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Thread: Help

  1. #1
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    Help

    The base material for a certain roadbed is 80% crushed rock when measured by weight. How many tons of this material must be mixed with another material containing 30% rock to make 150 tons of material that is 40% crushed rock?
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  2. #2
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    Re: Help

    Hello, mbruiz1!

    The base material for a certain roadbed is 80% crushed rock when measured by weight.
    How many tons of this material must be mixed with another material containing 30% crushed rock
    to make 150 tons of material that is 40% crushed rock?

    Let $\displaystyle x$ = tons of 80% material.
    This contains $\displaystyle 0.8x$ tons of crushed rock.

    Let $\displaystyle 150-x$ = tons of 30% material.
    This contains: $\displaystyle 0.3(150-x)$ tons of crushed rock.

    The mixture will contain: $\displaystyle 0.8x + 0.3(150-x)$ tons of crushed rock.


    But we know that the mixture will be 150 tons which is 40% crushed rock.
    . . It will contain: $\displaystyle 0.4(150) \,=\,60$ tons of crushed rock.


    We just described the final amount of crushed rock in two ways.

    There is our equaton! . . . $\displaystyle 0.8x + 0.3(150-x) \;=\;60$


    Got it?
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