Question 158245
I got the question incorrect, but I do not know what I did wrong.

The cost of manufacturing notebooks varies inversely as the number of notebooks. If it costs 50 cents a notebook when 10,000 are manufactured, how much will it cost if 18,000 are made?

MY WORK:
{{{50/10,000=x/18000}}}

{{{1/200=x/18000}}}                  

{{{200x=18000}}}

{{{x=90}}}cents

<pre><font size = 4 color = "indigo"><b>

That method is OK for direct variation, but not
for inverse variation.  

Indirect variation is the "cheaper by the dozen" idea.

In direct variation, when one quantity goes up, the other goes up 
also, and when one goes down, the other goes down also.

But in indirect variation, when one quantity goes up, the other
goes down, and vice-versa.

So in this problem, when the production goes up from 10,000 to
18,000, you should expect the cost per notebook to go down.  So
you should expect an answer less than 50 cents, not more!

Here is how to handle this inverse proportion problem:

Start this:

{{{C=k/N}}}

Substitute {{{C=50}}} and {{{N=10000}}}

{{{50=k/10000}}}

Multiply both sides by {{{10000}}}

{{{500000=k}}}

Substitute this into {{{C=k/N}}}

{{{C=500000/N}}}

Now substitute {{{N=18000}}}

{{{C=500000/18000}}}

{{{27.777777...}}}cents

or about 27.78 cents cost per notebook.

Edwin</pre>