document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201031>Question 1201031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate but do not solve the problem.\r<BR>\n" );
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document.write( "The management of Hartman Rent-A-Car has allocated $2.16 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $16,000 each, intermediate-size cars cost $24,000 each, and full-size cars cost $32,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)<BR>\n" );
document.write( "  ?= 2,160,000<BR>\n" );
document.write( "  ?= x<BR>\n" );
document.write( "  ?= 100 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835275 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=835275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a = numbr of compact cars<BR>\n" );
document.write( "b = number of intermediate size cars.<BR>\n" );
document.write( "c = number of full size cars.<BR>\n" );
document.write( "we'll work in thousands.<BR>\n" );
document.write( "16,000 = 16<BR>\n" );
document.write( "24,000 = 24<BR>\n" );
document.write( "31,000 = 32<BR>\n" );
document.write( "2.16 million = 2,160,000 = 2160<BR>\n" );
document.write( "a + b + c = 100<BR>\n" );
document.write( "16a + 24b + 32c = 2160<BR>\n" );
document.write( "since a = 2b, you can replace a with 2b in the equations to get:<BR>\n" );
document.write( "2b + b + c = 100<BR>\n" );
document.write( "16*2b + 24b + 31c = 2160<BR>\n" );
document.write( "simplify and combine like terms to get:<BR>\n" );
document.write( "3b + c = 100<BR>\n" );
document.write( "56b + 32c = 2160<BR>\n" );
document.write( "these are 2 equations that need to be solved simultaneously that you can then use to solve for b and c.<BR>\n" );
document.write( "from that, you can then solve for a.<BR>\n" );
document.write( "when you solve this, you should get a = 52, b = 26, c = 22, all in thousands.<BR>\n" );
document.write( "that results in 52 * 16000 + 26 * 24000 + 22 * 32000 = 2,160,000.<BR>\n" );
document.write( "let me know if you have any trouble doing that.<BR>\n" );
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