document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189692>Question 1189692</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stadium has 48000 seats. Seats sell for ​$35 in Section​ A, ​$30 in Section​ B, and ​$25 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in ​$1510500 from each​ sold-out event. How many seats does each section​ hold </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821131 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=821131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let<BR>\n" );
document.write( "A = number of seats in section A<BR>\n" );
document.write( "B = number of seats in section B<BR>\n" );
document.write( "C = number of seats in section C\r<BR>\n" );
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document.write( "The stadium has 48000 seats total<BR>\n" );
document.write( "A+B+C = 48000\r<BR>\n" );
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document.write( "\"The number of seats in Section A equals the total number of seats in Sections B and C.\"<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "A = B+C\r<BR>\n" );
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document.write( "The previous equation<BR>\n" );
document.write( "A+B+C = 48000<BR>\n" );
document.write( "updates to<BR>\n" );
document.write( "B+C+B+C = 48000<BR>\n" );
document.write( "2B+2C = 48000<BR>\n" );
document.write( "2(B+C) = 48000<BR>\n" );
document.write( "after replacing A with B+C\r<BR>\n" );
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document.write( "Let's solve for C<BR>\n" );
document.write( "2(B+C) = 48000<BR>\n" );
document.write( "B+C = 48000/2<BR>\n" );
document.write( "B+C = 24000<BR>\n" );
document.write( "C = 24000-B\r<BR>\n" );
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document.write( "Now use these two facts<BR>\n" );
document.write( "\"Seats sell for ​$35 in Section​ A, ​$30 in Section​ B, and ​$25 in Section C. \"<BR>\n" );
document.write( "\"he stadium takes in ​$1510500 \"<BR>\n" );
document.write( "to form this equation<BR>\n" );
document.write( "35A+30B+25C = 1510500\r<BR>\n" );
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document.write( "Plug in A = B+C<BR>\n" );
document.write( "35A+30B+25C = 1510500<BR>\n" );
document.write( "35(B+C)+30B+25C = 1510500<BR>\n" );
document.write( "35B+35C+30B+25C = 1510500<BR>\n" );
document.write( "65B+60C = 1510500\r<BR>\n" );
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document.write( "Now plug in C = 24000-B and solve for B<BR>\n" );
document.write( "65B+60C = 1510500<BR>\n" );
document.write( "65B+60(24000-B) = 1510500<BR>\n" );
document.write( "65B+1440000-60B = 1510500<BR>\n" );
document.write( "5B+1440000 = 1510500<BR>\n" );
document.write( "5B = 1510500-1440000<BR>\n" );
document.write( "5B = 70500<BR>\n" );
document.write( "B = 70500/5<BR>\n" );
document.write( "B = 14100\r<BR>\n" );
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document.write( "We can use this value to find C<BR>\n" );
document.write( "C = 24000-B<BR>\n" );
document.write( "C = 24000-14100<BR>\n" );
document.write( "C = 9900\r<BR>\n" );
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document.write( "Now we can find A<BR>\n" );
document.write( "A = B+C<BR>\n" );
document.write( "A = 14100+9900<BR>\n" );
document.write( "A = 24000\r<BR>\n" );
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document.write( "===================================================================================================\r<BR>\n" );
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document.write( "To summarize<BR>\n" );
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document.write( "A = 24000<BR>\n" );
document.write( "B = 14100<BR>\n" );
document.write( "C = 9900<BR>\n" );
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document.write( "which represents the number of seats from sections A, B, and C in that order.\r<BR>\n" );
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document.write( "As a check,<BR>\n" );
document.write( "35A+30B+25C = 1510500<BR>\n" );
document.write( "35*24000+30*14100+25*9900 = 1510500<BR>\n" );
document.write( "840000+423000+247500 = 1510500<BR>\n" );
document.write( "1510500 = 1510500\r<BR>\n" );
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document.write( "Also,<BR>\n" );
document.write( "A+B+C = 24000+14100+9900 = 48000<BR>\n" );
document.write( "The answer is confirmed.<BR>\n" );
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