document.write( "Question 999941: Why are these two similar problems set up differently? and why are they set up in that way at all?\r
\n" ); document.write( "\n" ); document.write( "Find two numbers whose difference is 60 and whose product is a minimum? Why does this use f(x) = x(x-60)\r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "Find two numbers whose sum is 60 and whose product is a maximum? Why does this one use f(x) = x(60-x)\r
\n" ); document.write( "\n" ); document.write( "I fundamentally don't understand what is happening and how that function was created at all.
\n" ); document.write( "And will there ever be a case where it's a difference and the product is a maximum. Or where it's a sum and the product is a minimum. I don't understand what this question is asking.\r
\n" ); document.write( "\n" ); document.write( "So confused...
\n" ); document.write( "Please help! \n" ); document.write( "
Algebra.Com's Answer #617532 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Why are these two similar problems set up differently? and why are they set up in that way at all?\r
\n" ); document.write( "\n" ); document.write( "Find two numbers whose difference is 60 and whose product is a minimum? Why does this use f(x) = x(x-60)\r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "Find two numbers whose sum is 60 and whose product is a maximum? Why does this one use f(x) = x(60-x)\r
\n" ); document.write( "\n" ); document.write( "I fundamentally don't understand what is happening and how that function was created at all.
\n" ); document.write( "And will there ever be a case where it's a difference and the product is a maximum. Or where it's a sum and the product is a minimum. I don't understand what this question is asking.\r
\n" ); document.write( "\n" ); document.write( "So confused...
\n" ); document.write( "Please help!
\n" ); document.write( "
1st problem:
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document.write( "Let larger number be x, and smaller, y
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document.write( "Then we have: x - y = 60______y = x - 60 ------- eq (i)
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document.write( "Also, y = xy ------- eq (ii)
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document.write( "y = x(x – 60) ------- Substituting x – 60 for y in eq (ii)
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document.write( "\"y+=+x%5E2+-+60x\" --------- eq (ii)
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document.write( "MINIMUM occurs at: \"x+=+-+b%2F%282a%29\", or at: \"x+=+-+%28-+60%29%2F%282+%2A+1%29\", or at \"x+=+60%2F2\", or at: x = 30
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document.write( "With MINIMUM occurring at x = 30, we get: 
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document.write( "y = 30 – 60 ----------- Substituting 30 for x in eq (i)
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document.write( "y = - 30
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document.write( "As seen, the numbers that differ by 60, and have a MINIMUM product are:  \"highlight_green%28system%28-+30_and%2C30%29%29\"
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document.write( "MINIMUM: 30(- 30), or - 900\r
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document.write( "\n" );
document.write( "2nd problem:
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document.write( "Let larger number be x, and smaller, y
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document.write( "Then we have: x + y = 60_____y = 60 - x ------- eq (i)
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document.write( "Also, y = xy ------- eq (ii)
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document.write( "y = x(60 - x) ------ Substituting 60 – x for y in eq (ii)
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document.write( "\"y+=+60x+-+x%5E2\"
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document.write( "MAXIMUM occurs at: \"x+=+-+b%2F%282a%29\", or at: \"x+=+%28-+60%29%2F%282+%2A+-+1%29\", or at \"x+=+%28-+60%29%2F%28-+2%29\", or at x = 30
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document.write( "With MAXIMUM occurring at x = 30, we get: 
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document.write( "y = 60 - 30
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document.write( "y = 30\r
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document.write( "\n" );
document.write( "As seen, the numbers that sum to 60, and that have a MAXIMUM product are the same, at: \"highlight_green%28system%2830_and%2C30%29%29\"
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document.write( "MAXIMUM: 30(30), or 900 \n" );
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