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Math Help - Finding certain real numbers...

  1. #1
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    Finding certain real numbers...

    I need to find two positive real numbers whose product is a maximum and where the sum of the first and three times the second is 60.

    And apparently, there're 5 steps to doing this, and I know none of them:
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  2. #2
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    step 1
    1.x + 3. y = 60

    step 2
    y = (60-x)/3

    step 3
    p(x) = x((60-x)/3)

    step 4
    p(x) = 20.x -(x^2)/3
    step 5
    max(p(x)) = 300
    occurs when x = 30 and y = 10
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Sweet, understand what the question is saying....

    The Product P is given by xy=P. The sum is given by ... what?
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  4. #4
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    Well, it could be by a lot of things... 60*1, 30*2, 6*10...
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  5. #5
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    Quote Originally Posted by tutor.mathitutor View Post
    step 1
    1.x + 3. y = 60

    step 2
    y = (60-x)/3

    step 3
    p(x) = x((60-x)/3)

    step 4
    p(x) = 20.x -(x^2)/3
    step 5
    max(p(x)) = 300
    occurs when x = 30 and y = 10
    You are amazing! Although step 4 didn't work right. I'll be damned if I know how you did that.
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by BeSweeet View Post
    Well, it could be by a lot of things...
    No...it can't.

    It given by "the sum of the first and three times the second"

    \overbrace{x}^{\text{First}}\underbrace{+}_{\text{  sum}}\overbrace{3y}^{\text{3 times the second}}

    x+3y=60
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