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Math Help - unit conversion

  1. #1
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    Jul 2008
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    unit conversion

    I can't seem to figure this one out. Can someone explain?

    The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the gound coffee beans required to make 1 cup of brewed coffee?

    A) \dfrac{d}{8c}

    B) \dfrac{cd}{8}

    C) \dfrac{8c}{d}

    D) \dfrac{8d}{c}

    E) 8cd

    The correct answer is A.
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  2. #2
    Super Member
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    Jun 2008
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    In these kind of problems, it is best to set up ratios and you have to be careful with your units.

    Price of ground coffee beans: \frac{d\ \text{dol}}{8\ \text{oz}}

    Ratio of ounces to cups: \frac{1\ \text{oz}}{c\ \text{cups}}

    ==========================

    Now I need to find the cost of the ground coffee beans required to make 1 cup of brewed coffee. So, what we do first, is convert 1 cup into oz using the ratio given:

    \frac{1\ \text{oz}}{c\ \text{cups}} \cdot 1\ \text{cup}

    Notice that the cup unit cancel (and don't leave the s behind! ):

    \frac{1\ \text{oz}}{c\ \text{\rlap{////}{cups}}} \cdot 1 \text{\rlap{///}{cup}}

    = \frac{1\ \text{oz}}{c}

    Now, last thing to do is to multiply the converted unit with the price:
    \frac{d\ \text{dol}}{8\ \text{oz}} \cdot \frac{1\ \text{oz}}{c}

    Again, the units cancel, leaving you with the price:
    \frac{d\ \text{dol}}{8\ \rlap{//}{\text{oz}}} \cdot \frac{1\ \rlap{//}\text{oz}}{c}

    = \frac{d}{8c}\ \text{dol}
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  3. #3
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    Ah, I see it thank you!
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