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anonymous

  • 5 years ago

How much 50% antifreeze solution should be mixed with a 40% antifreeze solution to give 80 gallons of a 46% antifreeze solution? pls anyone can help

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  1. nowhereman
    • 5 years ago
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    Say you'll take x of 50% antifreeze. Then you need of course take 80 - x of 40% antifreeze and in the end you want \[x\cdot 50\% + (80-x)\cdot 40\% = 46 \% \] so just solve that for x

  2. anonymous
    • 5 years ago
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    my problem is i dont know the formua to find the x

  3. anonymous
    • 5 years ago
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    If v is the volume of a solution and c is the concentration of antifreeze in that solution, then the amount of antifreeze in a solution is given by vc. Since the total amount of antifreeze is conserved.. \[ v_1c_1 + v_2c_2 = v_3c_3 \] Since the total volume is the sum of the individual volumes.. \[v_1 + v_2 = v_3 = 80\] Therefore \[50v_1 + 40v_2 = 46(80) \]

  4. nowhereman
    • 5 years ago
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    oh yeah, I forgot the 80 on the right side, sorry But then it's really kindergarten math.

  5. anonymous
    • 5 years ago
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    I keep getting 32 gallons is that right?

  6. anonymous
    • 5 years ago
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    Then just take the fact that: \[v_1 + v_2 = 80 \rightarrow v_1 = 80-v_2\] to substitute out v1 in the other equation and find v2, then plug back in here to find v1.

  7. nowhereman
    • 5 years ago
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    The correct solution should be 48

  8. anonymous
    • 5 years ago
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    how did you get the 48? i keep getting 32 or 42 gallons did I do wrong in my solution?

  9. nowhereman
    • 5 years ago
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    Unfortunately I can't read your calculations from here. From the above equations, it should be straight-forward, but I can show it to you: \[x\cdot 50\% + (80-x)\cdot 40\% = 80\cdot 46\%\] than you get \[x\cdot 10\% = 80\cdot 6\%\] and thus \[x = 80\cdot 60\% = 48\]

  10. anonymous
    • 5 years ago
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    ok thats help me thank you this is my first time to encounter this problem.thank you

  11. anonymous
    • 5 years ago
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    You still need to plug back in to find the other volume as well.

  12. radar
    • 5 years ago
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    I like that approach nowhereman, it gave the result that was requested

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