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A box contained some $5 notes. David took \( {1\over 3}{}{}\) of the notes and another 2 more 

notes to buy a wallet. Then he took 50% of the remaining notes and 2 more notes to 

buy a watch. Finally he took \( {1 \over 2}{}{}\) of what was left and another 2 notes to buy a book.

In the end, he had 7 pieces of notes left in the box. How much money was in the box

at first?

 Sep 7, 2021
 #1
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The box starts with x  notes.   (the money value is never important)

 

-----------------------------------------

 

He takes     \(\frac{x}{3}+2 = \frac{x+6}{3}\)

 

and leaves  \(\frac{2x}{3}-2=\frac{2x-6}{3}\\\)

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from the ones left 

 

he takes  \(\frac{1}{2}*\frac{2x-6}{3}+2=\frac{x-3}{3}+\frac{6}{3}=\frac{x+3}{3}\\ \)

 

and leaves   \(\frac{x-3}{3}-\frac{6}{3}=\frac{x-9}{3}\)

 

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from the ones left 

 

he takes  \(\frac{1}{2}*\frac{x-9}{3}+2\)

and leaves ...

 

AND you should be able to take it from there

 Sep 9, 2021

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