document.write( "Question 1153: 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? \n" ); document.write( "

Algebra.Com's Answer #342 by khwang(438) $\"\"$ $\"About$

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Sol: Assume there were x studented attended,so their average was 500/x dollars.
\n" ); document.write( " Since there were x + 5 students planned (note 5 were absent), the average
\n" ); document.write( " among the planned was 500/(x+5).
\n" ); document.write( " We know the difference between these two averages is 5, we have
\n" ); document.write( "
\n" ); document.write( " 500/x = 500/(x+5) + 5,
\n" ); document.write( " Dividing eqch term by 5:
\n" ); document.write( " 100/x = 100/(x+5) + 1,
\n" ); document.write( " Multiplying by x(x+5) to cancel the denominator:
\n" ); document.write( " 100(x+5) = 100x + x^2 + 5x,
\n" ); document.write( " Simplify: x^2 + 5x -500 = 0,
\n" ); document.write( " Factoring: (x-20)(x + 25) = 0,
\n" ); document.write( " So,x= 20 or -25(negative, invalid answer) \r
\n" ); document.write( "\n" ); document.write( " Answer : there were 20 students attended the get-together.
\n" ); document.write( " \n" ); document.write( "

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