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Math Help - Algebra Question Year 10 problem

  1. #1
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    Algebra Question Year 10 problem

    Can someone help me with the last part of this problem:

    A company makes calculation and has found that the cost C$ of producing X calculators is given by the rule:

    C=x(x-2) C is the cost in dollars and x is the number of calculators

    It has also fund tha the revenue $R from the sale of the calculators is given by the rule:

    R= (x(x+3)

    Using the fact that profit equals Revenue minus Cost show that the profit $P from the sale of x cakculators is given by the rule:
    P=5x

    I have done this bit and can prove that the answer to x(x+3) - x(x-2) is 5x

    However I cant get the next bit - please help

    The company engineer invents a new production process that shows some improvement and the new rule for producing x calcuators is given by:

    C=(x+20) (x-21) What would be the new rule for the profit $P using this new process. So I need to know how to work out

    x(x+3) - (x+20) (x-21) I think the last part has something to do with the difference of two squares rule. please show working. Thanks a million
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  2. #2
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    Quote Originally Posted by chreen15 View Post
    [snip]I need to know how to work out

    x(x+3) - (x+20) (x-21) I think the last part has something to do with the difference of two squares rule. please show working. Thanks a million
    Expand and simplify:

    x(x + 3) = x^2 + 3x.

    (x + 20)(x - 21) = x^2 - 21x + 20x - 420 = x^2 - x - 420.

    So x(x + 3) - (x + 20) (x - 21) = x^2 + 3x - (x^2 - x - 420) = x^2 + 3x - x^2 + x + 420 = .......
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  3. #3
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    Thank you

    Thanks
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