document.write( "Question 253118: the $75 cost for a party was to be shared equally by all those attending. since five more people attended than was expected, the price per person dropped by $.50. how many people attended the party? \n" ); document.write( "

Algebra.Com's Answer #185355 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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the $75 cost for a party was to be shared equally by all those attending.
\n" ); document.write( " since five more people attended than was expected, the price per person dropped by $.50.
\n" ); document.write( "how many people attended the party?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. that actually attended
\n" ); document.write( "then
\n" ); document.write( "(x-5) = no. that were anticipated to attend
\n" ); document.write( ":
\n" ); document.write( "Anticipated cost/person - actual cost/person = $.50
\n" ); document.write( " $\"75%2F%28%28x-5%29%29\"$ - $\"75%2Fx\"$ = $\"1%2F2\"$ ; (we're dealing in dollars here)
\n" ); document.write( "Multiply equation by 2x(x-5), results:
\n" ); document.write( "2x(75) - 2(x-5)(75) = x(x-5)
\n" ); document.write( ":
\n" ); document.write( "150x - 75(2x-10) = x^2 - 5x
\n" ); document.write( ":
\n" ); document.write( "150x - 150x + 750 = x^2 - 5x
\n" ); document.write( ":
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "0 = x^2 - 5x - 750
\n" ); document.write( "factors to:
\n" ); document.write( "(x - 30)(x + 25) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "x = 30 people actually attended
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check this by finding the cost for each person
\n" ); document.write( "75/25 = $3.00; anticipated
\n" ); document.write( "75/30 = $2.50; actual \n" ); document.write( "

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