document.write( "Question 119643: The profit on a watch is given by $\"P+=+x%5E2+%96+13x+%96+80\"$ , where $\"x\"$ is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss? \n" ); document.write( "

Algebra.Com's Answer #87643 by tangitehewagen(7) $\"\"$ $\"About$

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A $ $\"50\"$ loss means that profit $\"%28P%29\"$ is negative so set $\"P+=+-50\"$ and so $\"-50+=+x%5E2+-+13x+-+80\"$ .\r
\n" ); document.write( "\n" ); document.write( "We add $\"50\"$ to both sides of the equation to get \r
\n" ); document.write( "\n" ); document.write( " $\"0+=+x%5E2+-+13x+-+80+%2B+50\"$ which simplifies to \r
\n" ); document.write( "\n" ); document.write( " $\"0+=+x%5E2+-+13x+-+30\"$ .\r
\n" ); document.write( "\n" ); document.write( "Now lets see if we can factor the right hand side $\"x%5E2+-+13x+-+30\"$ .\r
\n" ); document.write( "\n" ); document.write( "The coefficient of the $\"x%5E2\"$ term is $\"1\"$ so we ask ourselves what factors of $\"-30\"$ have a sum of $\"-13\"$ .\r
\n" ); document.write( "\n" ); document.write( "The integer factors of $\"-30\"$ are $\"-1\"$ and $\"30\"$ , $\"1\"$ and $\"-30\"$ , $\"-2\"$ and $\"15\"$ , $\"2\"$ and $\"-15\"$ , $\"-3\"$ and $\"10\"$ , $\"3\"$ and $\"-10\"$ , $\"-5\"$ and $\"6\"$ , $\"5\"$ and $\"-6\"$ .\r
\n" ); document.write( "\n" ); document.write( "A quick inspection tells us the factors of $\"2\"$ and $\"-15\"$ add up to $\"-13\"$ .\r
\n" ); document.write( "\n" ); document.write( "So we can rewrite $\"0+=+x%5E2+-+13x+-+30\"$ as $\"0+=+%28x+%2B+2%29%28x+-+15%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "This means that either $\"x%2B2+=+0\"$ or $\"x-15=0\"$ which tells us that \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-2\"$ or $\"x+=+15\"$ .\r
\n" ); document.write( "\n" ); document.write( "But what does this mean, perhaps we had 2 more watches returned than what we sold or we sold a net of 15 watches. In either case, we have a $50 loss. \n" ); document.write( "

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