Question 1204068
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Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him. 
She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. 
She bought a pair of running shoes for $29.45 and had $17.75 left. 
How much did Julie receive when she cashed her paycheck?
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        Tutor @MathTherapy mentioned very productive idea on use the backward method for this problem. 

        In this my post I will show how effectively this idea works.



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So, let's stsart from the end.


Before Julie bought a pait of running choes, she had 17.75 + 29.45 = 47.20 dollars.

This amount was the "second half" of her "remaining" money - so, the "remaining" money amount 
was 2*47.20 = 94.40 dollars .


Hence, her paycheck was $ 94.40  PLUS  $30  PLUS  $30,  i.e.  94.40 + 10 + 30 = 134.40 dollars.


<U>ANSWER</U>.  The paycheck was $134.40.
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Solved.


The backward method in this problem works &nbsp;SO &nbsp;EFFECTIVELY, 
that the problem can be solved &nbsp;MENTALLY &nbsp;in couple of lines without using equations.