SOLUTION: The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be model

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be model      Log On


   

Question 388201: The profits of a company are found by subtracting the company's
costs from its revenue. If a company's cost can be modeled by
14x + 120,000 and its revenue can be modeled by 40x - 0.0002x2,
what is an expression for the profit?
Thank you for all help!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
As the problem tells you, profit is revenue minus the costs:
profit = %2840x+-+0.002x%5E2%29+-+%2814x+-+120000%29
All we have to do is simplify. For many reasons I like to change all subtractions into additions of the opposite. For the first and third subtractions above this is easy:
profit = %2840x+%2B+%28-0.002x%5E2%29%29+-+%2814x+%2B+%28-120000%29%29
The remaining subtraction is a little more difficult to change into an addition because we have to figure out what the opposite of %2814x+%2B+%28-120000%29%29 is. The opposite of an expression like this is the sum of the opposite of each individual term:
profit = %2840x+%2B+%28-0.002x%5E2%29%29+%2B++%28-14x+%2B+120000%29
Now that everything is addition we can change the order (the Commutative Property of Addition) and the grouping (the Associative Property of Addition) in any way we choose! My choice is:
profit = -0.002x%5E2+%2B+%2840x+%2B+%28-14x%29%29+%2B+120000%29
This puts the exponents in order and groups the like terms together. We can add the like terms giving us:
profit = -0.002x%5E2+%2B+26x+%2B+120000%29
This is a simplified expression for the profit.