There were 163 pink, grey and gold staplers in a box. 9 gold staplers were removed from the box and the ratio of the number of pink staplers to the number of grey staplers to the number of gold staplers became 2 : 5 : 7. Then some silver staplers were added and the ratio of the number of gold staplers to the number of silver staplers was 7 : 9.

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

	Pink	Grey	Gold	Silver	Total
Before	2 u	5 u	7 u + 9	0	163
Change 1	No change	No change	- 9		- 9
After 1	2 u	5 u	7 u		154
Change 2	No change	No change	No change	+ 9 u
After 2	2 u	5 u	7 u	9 u

(a)
Total number of staplers at first
= 2 u + 5 u + 7 u + 9
= 14 u + 9

14 u + 9 = 163
14 u = 163 - 9
14 u = 154

1 u = 154 ÷ 14 = 11

Number of pink staplers at first
= 2 u
= 2 x 11
= 22

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

Number of gold staplers at first
= 7 u + 9
= 7 x 11 + 9
= 86 

At first
Pink staplers : Grey staplers : Gold staplers
22 : 55 : 86

(b)
Total number of staplers in the box in the end
= 2 u + 5 u + 7 u + 9 u
= 23 u
= 253

Answer(s): (a) 22 : 55 : 86; (b) 253