document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079944>Question 1079944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Over the last 3 evenings, Latoya received a total of <BR>\n" );
document.write( "77 phone calls at the call center. The third evening, she received <BR>\n" );
document.write( "5 fewer calls than the first evening. The second evening, she received <BR>\n" );
document.write( "2 times as many calls as the third evening. How many phone calls did she receive each evening? <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 #694172 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=694172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she received 77 calls total.\r<BR>\n" );
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document.write( "let x = the number of calls she received the first evening<BR>\n" );
document.write( "let y = the number of calls she received the second evening.<BR>\n" );
document.write( "let z = the number of calls she received the third evening.\r<BR>\n" );
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document.write( "x + y + z = 77\r<BR>\n" );
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document.write( "the third evening she received 5 fewer calls than the first evening.\r<BR>\n" );
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document.write( "z = x - 5\r<BR>\n" );
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document.write( "the second evening she received 2 times as many call as as the third evening.\r<BR>\n" );
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document.write( "y = 2z\r<BR>\n" );
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document.write( "you have the following 3 equations that need to be solved simultaneously,\r<BR>\n" );
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document.write( "x + y + z = 77<BR>\n" );
document.write( "z = x - 5<BR>\n" );
document.write( "y = 2z\r<BR>\n" );
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document.write( "you want to eliminate 2 of the variables in the first equation so you can solve for the third.\r<BR>\n" );
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document.write( "replace z with x - 5 in the first equation to get:\r<BR>\n" );
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document.write( "x + y + x - 5 = 77\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "2x + y - 5 = 77\r<BR>\n" );
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document.write( "in the equation of y = 2z, replace z with x - 5 to get:\r<BR>\n" );
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document.write( "y = 2 * (x - 5)\r<BR>\n" );
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document.write( "simplify to get y = 2x - 10\r<BR>\n" );
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document.write( "in the equation of 2x + y - 5 = 77, replace y with 2x - 10 to get:\r<BR>\n" );
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document.write( "2x + 2x - 10 - 5 = 77\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "4x - 15 = 77\r<BR>\n" );
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document.write( "add 15 to both sides of the equation to get:\r<BR>\n" );
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document.write( "4x = 92\r<BR>\n" );
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document.write( "divide both sides of the equation by 4 to get:\r<BR>\n" );
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document.write( "x = 23\r<BR>\n" );
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document.write( "you started with:\r<BR>\n" );
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document.write( "x + y + z = 77<BR>\n" );
document.write( "z = x - 5<BR>\n" );
document.write( "y = 2z\r<BR>\n" );
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document.write( "since x = 23, these equations became:\r<BR>\n" );
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document.write( "24 + y + z = 77<BR>\n" );
document.write( "z = 23 - 5 = 18<BR>\n" );
document.write( "y = 2z = 2 * 18 = 36\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 23<BR>\n" );
document.write( "y = 36<BR>\n" );
document.write( "z = 18\r<BR>\n" );
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document.write( "x + y + z becomes 23 + 36 + 18 = 77<BR>\n" );
document.write( "z = x - 5 becomes z = 23 - 5 = 18<BR>\n" );
document.write( "y = 2z becomes y = 2 * 18 = 36\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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