document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071471>Question 1071471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solving age word problems (if mom + dad age now = 6 times the kids age, before 2 years mom + dad age = 10 times the kids age, after 6 years from now the age of mom + dad = 3 times the total of kids age. how many kids? total age mom and dad now? total kids age?) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686427 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=686427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the age of mom and dad today.<BR>\n" );
document.write( "let y = the age of the kids today.\r<BR>\n" );
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document.write( "your equations are:\r<BR>\n" );
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document.write( "x = 6y<BR>\n" );
document.write( "x-2 = 10 * (y-2)<BR>\n" );
document.write( "x+6 = 3 * (y+6)\r<BR>\n" );
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document.write( "in order to solve this, all equations must have a common solution.<BR>\n" );
document.write( "unfortunately they don't.\r<BR>\n" );
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document.write( "if you solve for a common solution for the first 2 equations, you will get:<BR>\n" );
document.write( "x = 27 and y = 4.5\r<BR>\n" );
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document.write( "if you solve for a common solution for the first and third equation, you will get:<BR>\n" );
document.write( "x = 24 and y = 4\r<BR>\n" );
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document.write( "if you solve for a common solution for the last 2 equations, you will get:<BR>\n" );
document.write( "x = 24.857 and y = 4.286\r<BR>\n" );
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document.write( "this means that you have no common solution for all 3 equations, therefore you have no solution.\r<BR>\n" );
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document.write( "this can be seen graphically below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/030501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "x-6y is the red equation and red line on the graph.<BR>\n" );
document.write( "x-2 = 10 * (6-2) is the blue equation and blue line on the graph.<BR>\n" );
document.write( "x+6 = 3 * (6+6) is the green equation and green line on the graph.\r<BR>\n" );
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document.write( "there is a common solution between red and blue.<BR>\n" );
document.write( "there is a common solution between red and green.<BR>\n" );
document.write( "therr is a common solution between blue and green.\r<BR>\n" );
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document.write( "but, there is not a common solution between all 3.\r<BR>\n" );
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document.write( "a common solution to all 3 equations cannot be found, therefore there is no solution.\r<BR>\n" );
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document.write( "one of those equations is not being presented correctly.\r<BR>\n" );
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document.write( "for example, assume 24 and 4 needed to be the answer.\r<BR>\n" );
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document.write( "first equation is ok because 24 = 6 * 4.<BR>\n" );
document.write( "third equation is ok because 30 = 3 * 10<BR>\n" );
document.write( "second equation is not ok.\r<BR>\n" );
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document.write( "in order for second equation to be ok, let x = 24 and let y = 4 and evaluate the equation as is:<BR>\n" );
document.write( "you will get 24 - 2 = 10 * (y-2).<BR>\n" );
document.write( "this becomes 22 = 10 * (2)<BR>\n" );
document.write( "you will get 22 = 20 which is not correct.<BR>\n" );
document.write( "look at the ages today.<BR>\n" );
document.write( "x = 24 and y = 4<BR>\n" );
document.write( "2 years ago, x = 22 and y = 2<BR>\n" );
document.write( "this makes x equal to 11 * 2.<BR>\n" );
document.write( "the equaton should be:<BR>\n" );
document.write( "x-2 = 11 * (y-2)<BR>\n" );
document.write( "now, when you replace x with 24 and y with 4, you get:<BR>\n" );
document.write( "22 = 11 * 2 which becomes 22 = 22 which is correct.\r<BR>\n" );
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document.write( "so, one of the equations is not in synch with the other equations.<BR>\n" );
document.write( "not sure which one, but one of them is definitely off.<BR>\n" );
document.write( "check your inputs to see that you got them correctly.<BR>\n" );
document.write( "if so, then there is no solution common to all 3 equations.\r<BR>\n" );
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document.write( "another problem is interpretation.<BR>\n" );
document.write( "if the sum of the parents age is 24, then they must have been very young.<BR>\n" );
document.write( "too young, in fact, to have children.<BR>\n" );
document.write( "you could have been talking about their average age.<BR>\n" );
document.write( "in this case, everything would be doubled and you would wind up with the same problem if you assume 2 parents and 2 children.\r<BR>\n" );
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document.write( "all in all, you have a pretty messed up problem here.<BR>\n" );
document.write( "there is no common solution as it is presented.<BR>\n" );
document.write( "it does not make sense unless there is more information available that is not presented.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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