document.write( "Question 928652: The girls’ softball team is sponsoring a fund-raising trip to see a professional baseball game. They charter a 60-passenger bus for $525. In order to make a profit, they will charge $15 per person if all seats on the bus are sold, but for each empty seat, they will increase the price by $1.50 per person.\r
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Algebra.Com's Answer #563857 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The girls’ softball team is sponsoring a fund-raising trip to see a professional baseball game.
\n" ); document.write( " They charter a 60-passenger bus for $525.
\n" ); document.write( " In order to make a profit, they will charge $15 per person if all seats on the bus are sold, but for each empty seat, they will increase the price by $1.50 per person.
\n" ); document.write( "What is the minimum number of passengers needed in order for the softball team not to lose money?
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\n" ); document.write( "let x = no. empty seats on the bus
\n" ); document.write( "Also
\n" ); document.write( "let x = no. of $1.50 increases for each empty seat
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\n" ); document.write( "f(x) = revenue - expense
\n" ); document.write( "f(x) = (60-x)(15+1.5x) - 525
\n" ); document.write( "FOIL
\n" ); document.write( "f(x) = 900 + 90x - 15x -1.5x^2 - 525
\n" ); document.write( "combine like terms to form a quadratic equation
\n" ); document.write( "f(x) = -1.5x^2 + 75x + 375
\n" ); document.write( "Breakeven points: f(x) = -0
\n" ); document.write( "-1.5x^2 + 75x + 375 = 0
\n" ); document.write( "Simplify, divide by -1.5
\n" ); document.write( "x^2 - 50x - 250 = 0
\n" ); document.write( "Using the quadratic formula, got a positive solution:
\n" ); document.write( "x = 54.58 we have to round it down to not lose money, therefore
\n" ); document.write( "x = 54 empty seats, only 6 paying passengers the minimum to not lose money
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\n" ); document.write( "We can confirm this, 54 empty seats means the cost for the remaining 6 will be
\n" ); document.write( "15 + (54*1.5) = $96 per person
\n" ); document.write( "6 * 96 = $576, they would make $51
\n" ); document.write( "However 55 empty seats, only 5 passengers
\n" ); document.write( "15 + (55*1.5) = $97.50 per person
\n" ); document.write( "5 * 97.5 = $487, they would lose about $38
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\n" ); document.write( "Did all this make sense to you? Any questions? ankor@att.net\r
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