The equation to this problem is


    x*(1 + x/100) = 75,


where x is the cost for the farmer to buy the sheep some-when earlier.


The equation says that the farmer has the profit of x percents by selling for 75$.


To solve the equation, multiply both sides by 100. you will get


    x*(100+x) = 7500

    x^2 + 100x - 7500 = 0

    (x + 150)*(x - 50) = 0.


Of the twoo roots, only positive x= 50 makes sense as the solution to the problem.


ANSWER.  x = 50 dollars.

Purchase price, per sheep: x

Profit on each sheep: 50%, or .5

Therefore, selling price = 1.5x

Since selling price of each sheep is also $75, we get: 1.5x = 75



It therefore can be said that each sheep cost $50, and she also made a 50% profit on the sale of each sheep. 

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