big and small widgets

**mathaddict** · December 29th 2008, 12:59 AM

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 ?

**Constatine11** · December 29th 2008, 06:21 AM

Originally Posted by mathaddict

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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