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Math Help - CD's

  1. #1
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    CD's

    A DJ found a music store that had a great collection of used CD's. he purshased 38 CD's for a total of $235. The purchase included CD's priced at either $5.00 or $8.00. How many CD's in each price category did the DJ buy?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wild_flowr69
    A DJ found a music store that had a great collection of used CD's. he purshased 38 CD's for a total of $235. The purchase included CD's priced at either $5.00 or $8.00. How many CD's in each price category did the DJ buy?
    Call the number of CDs bought at $5.00 x. Call the number of CDs bought at $8.00 y. We know that the total cost was $235, so:
    5x+8y=235.

    Additionally, we know that 38 CDs were bought, so:
    x+y=38.

    Two equations, two unknowns, so you can solve for x and y.

    -Dan
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  3. #3
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    Let me continue from topsquark's solution:
    The equations
    \left\{\begin{array}{cc}5x+8y&=235\\x+y&=38\end{ar  ray}\right
    In the second equation solve for y:
    y=38-x
    Substitute that into the first:
    5x+8(38-x)=235
    Now solve it,
    5x+304-8x=235
    Thus,
    -3x=-69
    Thus,
    x=23
    Thus,
    y=15
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