document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204546>Question 1204546</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Studio A                            Studio B<BR>\n" );
document.write( "classes|cost                       Classes|cost<BR>\n" );
document.write( "3        70                          4     80<BR>\n" );
document.write( "7        130                         6     120<BR>\n" );
document.write( "8        145                         9     180<BR>\n" );
document.write( "12       205                         11    220\r<BR>\n" );
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document.write( "The tables above show the cost of yoga classes at two different studios. Studio A charges a mat fee of $25, but Studio B has no initial fee. Write a system of equations that will determine when the two studios cost the same.     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840858 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given info<BR>\n" );
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document.write( " Studio A                            Studio B\r\n" );
document.write( "classes|cost                       Classes|cost\r\n" );
document.write( "3        70                          4     80\r\n" );
document.write( "7        130                         6     120\r\n" );
document.write( "8        145                         9     180\r\n" );
document.write( "12       205                         11    220\r\n" );
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document.write( "x = number of classes<BR>\n" );
document.write( "y = total cost\r<BR>\n" );
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document.write( "Two ordered pairs with studio A are: (3,70) and (7,130)\r<BR>\n" );
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document.write( "Let's use the slope formula on those points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C15%2C%22Given%22%2C%22points%3A%22%2C%22%28%22%2Cx%5B1%5D%2C%22%2C%22%2Cy%5B1%5D%2C%22%29+=+%22%2C%22%283%2C70%29%22%2C%22and%22%2C%22%28%22%2Cx%5B2%5D%2C%22%2C%22%2Cy%5B2%5D%2C%22%29+=+%22%2C%22%287%2C130%29%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+slope+=+rise%2Frun+=+matrix%281%2C3%2C%22change%22%2C%22in%22%2C%22y%22%29%2Fmatrix%281%2C3%2C%22change%22%2C%22in%22%2C%22x%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28130+-+70%29%2F%287+-+3%29 ALIGN=MIDDLE  ALT=\"m+=+%28130+-+70%29%2F%287+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2860%29%2F%284%29 ALIGN=MIDDLE  ALT=\"m+=+%2860%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+15 ALIGN=MIDDLE  ALT=\"m+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope 15 means the cost goes up $15 each time you take a new class. <BR>\n" );
document.write( "In other words, studio A charges $15 per class. This is on top of the $25 mat fee.<BR>\n" );
document.write( "We arrive at the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+15x%2B25 ALIGN=MIDDLE  ALT=\"y+=+15x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As a check, plug in x = 3 and you should get the result y = 70. I'll let the student do this confirmation and check the other values as well.\r<BR>\n" );
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document.write( "Follow similar steps for studio B and you should get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+20x ALIGN=MIDDLE  ALT=\"y+=+20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The system of equations is therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y+=+15x%2B25%2C+y+=+20x%29 ALIGN=MIDDLE  ALT=\"system%28y+=+15x%2B25%2C+y+=+20x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = number of classes<BR>\n" );
document.write( "y = total cost<BR>\n" );
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