Need help with Algebra problem! (Problem in description)

Question

An apartment renter must pay an initial $250 security deposit, and a monthly rent of $500. Write and graph an equation that gives the renter's average rent per month as a function of the number of months rented. After how many months will the average rent be $550?

Answer 1

Average rent is $500 + $250/ number of months

 

If he only rents 1 month, the average = $500 + ($250/1) = $750

 

If he rents 2 months, the average = $500 + ($250/2) = $625

 

The equation of A(n) = $500 + ($250/n)

 

Remember to graph this equation!

 

We want to know when A(n) = $550.

 

There are two ways to approach this from here...

 

A) Look at the y axis and see where $550 is.  

    Draw a horizontal line to the right until you hit the graph of the line.

    Look down at the x axis and see what the x value of that point is.

    If you don't graph accurately, you may get the wrong answer.

 

B) Set A(n) = 550 and solve.

   $500 + ($250/n) = $550

                $250/n =   $50

This one is easy to see .... n = 5.

 

But what if it wasn't easy to see.

 

$250   = $50

  n            1

 

Cross Multiply

 

1($250) = $50n

 

$250 = $50n

 

$250   = n   and n = 5.  Notice that the Dollar Signs cancel.

  $50