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Thread: Applied word problems involving fractional equations Mixture problems

  1. #1
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    Question Applied word problems involving fractional equations Mixture problems

    A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.

    i was working on this equation which I don't know if it's correct or not

    Started with + We add = What we end up with

    8 + X = 0.1 ( 40 + X )
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  2. #2
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    Re: Applied word problems involving fractional equations Mixture problems

    Quote Originally Posted by diehardmath4 View Post
    A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.

    i was working on this equation which I don't know if it's correct or not

    Started with + We add = What we end up with

    8 + X = 0.1 ( 40 + X )
    let $X$ be the amount of zinc that needs to be added in $kg$

    $\dfrac{8 + X}{40+8+X} = \dfrac{1}{10}$

    $8+X = 0.1(48+X)$

    so not quite, you forgot about the initial amount of zinc present in the total.
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    Re: Applied word problems involving fractional equations Mixture problems

    Quote Originally Posted by romsek View Post
    let $X$ be the amount of zinc that needs to be added in $kg$

    $\dfrac{8 + X}{40+8+X} = \dfrac{1}{10}$

    $8+X = 0.1(48+X)$

    so not quite, you forgot about the initial amount of zinc present in the total.
    the zinc alloy must be defined
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    Re: Applied word problems involving fractional equations Mixture problems

    Quote Originally Posted by bjhopper View Post
    the zinc alloy must be defined
    you don't think they mean 10% zinc, 90% copper?
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    Re: Applied word problems involving fractional equations Mixture problems

    Quote Originally Posted by romsek View Post
    you don't think they mean 10% zinc, 90% copper?
    Zinc alloy contains another component. It is left out in this reply.
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    Re: Applied word problems involving fractional equations Mixture problems

    The answer the book is giving me is 40 kg
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    Re: Applied word problems involving fractional equations Mixture problems

    Zinc alloy contains another component. It is left out in this reply.
    Are you reading this as 40 kg of copper and a separate amount of an alloy that contains 8 kg of zinc?

    I interpret it as 40 kg of a combined copper & zinc alloy that contains 8 kg zinc $\implies$ 32 kg of copper in the starting 40 kg.

    Using my interpretation, the starting copper-zinc alloy has 20% zinc to start with ... adding 40kg more of copper will result in a 10% zinc alloy.
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    Re: Applied word problems involving fractional equations Mixture problems

    Quote Originally Posted by diehardmath4 View Post
    A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.

    i was working on this equation which I don't know if it's correct or not

    Started with + We add = What we end up with

    8 + X = 0.1 ( 40 + X )
    ok let's try this again

    we start with

    40kg of an allow made of copper and zinc. 8kg is zinc. 32kg is copper.

    You want to add copper to this to obtain a new alloy contain 10% zinc.

    $\dfrac{8}{40+X}=0.1$

    $40+X=80$

    $X=40$

    So we need to add $40kg$ of copper.

    That gets us $80kg$ total with $8kg$ of zinc, i.e. $10\%$

    basically everything Skeeter just said.
    Thanks from diehardmath4
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    Re: Applied word problems involving fractional equations Mixture problems

    Quote Originally Posted by diehardmath4 View Post
    A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.
    The present 8 kg zinc will represent 10% of total, so total of 80 required.
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    Re: Applied word problems involving fractional equations Mixture problems

    Analyze the problem "A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc", here zinc is $20\%$ of the total.

    Since you need new alloy containing $10\%$ zinc. we know that 8 kg of 40 kg is $20\%$, so 8 kg of 80 kg will be $10\%$.

    Since you have 32 kg copper, so you need more 40 kg copper to make a new allow containing $10\%$ zinc and total 80kg allow.
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