SOLUTION: A farmer bought a number of pigs for $100. However, 5 of them died before he could sell the rest at a profit of 5 per pig. His total profit was $50. How many pigs did he originally

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A farmer bought a number of pigs for $100. However, 5 of them died before he could sell the rest at a profit of 5 per pig. His total profit was $50. How many pigs did he originally      Log On


   

Question 1138432: A farmer bought a number of pigs for $100. However, 5 of them died before he could sell the rest at a profit of 5 per pig. His total profit was $50. How many pigs did he originally buy?
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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Let n be that number under the question.

The price for 1 pig when the farmer bought them was  100%2Fn.

The price for 1 pig when the farmer sold the rest (n-5) of them was  150%2F%28n-5%29.


The condition says that

    150%2F%28n-5%29 - 100%2Fn = 5   dollars per pig.


Simplify

    30%2F%28n-5%29 - 20%2Fn = 1.


The solution is seen by an unarmed eye: it is n = 20.


If you need formal solution, here it is step by step.


    30n - 20*(n-5) = n*(n-5)

    30n - 20n + 100 = n^2 - 5n

    n^2 -15n - 100 = 0

    (n-20)*(n+5) = 0.


The roots are 20 and -5, and only positive root is a meaningful solution.


ANSWER.  20 pigs.

Solved.