document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201494>Question 201494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Would you please help me identify the equation for the following problem: <BR>\n" );
document.write( "\"Together we are 98 years old. I am twice as old as you were when I was as old as you are now.\"<BR>\n" );
document.write( "I understand A+B=98, but cannot figure the second statement. <BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Caroline\r<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 #427053 by </B><A HREF=/tutors/aboutme.mpl?userid=valgaze><B>valgaze(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=valgaze><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=427053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's pretend that we can only have whole numbers as a solution for their ages, no decimals or fractions.\r<BR>\n" );
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document.write( "First things first, let's take inventory of what we know: \r<BR>\n" );
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document.write( "1) There are two people whose ages we don't know (let's call them x & y)<BR>\n" );
document.write( "2) Their combined ages are 98 years old (x + y = 98)<BR>\n" );
document.write( "3) Tricky part: X's age TODAY is twice what Y's age was at the time X was Y's age TODAY. (In other words, in the past X was a certain age, let's say X*, and Y was a certain age, let's say Y*. In algebra terms, being very careful to note we are saying Y* and Y, we could say X=2Y*)\r<BR>\n" );
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document.write( "In straight algebra terms, we have the following problem:<BR>\n" );
document.write( "1) X+Y=98<BR>\n" );
document.write( "2) X=2Y*\r<BR>\n" );
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document.write( "We need to figure out a way to solve those equations, if we can even get just one age (X or Y) we will be able figure out the other one, but we have a problem: right now we have more variables than equations (two equations and three unknown variables.)\r<BR>\n" );
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document.write( "We either need to come up with another equation/relationship or come up with a clever way to have one of the variables drop/cancel out and solve from there.\r<BR>\n" );
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document.write( "The key to this problem is to think about what makes the age between two people special. \r<BR>\n" );
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document.write( "For example, imagine you had an older brother or sister, would you ever \"catch up\" to their age in the future? Unfortunately, and I speak from experience, the \"distance\" in age between you and your older siblings is a race you will never win. If I am 3 years younger than my sibling today, fifteen years ago I was 3 still 3 years younger and in the future I will still be 3 years younger.\r<BR>\n" );
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document.write( "So in our problem, we know another important relationship: The distance between the ages is some constant number D. This distance D applies no matter what time period you are talking about because the distance in age never changes.\r<BR>\n" );
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document.write( "So now know:<BR>\n" );
document.write( "X-Y=D and X*-Y*=D which crucially means X-Y=D=X*-Y* or finally X-Y=X*-Y*\r<BR>\n" );
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document.write( "We have three relationships to play with:<BR>\n" );
document.write( "1) X + Y = 98<BR>\n" );
document.write( "2) X=2Y*<BR>\n" );
document.write( "3) X-Y=X*-Y*\r<BR>\n" );
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document.write( "The last thing to think about is what is the relationship between X* and Y. Maybe try drawing a number line labeled 0 to 100 years with X, Y, X*, Y* on it and label the distances between X & Y as D and X* & Y* as D as well and see what you come up with.\r<BR>\n" );
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document.write( "Best,<BR>\n" );
document.write( "Vic </SPAN>\n" );
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