There were 163 red, green and black staplers in a box. 7 black staplers were removed from the box and the ratio of the number of red staplers to the number of green staplers to the number of black staplers became 3 : 2 : 7. Then some yellow staplers were added and the ratio of the number of black staplers to the number of yellow staplers was 7 : 4.

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

	Red	Green	Black	Yellow	Total
Before	3 u	2 u	7 u + 7	0	163
Change 1	No change	No change	- 7		- 7
After 1	3 u	2 u	7 u		156
Change 2	No change	No change	No change	+ 4 u
After 2	3 u	2 u	7 u	4 u

(a)
Total number of staplers at first
= 3 u + 2 u + 7 u + 7
= 12 u + 7

12 u + 7 = 163
12 u = 163 - 7
12 u = 156

1 u = 156 ÷ 12 = 13

Number of red staplers at first
= 3 u
= 3 x 13
= 39

Number of green staplers at first
= 2 u
= 2 x 13
= 26

Number of black staplers at first
= 7 u + 7
= 7 x 13 + 7
= 98 

At first
Red staplers : Green staplers : Black staplers
39 : 26 : 98

(b)
Total number of staplers in the box in the end
= 3 u + 2 u + 7 u + 4 u
= 16 u
= 208

Answer(s): (a) 39 : 26 : 98; (b) 208