SOLUTION: The profit P, in dollars, gained by selling x computers is modeled by the equation P = -5x^2 +1000x + 5000. How many computers must be sold to obtain a profit of $55,000.00?

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Question 210196: The profit P, in dollars, gained by selling x computers is modeled by the equation
P = -5x^2 +1000x + 5000. How many computers must be sold to obtain a profit of $55,000.00?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P+=+-5x%5E2+%2B1000x+%2B+5000 Start with the given equation.


55000+=+-5x%5E2+%2B1000x+%2B+5000 Plug in P=55000


0=+-5x%5E2+%2B1000x+%2B+5000-55000+ Subtract 55000 from both sides.


0=+-5x%5E2+%2B1000x++-50000+ Combine like terms.


Notice that the quadratic -5x%5E2%2B1000x-50000 is in the form of Ax%5E2%2BBx%2BC where A=-5, B=1000, and C=-50000


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


Plug in A=-5, B=1000, and C=-50000


x+=+%28-1000+%2B-+sqrt%28+1000000-4%28-5%29%28-50000%29+%29%29%2F%282%28-5%29%29 Square 1000 to get 1000000.


x+=+%28-1000+%2B-+sqrt%28+1000000-1000000+%29%29%2F%282%28-5%29%29 Multiply 4%28-5%29%28-50000%29 to get 1000000


x+=+%28-1000+%2B-+sqrt%28+0+%29%29%2F%282%28-5%29%29 Subtract 1000000 from 1000000 to get 0


x+=+%28-1000+%2B-+sqrt%28+0+%29%29%2F%28-10%29 Multiply 2 and -5 to get -10.


x+=+%28-1000+%2B-+0%29%2F%28-10%29 Take the square root of 0 to get 0.


x+=+%28-1000+%2B+0%29%2F%28-10%29 or x+=+%28-1000+-+0%29%2F%28-10%29 Break up the expression.


x+=+%28-1000%29%2F%28-10%29 or x+=++%28-1000%29%2F%28-10%29 Combine like terms.


x+=+100 or x+=+100 Simplify.


So the only solution is x+=+100


This means that 100 computers must be sold to reach a profit of $55,000