\(x\)-total number of pumpkins
First witch took \(\frac{x-1}{3}\) pumpkins.
The number of pumpkins remained \(2\frac{x-1}{3} = \frac{2(x-1)}{3} = \frac{2x-2}{3}\)
Second witch took \(\frac{\frac{2x-2}{3}-1}{3} = \frac{2x-5}{9}\)
The number of pumpkins remained \(2\frac{2x-5}{9}= \frac{4x-10}{9}\)
Third witch took \(\frac{\frac{4x-10}{9}-1}{3} = \frac{4x-19}{27}\)
Ghost took 3 pumpkins. The number of pumpkins remained is 3,6 or 9.
Solve equation for each case.
1) \(\frac{2x-2}{3}+\frac{2x-5}{9}+\frac{4x-19}{27}+3+3=x\)
2) \(\frac{2x-2}{3}+\frac{2x-5}{9}+\frac{4x-19}{27}+3+6=x\)
3) \(\frac{2x-2}{3}+\frac{2x-5}{9}+\frac{4x-19}{27}+3+9=x\)
Only equation 2) has a solution which is a whole number: 25
The total number of pumpkins is 25.