document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=723161>Question 723161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. McCaffery decides to paint the ceiling and the walls of a room. He spends $120 on 2 gallons of paint for the ceiling and 4 gallons of paing for the walls. Then he decides to paint a different room with the same kind of ceiling and wall paint. Write a system of linear equations that model the situation. A gallon of ceiling paint costs $3 more than a gallon of wall paint. What is the cost of one gallon of each type of paint? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443051 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "There is no mention of the amount of paint required to do either the ceiling or the walls in the second room, so let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a_2\"> be the number of gallons of ceiling paint that costs <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> dollars per gallon and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b_2\"> be the number of gallons of wall paint that costs <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> dollars per gallon.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C_2\"> be the total cost of paint for the second room.\r<BR>\n" );
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document.write( "The equation that models the first room is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 4y\ =\ 120\">\r<BR>\n" );
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document.write( "The equation that models the second room is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_2x\ +\ b_2y\ =\ C_2\">\r<BR>\n" );
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document.write( "Knowing the cost relationship between the two types of paint allows us to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x\ -\ 3\">\r<BR>\n" );
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document.write( "Then by substitution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 4(x\ -\ 3)\ =\ 120\">\r<BR>\n" );
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document.write( "From which you can determine the cost of the ceiling paint.  Using the cost of the ceiling paint, that is to say <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">, you can then subtract 3 to determine the cost of the wall paint, that is: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">.\r<BR>\n" );
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document.write( "Once you know the costs you can plug those numbers into:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_2x\ +\ b_2y\ =\ C_2\">\r<BR>\n" );
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document.write( "to develop a formula for any size room where the same types of paint are used.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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