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Math Help - big and small widgets

  1. #1
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    big and small widgets

    A machine makes big widgets . Another machine makes small widgets . Three small widgets have the same mass as two big widgets .It takes the same amount of time to make 3 big widgets as it does to make 5 small widgets . The machines start at the same time and make widgets until the total mass of all of the widgets made is equal to the mass of 380 small widgets . What is the total number of widgets made ?
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    A machine makes big widgets . Another machine makes small widgets . Three small widgets have the same mass as two big widgets .It takes the same amount of time to make 3 big widgets as it does to make 5 small widgets . The machines start at the same time and make widgets until the total mass of all of the widgets made is equal to the mass of 380 small widgets . What is the total number of widgets made ?
    There may be a neater way of doing this but a systematic method follows.

    Mass equation:

    380\times m_s=n_l \times m_l+n_s\times m_s

    but m_l=\frac{3}{2}\times m_s, so the mass equation becomes:

     <br />
380\times m_s=\frac{3}{2}\times n_l \times m_s+n_s\times m_s<br />
    or:

    380=\frac{3}{2}\times n_l +n_s

    Time equation:

    t_l\times n_l= t_s \times n_s

    but:

    t_l=\frac{5}{3}\times t_s

    so:

    n_l=\frac{3}{5}\times n_s

    From which if no error has crept in the answer follows.

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