Can anyone solve this question? i’m lost

We'll start by calling the number of pigeons we started with x, because it's the unknown.

After she clapped 1/3 flew away so she was left with

(1 - 1/3) x = (2/3) x

Two flew back, so now there are

(2/3) x + 2

She clapped again and half left, half stayed, so now

(1/2) ( (2/3) x + 2 )

One came back and there were five,

(1/2) ( (2/3) x + 2 ) + 1 = 5

Solving is unraveling.

(1/2) ( (2/3) x + 2 )  = 4

(2/3) x + 2   = 8

(2/3) x  = 6

x = (3/2) 6 = 9

9 pigeons

Check: Reviewing the story,  9 -> 6 -> 8 -> 4 -> 5 good

Idon't know the answer