SOLUTION: A realtor bought a group of lots for $90,000. He then sells them at a gain of $3,750 per lot and has a total profit equal to the amount he received for the last 4 lots sold. How ma

Question 1184423: A realtor bought a group of lots for $90,000. He then sells them at a gain of $3,750 per lot and has a total profit equal to the amount he received for the last 4 lots sold. How many lots were originally in the group?
Answer by ikleyn(52905) (Show Source): You can put this solution on YOUR website!
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A realtor bought a group of lots for $90,000. He then sells them at a gain of $3,750 per lot
and has a total profit equal to the amount he received for the last 4 lots sold.
How many lots were originally in the group?
~~~~~~~~~~~~~~~~~

Let "n" be the number of lots, now unknown.


Then the bought price for each lot was  ;  the profit of selling all these lots was 3,750n dollars.


Write the equation for the profit as you read the problem

    3750n = .


Divide both sides by 3750

    n = .


Multiply both sides by n 

    n^2 = 96 + 4n


Simplfy

    n^2 - 4n - 96 = 0


Factor left side

    (n-12)*(n+8) = 0.


Of the two roots,  n= 12 and n= -8, only positive root n= 12 gives a meaningful solution.


ANSWER.  12 lots.

Solved and thoroughly explained.

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