# Thread: big and small widgets

1. ## 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 ?

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:

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

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

$\displaystyle 380\times m_s=\frac{3}{2}\times n_l \times m_s+n_s\times m_s$
or:

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

Time equation:

$\displaystyle t_l\times n_l= t_s \times n_s$

but:

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

so:

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

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

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