document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094421>Question 1094421</A>: <I><SPAN STYLE=\"word-break: break-all;\"> &#8203;Joe's Tire shop sells three types of tires.  High performance tires sell for &#8203;$50/tire.  Ultra performance tires sell for &#8203;$60&#8203;/tire.  Extreme performance tires sell for &#8203;$80&#8203;/tire.  Last&#8203; week, the revenue generated by the sales of ultra performance tires exceeded the revenue from the sale of extreme performance tires by &#8203;$1600.  If the tire shop sold a total of 220 tires last week for a total revenue of &#8203;$13,000&#8203;, how many of each type of tire were&#8203; sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709040 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=709040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h = number of high performance tires.<BR>\n" );
document.write( "u = number of ultra performance tires.<BR>\n" );
document.write( "e = number of extreme performance tires.\r<BR>\n" );
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document.write( "your equations are:\r<BR>\n" );
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document.write( "h + u + e = 220\r<BR>\n" );
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document.write( "50 * h + 60 * u + 80 * e = 13000\r<BR>\n" );
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document.write( "60 * u - 80 * e = 1600\r<BR>\n" );
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document.write( "first equation tells you the total number of tires sold by type.<BR>\n" );
document.write( "second equation tells you the total revenue generated by type.<BR>\n" );
document.write( "third equation tells you that the total revenue from ultra performance tires exceeds the total revenue from extreme performance tires by 1600.\r<BR>\n" );
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document.write( "from the third equation, solve for u to get u = (1600 + 80 * e) / 60\r<BR>\n" );
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document.write( "use that relationship in the first two equations to eliminate u as a variable in those two equations.\r<BR>\n" );
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document.write( "h + u + e = 220 becomes h + (1600 + 80 * e) / 60) + e = 220\r<BR>\n" );
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document.write( "multiply both sides of this equation by 60 to get 60 * h + 1600 + 80 * e + 60 * e = 60 * 220\r<BR>\n" );
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document.write( "combine like terms and simplify to get 60 * h + 140 * e + 1600 = 13200\r<BR>\n" );
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document.write( "subtract 1600 from both sides to get 60 * h + 140 * e = 11600\r<BR>\n" );
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document.write( "50 * h + 60 * u + 80 * e = 13000 becomes 50 * h + 60 * (1600 + 80 * e) / 60) + 80 * e = 13000\r<BR>\n" );
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document.write( "simplify this to get 50 * h + 1600 + 80 * e + 80 * e = 13000\r<BR>\n" );
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document.write( "combine like terms to get 50 * h + 160 * e + 1600 = 13000\r<BR>\n" );
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document.write( "subtract 1600 from both sides to get 50 * h + 160 * e = 11400\r<BR>\n" );
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document.write( "your two equations to solve simultaneously are:\r<BR>\n" );
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document.write( "60 * h + 140 * e = 11600<BR>\n" );
document.write( "50 * h + 160 * e = 11400\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 5 and both sides of the second equation by 6 to get:\r<BR>\n" );
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document.write( "300 * h + 700 * e = 58000<BR>\n" );
document.write( "300 * h + 960 * e = 68400\r<BR>\n" );
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document.write( "subtsract first equation from the second to get:\r<BR>\n" );
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document.write( "260 * e = 10400\r<BR>\n" );
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document.write( "divide both sides by 260 to get e = 40\r<BR>\n" );
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document.write( "you already solved for u in terms of e.\r<BR>\n" );
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document.write( "that equation was u = (1600 + 80 * e) / 60\r<BR>\n" );
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document.write( "since e = 40, that equation becomes u = (1600 + 80 * 40) / 60\r<BR>\n" );
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document.write( "solve for u to get u = 80\r<BR>\n" );
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document.write( "since h + u + e = 220, then h + 80 + 40 = 220\r<BR>\n" );
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document.write( "solve for h to get h = 100\r<BR>\n" );
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document.write( "your numbers should be:\r<BR>\n" );
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document.write( "h = 100<BR>\n" );
document.write( "u = 80<BR>\n" );
document.write( "e = 40\r<BR>\n" );
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document.write( "if you did this correctly then everything should check out.\r<BR>\n" );
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document.write( "h + u + e = 220 becomes 100 + 80 + 40 = 220 which becomes 220 = 220<BR>\n" );
document.write( "this one checks out ok.\r<BR>\n" );
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document.write( "50 * h + 60 * u + 80 * e = 13000 becomes 50 * 100 + 60 * 80 + 80 * 40 = 13000 which becomes 13000 = 13000.<BR>\n" );
document.write( "this one checks out ok.\r<BR>\n" );
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document.write( "60 * u - 80 * e = 1600 becomes 60 * 80 - 80 * 40 = 1600 which becomes 1600 = 1600<BR>\n" );
document.write( "this one checks out ok.\r<BR>\n" );
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document.write( "everything checks out ok so your solution is:\r<BR>\n" );
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document.write( "number of high performance tires sold is 100.<BR>\n" );
document.write( "number of ultra performance tires sold is 80.<BR>\n" );
document.write( "number of extreme performance tires sold is 40.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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