document.write( "Question 144622: Some students planned for a get-together. The budget for 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?\r
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Algebra.Com's Answer #105390 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Some students planned for a get-together. The budget for 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 x = no. of students that attended
\n" ); document.write( "then
\n" ); document.write( "(x+5) = no. of planned students
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\n" ); document.write( "Planned cost per student = $\"500%2F%28%28x%2B5%29%29\"$
\n" ); document.write( "Actual cost per student = $\"500%2Fx\"$
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\n" ); document.write( "Actual cost = planned cost + $5
\n" ); document.write( " $\"500%2Fx\"$ = $\"500%2F%28%28x%2B5%29%29\"$ + 5
\n" ); document.write( "Multiply equation by x(x+5), resulting in:
\n" ); document.write( "500(x+5) = 500x + 5x(x+5)
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\n" ); document.write( "500x + 2500 = 500x + 5x^2 + 25x
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\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "5x^2 + 25x - 2500 = 0
\n" ); document.write( "Simplify
\n" ); document.write( "x^2 + 5x - 500 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "(x+25)(x-20) = 0
\n" ); document.write( "positive solution
\n" ); document.write( "x = 20 students actually attended
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\n" ); document.write( "Check solution by finding the cost of each
\n" ); document.write( "500/20 = 25
\n" ); document.write( "500/25 = 20 \n" ); document.write( "

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