document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187750>Question 1187750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Milan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. <BR>\n" );
document.write( "Each client does either one or the other (not both). <BR>\n" );
document.write( "On Friday there were 3 clients who did Plan A and 2 who did Plan B. <BR>\n" );
document.write( "On Saturday there were 8 clients who did Plan A and 4 who did Plan B. <BR>\n" );
document.write( "Milan trained his Friday clients for a total of 7hours and his Saturday clients for a total of 17hours. <BR>\n" );
document.write( "How long does each of the workout plans last?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819185 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=819185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a equal the the number of hours spent on plan A.<BR>\n" );
document.write( "let b equal the number of hours spent on plan B.\r<BR>\n" );
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document.write( "on friday, there were 3 who did plan A and 2 who did plan B for a total of 7 hours.\r<BR>\n" );
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document.write( "on saturday, there were 8 who did plan A and 4 who did plan B for a total of 17 hours.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "that means the same value of a and b for both equations.\r<BR>\n" );
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document.write( "the requations are:\r<BR>\n" );
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document.write( "3a + 2b = 7<BR>\n" );
document.write( "8a + 4b = 17\r<BR>\n" );
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document.write( "multiply both sides of the first equAtion by 2 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "6a + 4b = 14<BR>\n" );
document.write( "8a + 4b = 17\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "2a = 3\r<BR>\n" );
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document.write( "solve for a to get:\r<BR>\n" );
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document.write( "a = 3/2\r<BR>\n" );
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document.write( "replace a with 3/2 in either equation to get:\r<BR>\n" );
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document.write( "6a + 4b = 14 becomes 6 * 3/2 + 4b = 14 which becomes 9 + 4b = 14<BR>\n" );
document.write( "8a + 4b = 17 becomes 8 * 3/2 + 4b = 17 which becomes 12 + 4b = 17\r<BR>\n" );
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document.write( "solve for b in both equations to get:\r<BR>\n" );
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document.write( "4b = 14 - 9 which becomes 4b = 5 which becomes b = 5/4.<BR>\n" );
document.write( "4b = 17 - 12 which becomes 4b = 5 which becomes b = 5/4.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "a = 3/2 and b = 5/4.\r<BR>\n" );
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document.write( "replace a and b in your original equaiton to see if they are true.\r<BR>\n" );
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document.write( "3a + 2b = 7 becomes 3 * 3/2 + 2 * 5/4 = 7 which becomes 9/2 + 10/4 = 7 which becomes 18/4 + 10/4 = 7 which becomes 28/4 = 7 which becomes 7 = 7, confirming the values of a and b are good for the first equation.\r<BR>\n" );
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document.write( "8a + 4b = 17 becomes 8 * 3/2 + 4 * 5/4 = 17 which becomes 24/2 + 20/4 = 17 which becomes 48/4 + 20/4 = 17 which becomes 68/4 = 17 which becomes 17 = 17, confirming the value of a and b are good for the second equation.\r<BR>\n" );
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document.write( "your solution is that plan A workout lasts 1.5 hours and plan B workout lasts 1.25 hours.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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