Question 1207675
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Sarah spent 3/8 of her allowance on food and 1/3 of the remainder on clothes. 
Then she shares the rest of her allowance equally with her sisters such that 
each of them received 1/12 of her total allowance.
How many sisters does she have.
Given that they each received $208 dollars, how much does Sarah spend on clothes.
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        The treatment of the problem by  Edwin is incorrect.

        It is incorrect,  because  Edwin ignored  (did not use)
        the condition that every sibling got  1/12  of the  Sarah's total allowance.


        So,  in Edwin' solution this last condition was,  actually,  ignored.
        This brought  Edwin to  Diophantine equation,  while the true logic is much simpler.



<pre>
Starts with T.
Spends (3/8)T on food.  Has (5/8)T left.
Spends (1/3)(5/8)T = (5/24)T on clothes. Has (5/8)T-(5/24)T = (5/12)T left.
Shares equally with N sisters.
Since it says she shares equally with sisters, that doesn't mean she gives
it all to them. 
She gives each of the siblings, including herself, (1/12)T,
which is 208 dollars.


So, to compute the number of sisters, including Sarah, we should divide (5/12)T by (1/12)T.

Obviously, the quotient is 5.  So, the number of sisters (including Sarah) is 5.


Also, from the analysis above,  (1/12)T = 208;  hence,  T = 208*12 = 2496 dollars.


The amount, which Sarah spent on clothes is (5/24)*2496 = 520 dollars.


<U>ANSWER</U>.  Sarah has 5-1 = 4 sisters.

         The amount Sarah spent on clothes was $520.
</pre>

Solved.


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Edwin's error is a typical error what mathematicians make when they solve simple problems: 
they over-complicate them in their minds.