There were 88 black, green and brown staplers in a box. 8 brown staplers were removed from the box and the ratio of the number of black staplers to the number of green staplers to the number of brown staplers became 3 : 4 : 9. Then some gold staplers were added and the ratio of the number of brown staplers to the number of gold staplers was 9 : 6.

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

	Black	Green	Brown	Gold	Total
Before	3 u	4 u	9 u + 8	0	88
Change 1	No change	No change	- 8		- 8
After 1	3 u	4 u	9 u		80
Change 2	No change	No change	No change	+ 6 u
After 2	3 u	4 u	9 u	6 u

(a)
Total number of staplers at first
= 3 u + 4 u + 9 u + 8
= 16 u + 8

16 u + 8 = 88
16 u = 88 - 8
16 u = 80

1 u = 80 ÷ 16 = 5

Number of black staplers at first
= 3 u
= 3 x 5
= 15

Number of green staplers at first
= 4 u
= 4 x 5
= 20

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

At first
Black staplers : Green staplers : Brown staplers
15 : 20 : 53

(b)
Total number of staplers in the box in the end
= 3 u + 4 u + 9 u + 6 u
= 22 u
= 110

Answer(s): (a) 15 : 20 : 53; (b) 110