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Math Help - Help with a puzzle

  1. #1
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    Help with a puzzle

    Hi there! On wednesday I'm having a really important test at University and in the practice-book I found a puzzle I just can't solve, it goes like this:

    In a coffee storea new coffee is being prepared. It contains: 10kg of a $20/kg coffee and some of $12/kg. How many Kilos of $12/kg coffeemust the mix contain so that charging it $18/kg they obtain 10% profit over the cost?

    Sorry if it's grammatically wrong.

    Thanx !
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  2. #2
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    Re: Help with a puzzle

    Quote Originally Posted by nicoT30 View Post
    In a coffee storea new coffee is being prepared. It contains: 10kg of a $20/kg coffee and some of $12/kg. How many Kilos of $12/kg coffeemust the mix contain so that charging it $18/kg they obtain 10% profit over the cost?
    Quite unclear; "charging it" means charging the mixture or only the $12 coffee?
    Is the $20:$12 including the 10%, or will it be sold at $22:$13.20 ?

    Anyhow, leaving the "profit out":
    x = kg of $20 coffee
    [20x + 12(10 - x)] / 10 = 18
    Solve to get x = 7.5 kg

    Do you know the answer? We can probably figure out the meaning from that.
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  3. #3
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    Re: Help with a puzzle

    Hello, nicoT30!

    The information is incomplete . . .


    In a coffee store a new coffee is being prepared.
    It contains: 10kg of a $20/kg coffee and some of $12/kg.

    How many kilos of $12/kg coffee must the mix contain
    so that charging $18/kg they obtain 10% profit over the cost?

    Ignoring profit, we can reason as follow . . .

    We have 10 kg of Brand A at $20/kg.
    . . Its value is:. 10\cdot20 \,=\,200 dollars.

    We add x kg of Brand B at $12/kg.
    . . Its value is:. 12x dollars.

    The total value of the mixture is:. 200 + 12x dollars. .[1]


    The mixture will be x+10 kg at $18/kg.
    . . Its value is:. 18(x+10) dollars. .[2]


    We just described the value of the mixture in two ways.

    There is our equation! , \hdots\quad200 + 12x \:=\:18(x+10)

    Solve for x\!:\;\;12x + 200 \:=\:18x + 180 \quad\Rightarrow\quad 6x \:=\:20

    . . Hence: . x \:=\:\frac{10}{3}\:=\:3\tfrac{1}{3}\text{ kg of Brand B}


    To determine 10% profit, we must know
    . . the unit cost of Brand A and Brand B.
    And this was not provided.
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  4. #4
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    Re: Help with a puzzle

    Really interesting I've burnt my mind and couldn't do it. About the 10% I got to this..

    Real price of Mix = X
    So.. $18= X + 10/100 X
    $18= 110/100 X
    $18 / (110/100) = X
    $16,36 = X

    Sorry about the way I wrote the equation, I did not learn the other way yet, I have to read the tutorial. I hope you have at least enjoyed a bit this problem

    Thanx for helping!
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