document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170564>Question 1170564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dave is x years old his sister is 5 years older his father is 5 times older than dave what age is dave  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795419 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=795419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there could be multiple answers to this questions the way it is presented.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "when the father is 20, dave is 4 and his sister is 9.<BR>\n" );
document.write( "when the father is 25, dave is 5 and his sister is 10<BR>\n" );
document.write( "when the father is 30, dave is 6 and his sister is 11.<BR>\n" );
document.write( "when the father is 35, dave is 7 and his sister is 12.<BR>\n" );
document.write( "etc.....<BR>\n" );
document.write( "in other words, there are multiple answers to this problem as it is presented.\r<BR>\n" );
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document.write( "please check the problem again to see if there is something missing.<BR>\n" );
document.write( "usually there is something that allows you to pin one of the variable to a specific age, like:<BR>\n" );
document.write( "today his father is 5 times as old as he is.<BR>\n" );
document.write( "in 5 years, his father is 4 times as old as he is.\r<BR>\n" );
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document.write( "this leads go two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they would be:<BR>\n" );
document.write( "y = 5x<BR>\n" );
document.write( "y+5 = 4*(x+5)<BR>\n" );
document.write( "you would simplify the second equation to get:<BR>\n" );
document.write( "y + 5 = 4x + 20<BR>\n" );
document.write( "you would then replace y with 5x to get:<BR>\n" );
document.write( "5x + 5 = 4x + 20<BR>\n" );
document.write( "you would then solve for x to get:<BR>\n" );
document.write( "x = 15\r<BR>\n" );
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document.write( "when x = 15, y = 75<BR>\n" );
document.write( "y + 5 = 80 and x + 5 = 20<BR>\n" );
document.write( "75 is equal to 5 * 15.<BR>\n" );
document.write( "80 is equal to 4 * 20.\r<BR>\n" );
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document.write( "the problem was able to be solved to a specific value.\r<BR>\n" );
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document.write( "a key factor is that the value of y and the value of x in both equations need to represent the same thing.<BR>\n" );
document.write( "in the equation just solved, y represented his father's age and x represented his age.\r<BR>\n" );
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document.write( "you could have said there were two equations, such as:<BR>\n" );
document.write( "y = x + 5<BR>\n" );
document.write( "y = 5x\r<BR>\n" );
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document.write( "unfortunately, now y represents two different values.\r<BR>\n" );
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document.write( "the y in the first equation represents his sister's age.<BR>\n" );
document.write( "the y in the second equation represents his father's age.\r<BR>\n" );
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document.write( "these equations could not be solved simultaneously for that reason.\r<BR>\n" );
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document.write( "if you did try to solve these equations simultaneously, you would replace y with x + 5 to get:<BR>\n" );
document.write( "x + 5 = 5x<BR>\n" );
document.write( "you would then subtract x from both sides of the equation to get:<BR>\n" );
document.write( "5 = 4x<BR>\n" );
document.write( "you would then solve for x to get:<BR>\n" );
document.write( "x = 5/4.\r<BR>\n" );
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document.write( "you would then replace x with 5/4 in your two original equations to get:<BR>\n" );
document.write( "y = x + 5 becomes y = 5/4 + which gets you y = 25/4 = 6 and 1/4.<BR>\n" );
document.write( "y = 5x becomes y = 5 * 5/4 which gets you y = 25/4 = 6 and 1/4.\r<BR>\n" );
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document.write( "you have a solution, but the solution means:\r<BR>\n" );
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document.write( "y = his sister's age.<BR>\n" );
document.write( "y = his father's age.<BR>\n" );
document.write( "since they can't be the same age, then the solution is invalid.\r<BR>\n" );
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document.write( "the equation is invalid because all instances of y have to represent the same  thing in both equations and all instances of x have to represent the same thing in both equations.\r<BR>\n" );
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document.write( "x is ok because it represents dave's age in both equation.\r<BR>\n" );
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document.write( "y is not ok because it represents his sister's age in one equation and his father's age in the other equation.\r<BR>\n" );
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document.write( "if you have any questions, let me know.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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