SOLUTION: 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

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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?
Found 2 solutions by Edwin McCravy, unlockmath:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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? 

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 %22%24N%22. Then he spent %22%243%22 on a magazine and had %22%24%28N-3%29%22 left. He spent half 
of his remaining money on a video, and had half of it left, which was %22%24%22%28N-3%29%2F2.  He then 
spent half of his remaining money on a book, so that he had %22%24%22%28N-3%29%2F2%22%D7%221%2F2 or %22%24%22%28N-3%29%2F4 left.  

The problem says "He had $12 left".

Therefore

%22%24%22%28N-3%29%2F4%22=%22%22%2412%22

%28N-3%29%2F4=12

 or multiplying both sides by 4,

N-3=48

N=51.

Edwin

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
I'll see if I can help you on this one. (It's written a bit unclear)
Let x represent the total amount of money Mylan starts with so we can write the following:
3+(x-3)/2+(x-3)/4+12=x Multiply by 4 to get rid of the fractions:
12+2(x-3)+(x-3)+48=4x Combine like terms to get:
51+3x=4x Subtract 3x from both sides to get:
x=51
There we go. He started with $51. check it out to see if it works.
Good problem!
RJ
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