SOLUTION: A pet shop bought a litter of puppies for $80. All but 3 of them were sold , at a profit of $6 each, for a total of $80. How many puppies were in the litter?

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Question 1184800: A pet shop bought a litter of puppies for $80. All but 3 of them were
sold , at a profit of $6 each, for a total of $80. How many puppies were in the litter?
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of puppies he bought.

Since the cost of the puppies was $80, the cost per puppy was (80/x) dollars.

Then the selling price per puppy, to make a $6 profit on each, was ((80/x)+6).

The number of puppies sold was x-3.

The total sales -- (x-3) puppies at ((80/x)+6) dollars each, was $80:

%28x-3%29%28%2880%2Fx%29%2B6%29=80
80%2B6x-240%2Fx-18=80
6x-240%2Fx-18=0

Multiply the whole equation by x to clear the fractions. Note x=0 is impossible in the problem, so multiplying both sides of the equation by x is valid.

6x%5E2-18x-240=0
x%5E2-3x-40=0
%28x-8%29%28x%2B5%29=0

x=8 or x=-5; the negative answer makes no sense, so x=8.

ANSWER: There were x=8 puppies in the litter.

CHECK:
8 puppies bought
cost $80, so $10 each
sold for $16 each, a profit of $6 each
5 puppies sold for a total of 5($16)=$80