document.write( "Question 1092291: A student club is planning a fundraising carwash. Last year, they charged 100 per vehicle & washed 120 vehicles. If for every 20 increase in price, they know they will wash 5 fewer vehicles. Determine the best price to charge for the car wash so that the proceeds is maximum. \n" ); document.write( "

Algebra.Com's Answer #706942 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+P+=+%28+100+%2B+20n+%29%2A%28+120+-+5n+%29+\"$
\n" ); document.write( " $\"+P+=+12000+%2B+2400n+-+500n+-+100n%5E2+\"$
\n" ); document.write( " $\"+P+=+-100n%5E2+%2B+1900n+%2B+12000+\"$
\n" ); document.write( "The formula for the n-value of the vertex is
\n" ); document.write( " $\"+n%5Bmax%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+n%5Bmax%5D+=+-1900+%2F+%282%2A%28-100%29%29+\"$
\n" ); document.write( " $\"+n%5Bmax%5D+=+9.5+\"$
\n" ); document.write( "and, also
\n" ); document.write( " $\"+P%5Bmax%5D+=+-100%2A9.5%5E2+%2B+1900%2A9.5+%2B+12000+\"$
\n" ); document.write( " $\"+P%5Bmax%5D+=+-100%2A90.25+%2B+18050+%2B+12000+\"$
\n" ); document.write( " $\"+P%5Bmax%5D+=+-9025+%2B+30050+\"$
\n" ); document.write( " $\"+P%5Bmax%5D+=+21025+\"$
\n" ); document.write( "--------------------------------
\n" ); document.write( "The best price to charge is:
\n" ); document.write( " $\"+100+%2B+20n+=+100+%2B+20%2A9.5+\"$
\n" ); document.write( " $\"+100+%2B+20n+=+290+\"$
\n" ); document.write( "$290 per vehicle
\n" ); document.write( "---------------------------------
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+700%2C+400%2C+-2%2C+25%2C+-25%2C+250%2C+-x%5E2+%2B+19x+%2B+120+%29+\"$
\n" ); document.write( "The P-values are all divided by $\"+100+\"$
\n" ); document.write( "Definitely try to get another opinion if needed\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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