document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946772>Question 946772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3 number equal 91.<BR>\n" );
document.write( " one number is multiplied by 6, one number has 6 added to it and the third has 6 subtracted from it, the answers are all the same.\r<BR>\n" );
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document.write( "What are the 3 numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577610 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=577610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your numbers are represented by x, y, and z.\r<BR>\n" );
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document.write( "you are given that 6x = y+6 = z-6\r<BR>\n" );
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document.write( "you are also given that x + y + z = 91\r<BR>\n" );
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document.write( "one way to solve this is to express all the variables in terms of one variable and then solve for that variable.\r<BR>\n" );
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document.write( "i'll express everything in terms of z.\r<BR>\n" );
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document.write( "6x = z-6 becomes x = (z-6)/6\r<BR>\n" );
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document.write( "y+6 = z-6 becomes y = z-12\r<BR>\n" );
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document.write( "after replacement, your eaution of x + y + z = 91 becomes (z-6)/6 + z-12 + z = 91\r<BR>\n" );
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document.write( "multiply both sides of this equation by 6 to get:\r<BR>\n" );
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document.write( "z-6 + 6z - 72 + 6z = 546\r<BR>\n" );
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document.write( "combine like terms to get 13z - 78 = 546\r<BR>\n" );
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document.write( "add 78 to both sides of this equation to get 13z = 624\r<BR>\n" );
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document.write( "divide both sides of this equation by 13 to get z = 48\r<BR>\n" );
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document.write( "since 6x = z-6, then 6x = 48-6 becomes 6x = 42 which becomes x = 7\r<BR>\n" );
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document.write( "since y+6 = z-6, then y+6 = 48-6 becomes y+6 = 42 which becomes y = 36\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x = 7<BR>\n" );
document.write( "y = 36<BR>\n" );
document.write( "z = 48\r<BR>\n" );
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document.write( "x + y + z = 91 becomes 7 + 36 + 48 = 91 which becomes 91 = 91 which is true, confirming that the values of x, y and z are good.\r<BR>\n" );
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document.write( "6x = y+6 becomes 42 = 36+6 = 42 is also true.\r<BR>\n" );
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document.write( "6x = z-6 becomes 42 = 48-6 = 42 is also true.\r<BR>\n" );
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document.write( "36+6 = z-6 becomes 42 = 42 is also true.\r<BR>\n" );
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document.write( "all statements are true so the solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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