Question 277188
Mylan spent $3 on a magazine. He spent half of his remaining money on a video. He then spent half of his remaining money on a book. He had $12 left. How much money did Mylan begin with?

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You can do it in your head or by algebra.  I'll show you both ways.

In your head:

Retrace his steps.  After buying the book he had $12, so he must have had $24
before buying the book, since he spent half his remaining money on the book
and ended up with $12.  That $24 is how much he had after buying the video. 
So he must have had $48 before buying the video, since he spent half his
remaining money on the video and ended up with $24.  That $48 is how much he
had just after he bought the $3 magazine. Therefore he must have started with
$51.

By algebra:

He started with {{{"$N"}}}. Then he spent {{{"$3"}}} on a magazine and had {{{"$(N-3)"}}} left. He spent half 
of his remaining money on a video, and had half of it left, which was {{{"$"}}}{{{(N-3)/2}}}.  He then 
spent half of his remaining money on a book, so that he had {{{"$"}}}{{{(N-3)/2}}}{{{"×"}}}{{{1/2}}} or {{{"$"}}}{{{(N-3)/4}}} left.  

The problem says "He had $12 left".

Therefore

{{{"$"}}}{{{(N-3)/4}}}{{{"="}}}{{{"$12"}}}

{{{(N-3)/4=12}}}

 or multiplying both sides by 4,

{{{N-3=48}}}

{{{N=51}}}.

Edwin</pre>