document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100047>Question 1100047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ginelle is operating a tutorial center. She is operating at a loss of 15,000 pesos. Her tutorial fees are at 450 pesos per hour, and she has to pay a maintenance fee of 250 pesos per hour. What is the function that illustrates the flow of money of the tutorial center? Let x be the number of hours. Combine like terms. How many hours of tutorial service does her center have to operate in order to gain a profit of 15,000 pesos? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714538 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> profit = revenue minus cost.\r<BR>\n" );
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document.write( "her revenue is 450 pesos per hour.\r<BR>\n" );
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document.write( "her cost is equal to a fixed cost plus a variable cost of 250 pesos per hour.\r<BR>\n" );
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document.write( "if we allow:\r<BR>\n" );
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document.write( "p = profit<BR>\n" );
document.write( "r = revenue<BR>\n" );
document.write( "f = fixed cost<BR>\n" );
document.write( "v = variable cost<BR>\n" );
document.write( "x = number of hours\r<BR>\n" );
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document.write( "then the formula becomes p = r*x - f - v*x\r<BR>\n" );
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document.write( "her revenue is 450 pesos per hour and her variable cost is 250 pesos per hour.\r<BR>\n" );
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document.write( "the formula becomes p = 450*x - f - 250*x\r<BR>\n" );
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document.write( "if we combine like terms, then the formula becomes p = 200 * x - f\r<BR>\n" );
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document.write( "if p is positive, then she has a profit.\r<BR>\n" );
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document.write( "if p is negative, then she has a loss.\r<BR>\n" );
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document.write( "you say she's operating at a loss of 15000 pesos.\r<BR>\n" );
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document.write( "the formula becomes -15000 = 200*x - f\r<BR>\n" );
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document.write( "we now need to know how many hours she was teaching when she was operating at a loss of 15000 pesos.\r<BR>\n" );
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document.write( "if it was 0 hours, then her fixed cost had to be 15000 pesos.\r<BR>\n" );
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document.write( "the formula would become -15000 = 200*0 - f\r<BR>\n" );
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document.write( "we would solve for f to get f = 15000.\r<BR>\n" );
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document.write( "the formula becomes -15000 = 200*x - 15000.\r<BR>\n" );
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document.write( "we would solve for x to get x = 0/200 = 0.\r<BR>\n" );
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document.write( "you then want to know how many hours she would have to teach in order to get a profit of 15000 pesos (positive 15000).\r<BR>\n" );
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document.write( "the formula would become 15000 = 200 * x - 15000\r<BR>\n" );
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document.write( "add 15000 to both sides of this equation to get 30000 = 200 * x\r<BR>\n" );
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document.write( "divide both sides of this equation by 200 and solve for x to get x = 30000 / 200 = 150.\r<BR>\n" );
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document.write( "she would have to teach for 150 hours to make a profit of 15000 pesos, if her fixed cost was 15000 pesos.\r<BR>\n" );
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document.write( "you did not specify what the fixed cost was, so i assumed 15000.\r<BR>\n" );
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document.write( "it could have been anything.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume the fixed cost was 100,000 pesos.\r<BR>\n" );
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document.write( "the formula would then become p = r*s - f - v*x which would becomes p = 450*x -  100,000 - 250 * x which would be simplified to p = 200*x - 100,000.\r<BR>\n" );
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document.write( "if she was operating at a loss of 15000 pesos, then the formula would become -15000 = 200*x - 100,000.\r<BR>\n" );
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document.write( "you would add 100,000 to both sides of this equation to get 85,000 = 200*x and you would solve for x to get x = 85,000 / 200 = 425 hours.\r<BR>\n" );
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document.write( "when the fixed cost was 100,000 pesos, she would be operating at a loss of 15000 pesos if she was tutoring for 425 hours.\r<BR>\n" );
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document.write( "p = 200*425 - 100,000 = -15000.\r<BR>\n" );
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document.write( "in order to be operating at a profit of 15000, the same formula would be used, except p = 15000 and you would get 15000 = 200*x - 100,000\r<BR>\n" );
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document.write( "you would then add 100,000 to both sides to get 115,000 = 200*x and you would solve for x to get x = 115,000 / 200 = 575 hours.\r<BR>\n" );
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document.write( "she would have to tutor for 575 hours to make a profit of 15000 pesos.\r<BR>\n" );
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document.write( "p = 200*575 - 100,000 = 15000.\r<BR>\n" );
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document.write( "bottom line is the problem wasn't defined very well since i wasn't sure what the fixed cost was.\r<BR>\n" );
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document.write( "i assumed 15000 and got one answer.<BR>\n" );
document.write( "i assumed 100,000 and got another answer.\r<BR>\n" );
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document.write( "the formula, however, is the same, so if you know what the fixed cost is supposed to be, you can solve for the he rest.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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