document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=646749>Question 646749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A city government has approved the construction of a $800 million sports arena. Up to $480 million will be raised by selling bonds that pay simple interest at a rate of 4% annually. The remaining amount (up to $640 million) will be obtained by borrowing money from an insurance company at a simple interest rate of 9%. Determine whether the arena can be financed so that the annual interest is $59 million. (If it is not possible, enter NONE for each answer.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #405934 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=405934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + y = 800<BR>\n" );
document.write( "x <= 480 <BR>\n" );
document.write( "interest rate on x = .04<BR>\n" );
document.write( "y <= 640<BR>\n" );
document.write( "interest rate on y = .09<BR>\n" );
document.write( ".04x + .09y = 59<BR>\n" );
document.write( "x+y = 800<BR>\n" );
document.write( "from x + y = 800, solve for y to get:<BR>\n" );
document.write( "y = 800 - x<BR>\n" );
document.write( "substitute for y in .04x + .09y = 59 to get<BR>\n" );
document.write( ".04x + .09(800-x) = 59<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( ".04x + 72 - .09x = 59<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "-.05x + 72 = 59<BR>\n" );
document.write( "subtract 72 from both sides of the equation to get:<BR>\n" );
document.write( "-.05x = -13<BR>\n" );
document.write( "divide both sides of the equation by -.05 to get:<BR>\n" );
document.write( "x = 260<BR>\n" );
document.write( "this makes y = 540<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "x = 260<BR>\n" );
document.write( "y = 540<BR>\n" );
document.write( "x + y = 800<BR>\n" );
document.write( ".04x + .09y = .04(260) + .09(540) = 10.4 + 48.6 = 59<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "260 million raised at 4%<BR>\n" );
document.write( "540 million raised at 9%.<BR>\n" );
document.write( "total annual interest = 59 million.<BR>\n" );
document.write( "interest is simple interest so the same amount of interest is payed out each year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );