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Math Help - primes and divisibility

  1. #1
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    primes and divisibility

    I am having trouble in my new math course understanding what is going on. i do not know where to start on this problem i attached
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  2. #2
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    Hello, ihavvaquestion!

    This more of a math puzzle then a "real" math problem.


    Someone spilled ink on a bill for 36 sweatshirts.
    The result looked like the following.
    There is one digit missing in front of the 8 and one digit missing after the 9.
    The cost per shirt was not a frational part of a penny.

    How much did each sweatshirt cost?
    Find all possible costs per sweatshirt.


    . . \begin{array}{cccccccc}<br />
&  ? & ? & . & ? & ? && \text{unit price}\\<br />
& \times & & & 3 & 6 && \text{no. shirts}\\ \hline<br />
? & 8 & 3 & . & 9 & ? && \text{Total}\end{array}

    Since the Total is a multiple of 4, it must end in a two-digit number divisible by 4.
    . . There are two choices: . 92\,\text{ or }\,96


    Since the Total is a multiple of 9, the sum of its digits must be a multiple of 9.


    If the Total is ?83.{\color{red}92}, the Total must be {\color{red}5}83.92

    . . Then: . \frac{583.92}{36} \:=\:16.22


    If the Total is ?83.{\color{red}96}, the Total must be {\color{red}1}83.96

    . . Then: . \frac{183.96}{36} \:=\:5.11


    Therefore, the unit price is either: . {\color{blue}\$16.22}\,\text{ or }\,{\color{blue}\$5.11}

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  3. #3
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    2 questions...

    how do you know the total is a multiple of four? is it because 36 is divisible by 4?

    also, what total is divisible by 9? the 36 shirts?
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