document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061800>Question 1061800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every boy had 5 hot dogs and 7 sodas.  Every girl had 3 hot dogs and 4 sodas.  Together, the children ate 51 hot dogs and 70 sodas.  How many children were there?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676542 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=676542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of boys<BR>\n" );
document.write( "let y = number of girls.\r<BR>\n" );
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document.write( "since each boy ate 5 hot dogs and each girls ate 3 hot dogs and the total number of hot dogs eaten were 51, you get:\r<BR>\n" );
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document.write( "5x + 3y = 51\r<BR>\n" );
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document.write( "since each boy drank 7 sodas and each girl drank 4 sodas and the total number of sodas that were drunk was 70, you get:\r<BR>\n" );
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document.write( "7x + 4y = 70\r<BR>\n" );
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document.write( "these are two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "once solved, you will get x = 6 and y = 7.\r<BR>\n" );
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document.write( "i solved using elimination.\r<BR>\n" );
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document.write( "i started with:\r<BR>\n" );
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document.write( "5x + 3y = 51<BR>\n" );
document.write( "7x + 4y = 70\r<BR>\n" );
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document.write( "i multiplied both sides of the first equation by 7 and multiplied both sides of the second equation by 5 to get:\r<BR>\n" );
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document.write( "35x + 21y = 357<BR>\n" );
document.write( "35x + 20y = 350\r<BR>\n" );
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document.write( "i then subtracted the second equation from the first equation to get:\r<BR>\n" );
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document.write( "y = 7\r<BR>\n" );
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document.write( "i then replaced y with 7 in the first original equation to get:\r<BR>\n" );
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document.write( "5x + 21 = 51\r<BR>\n" );
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document.write( "i then solved for x to get x = 6.\r<BR>\n" );
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document.write( "you can confirm the solution is good by replacing x with 6 and y with 7 in both equations to see that both equations are true.\r<BR>\n" );
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document.write( "i did, and they are, so i can assume the solution is good.\r<BR>\n" );
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