document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262410>Question 262410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> constructing equations\r<BR>\n" );
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document.write( "how do you construct this into a equatin?<BR>\n" );
document.write( "a spa had specials for new members. they can get 3 facials and 5 manicures for $114 or 3 facials and 2 manicures for $78. what are the prices for facials and manicures? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193334 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=193334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let f equal the cost for a facial.<BR>\n" );
document.write( "let m = the cost for a manicure.\r<BR>\n" );
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document.write( "first equation is:\r<BR>\n" );
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document.write( "3*f + 5*m = 114\r<BR>\n" );
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document.write( "second equation is:\r<BR>\n" );
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document.write( "3*f + 2*m = 78\r<BR>\n" );
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document.write( "you need to solve these 2 equations simultaneously.\r<BR>\n" );
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document.write( "we will solve by elimination.\r<BR>\n" );
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document.write( "the two equations are:\r<BR>\n" );
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document.write( "3*f + 5*m = 114<BR>\n" );
document.write( "3*f + 2*m = 78\r<BR>\n" );
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document.write( "subtract second equation from first equation to get:\r<BR>\n" );
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document.write( "3*m = 36\r<BR>\n" );
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document.write( "solve for m to get:\r<BR>\n" );
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document.write( "m = 12\r<BR>\n" );
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document.write( "substitute in first equation to get:\r<BR>\n" );
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document.write( "3*f + 5*12 = 114\r<BR>\n" );
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document.write( "solve for f to get:\r<BR>\n" );
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document.write( "f = 54/3 = 18\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "m = 12<BR>\n" );
document.write( "f = 18\r<BR>\n" );
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document.write( "substitute in first equation to get:\r<BR>\n" );
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document.write( "3*f + 5*m = 114 becomes 3*18 + 5*12 = 54 + 60 = 114\r<BR>\n" );
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document.write( "substitute in second equation to get:\r<BR>\n" );
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document.write( "3*f + 2*m = 78 becomes 3*18 + 2*12 = 54 + 24 = 78\r<BR>\n" );
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document.write( "both original equations are true confirming the values for m and f are good.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "cost of a facial is 18 dollars.<BR>\n" );
document.write( "cost of a manicure is 12 dollars.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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