There were 177 black, pink and white staplers in a box. 8 white staplers were removed from the box and the ratio of the number of black staplers to the number of pink staplers to the number of white staplers became 4 : 2 : 7. Then some grey staplers were added and the ratio of the number of white staplers to the number of grey staplers was 7 : 8.

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

	Black	Pink	White	Grey	Total
Before	4 u	2 u	7 u + 8	0	177
Change 1	No change	No change	- 8		- 8
After 1	4 u	2 u	7 u		169
Change 2	No change	No change	No change	+ 8 u
After 2	4 u	2 u	7 u	8 u

(a)
Total number of staplers at first
= 4 u + 2 u + 7 u + 8
= 13 u + 8

13 u + 8 = 177
13 u = 177 - 8
13 u = 169

1 u = 169 ÷ 13 = 13

Number of black staplers at first
= 4 u
= 4 x 13
= 52

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

Number of white staplers at first
= 7 u + 8
= 7 x 13 + 8
= 99 

At first
Black staplers : Pink staplers : White staplers
52 : 26 : 99

(b)
Total number of staplers in the box in the end
= 4 u + 2 u + 7 u + 8 u
= 21 u
= 273

Answer(s): (a) 52 : 26 : 99; (b) 273