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Math Help - Cement Mixture

  1. #1
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    Cement Mixture

    A 20 pound bag of cement mix has 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

    Another mixture question in my state exam study booklet.

    What is the table or chart that will lead to the right answer?

    What's the answer?

    What is the best way to set up mixture tables and/or chart?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    A 20 pound bag of cement mix has 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?...
    Hello,

    I'll use decimal numbers instead of percents:

    25% = 0.25
    75% = 0.75
    40% = 0.4

    In the original bag are 20 * 0.25 = 5 pounds of pure cement.

    Let x be the amount of pure cement which has to be added. Then you get the proportion:

    \frac{20 \cdot 0.25+x}{20+x}=0.4 \Longleftrightarrow 5+x=8+0.4 \cdot x \Longleftrightarrow x = 5

    Add 5 pounds of pure cement to this mixture and then it contains 40% of cement.

    EB
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