Question 1164247
<pre>
OH CRAP!!!  Ikleyn did it for you before I could post this!

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Instead of doing your problem for you, I'll do one EXACTLY like yours so
that you can use it as a model for your problem:

Some mathematics professors would like to purchase a $300 microwave oven for
the department workroom. If 6 of the professors do not contribute,
everyone's share will increase by $45. How many professors are in the
department? 

<pre>
If all N professors shared, then everyone's share would be 300/N

If 6 professors do not contribute, the share for the N-6 professors who do
contribute will be $45 more than that or $(300/N + 45)

So the equation is:

(N-6)(300/N+45) = 300

Use FOIL to multiply that out:

N(300/N) + 45N - 1800/N + 270 = 300

     300 + 45N - 1800/N + 270 = 300

           45N - 1800/N + 270 = 0

Multiply through by N to clear the fraction:

           45N² - 1800 + 270N = 0

           45N² + 270N - 1800 = 0

Divide through by 45

                 N² + 6N - 40 = 0 

Factor         (N - 10)(N + 4) = 0

             N - 10 = 0; N + 4 = 0
                  
                 N = 10;    N = -4

N = 10 professors.  Ignore the negative answer.

Now use this as a model to do yours.

Edwin</pre>