Question 1187522
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Donna {{{highlight(cross(baught))}}} <U>bought</U> a notebook for $3.50 and then spent half of her remaining money for a textbook. 
Next she {{{highlight(cross(baught))}}} <U>bought</U> sheet music for $4 and then spent half of the remaining money on a calculator. 
She has $8 left. How much money did she start with?
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is a nice problem to solve it in the backward manner.



<pre>
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.
</pre>

Solved.


Nice method, isn't it ?