Make the sheet of her purchases, step by step:


    1.   bought a notebook for $3.50

    2.  spent half of her remaining money for a textbook

    3.  bought the sheet music for $4.

    4.  spent half of the remaining money on a calculator.

    5.  she has $8 left.


Now we will move from the bottom to the top.


    - before step 4, she had twice $8, i.e 16 dollars.

    - before step 3, sha had  16 + 4 = 20 dollars.

    - before step 2, she had twice $20, i.e. 40 dollars.

    - before step 1, she had 40 + 3.50 = 43.50 dollars.


It is what she started with.


You may check that my solution and my answer are correct at each step, moving from step 1 to the end.