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Math Help - Problem Problem

  1. #1
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    Unhappy Problem Problem

    A Machine makes big widgets. Another Machine makes small widgets.3 small widgets have same mass as 2 big widgets. it takes the same amount off time to make 3 big widgets as does take 5 small widgets. The Machine start at the same time and make widgets untill the total mass off all the widgets made is equal to the mass off 380 small widgets.

    What is the total number off widgets made
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  2. #2
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    Hastings
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    Can you give us any more information?

    I think this problem has too many variables for us to figure out anything.

    It has 5 variables: Time to make 3 big and 5 small, weight of big widget, weight of small widget, amount of big widgets created, amount of small widgets created... and we are only given 3 pieces of information. There is insufficient information for us to put them into simultaneous equations.
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  3. #3
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    Hi,

    let x be the number of small widgets, and y the number of big widgets.
    Since "it takes the same amount off time to make 3 big widgets as does take 5 small widgets.", at any time, we have 5y=3x (you can easily verify that).
    Moreover, let m be the mass of a small object and n be the mass of a big object.
    Then, we have 3m=2n.

    at the end, we have mx+ny=380m , it is to say x+(n/m)y=380. Let use the second equation, it gives : x+3y/2=380
    Now, let use the first equation, it gives to us : x+9x/10=380
    x*(19/10)=380
    finally, x=200, and y=120

    (i'm french, so, please tell me when i write things that doesn't have any meaning)
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  4. #4
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    Hi,
    Thorin

    can you please do more steps, i am a bit lots please,
    Thanks
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  5. #5
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    I'm gonna explain why we have "5y=3x", because it is the only difficulty, all the rest is only the translation of the exercise.

    let u be the time we need to make a small widget, and v the time we need to make a big widget.
    the, we clearly have 5u=3v.
    After a time t, we have x small widgets and y big widgets, and t=xu and t=yv also
    so, we have u=t/x and v=t/y, so, we have 5t/x=3t/y, so, we have 5y=3x
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