document.write( "Question 89907: Some students planned a get together. The budget for the food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together? \n" ); document.write( "
Algebra.Com's Answer #65280 by stanbon(75887)\"\" \"About 
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Some students planned a get together. The budget for the food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
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\n" ); document.write( "Let number of students be \"x\".
\n" ); document.write( "Budget was $500 or average of $500/x per student
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\n" ); document.write( "Five no-shows leaves \"x-5\" students with average of $500/(x-5)
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\n" ); document.write( "EQUATION:
\n" ); document.write( "new average - old average = $5
\n" ); document.write( "500/(x-5) - (500/x) = 5
\n" ); document.write( "Multiply thru by x(x-5) to get:
\n" ); document.write( "500x - 500(x-5) = 5x(x-5)
\n" ); document.write( "500x - 500x+ 2500 = 5x^2-25x
\n" ); document.write( "5x^2-25x-2500 = 0
\n" ); document.write( "x^2-5x-500=0
\n" ); document.write( "x = [5+-sqrt(5^2-4*-500)]/2
\n" ); document.write( "Positive answer only:
\n" ); document.write( "x = [5+sqrt(2025)]/2
\n" ); document.write( "x = [5+45]/2
\n" ); document.write( "x = 25 students
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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