How many staplers were in the box in the end?

	Green	Yellow	Black	Blue	Total
Before	3 u	2 u	9 u + 19	0	117
Change 1	No change	No change	- 19		- 19
After 1	3 u	2 u	9 u		98
Change 2	No change	No change	No change	+ 2 u
After 2	3 u	2 u	9 u	2 u

(a)
Total number of staplers at first
= 3 u + 2 u + 9 u + 19
= 14 u + 19

14 u + 19 = 117
14 u = 117 - 19
14 u = 98

1 u = 98 ÷ 14 = 7

Number of green staplers at first
= 3 u
= 3 x 7
= 21

Number of yellow staplers at first
= 2 u
= 2 x 7
= 14

Number of black staplers at first
= 9 u + 19
= 9 x 7 + 19
= 82 

At first
Green staplers : Yellow staplers : Black staplers
21 : 14 : 82

(b)
Total number of staplers in the box in the end
= 3 u + 2 u + 9 u + 2 u
= 16 u
= 112

Answer(s): (a) 21 : 14 : 82; (b) 112