There are approximately 4 weeks in a month.
The shop owner added 3 bikes every week for 4 weeks for a total addition of 3*4 = <<3*4=12>>12 bikes
The shop owner now has the original number of bikes + <<12=12>>12 bikes
She sold 18 bikes within the same time frame
She now has a total of 45 bikes which is: the original number of bikes + 12 - 18 = <<45=45>>45 bikes
The original number of bikes = 45-12+18 = <<45-12+18=51>>51 bikes
#### 51