document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058097>Question 1058097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The&#8203; U-Drive Rent-A-Truck company plans to spend &#8203;$16<BR>\n" );
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document.write( "million on 310<BR>\n" );
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document.write( "new vehicles. Each commercial van will cost &#8203;$45000<BR>\n" );
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document.write( "each small truck &#8203;$40000<BR>\n" );
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document.write( "and each large truck&#8195;&#8195;&#8203;$80000<BR>\n" );
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document.write( "Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they&#8203; buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673181 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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=673181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let C represent the number of commercial vans, S represent the number of small trucks, and L the number of large trucks.\r<BR>\n" );
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document.write( "Since the company intends to purchase 310 vehicles, you can write the following equation:\r<BR>\n" );
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document.write( "(Eq. 1) C + S + L = 310\r<BR>\n" );
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document.write( "The total cost of the vehicles is:\r<BR>\n" );
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document.write( "(Eq. 2) 45C + 40S + 80L = 16,000   (all values were divided by 1000 to keep the numbers small)\r<BR>\n" );
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document.write( "Then, since the number of commercial vans is twice the number of small trucks, you can write:\r<BR>\n" );
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document.write( "C = 2S\r<BR>\n" );
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document.write( "Substituting 2S in place of C in Eq. 1 and Eq. 2 gives the following equations:\r<BR>\n" );
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document.write( "2S + S + L = 310\r<BR>\n" );
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document.write( "45(2S) + 40S + 80L = 16,000\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "3S + L = 310\r<BR>\n" );
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document.write( "130S + 80L = 16,000\r<BR>\n" );
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document.write( "Multiplying the first of those equations by 80 gives the following system:\r<BR>\n" );
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document.write( "240S + 80L = 24,800<BR>\n" );
document.write( "130S + 80L = 16,000\r<BR>\n" );
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document.write( "Subtracting the second equation from the first leaves:\r<BR>\n" );
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document.write( "110S = 8800\r<BR>\n" );
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document.write( "S = 80\r<BR>\n" );
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document.write( "Then:\r<BR>\n" );
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document.write( "C = 2S = 2(80) = 160\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "C + S + L = 310\r<BR>\n" );
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document.write( "160 + 80 + L = 310\r<BR>\n" );
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document.write( "L = 310 - 160 - 80\r<BR>\n" );
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document.write( "L = 70\r<BR>\n" );
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document.write( "Solution: The company should purchase 160 commercial vans, 80 small trucks, and 70 large trucks.\r<BR>\n" );
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document.write( "Check: The total cost would be:\r<BR>\n" );
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document.write( "45000(160) + 40000(80) + 80000(70) = 16,000,000<BR>\n" );
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