document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=506>Question 506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> First question:<BR>\n" );
document.write( "Right now, Alan's mother is 4 times older than he is. In 4 years, she will be 3 times older than he is. How old are Alan and his mother right now?\r<BR>\n" );
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document.write( "Second question:<BR>\n" );
document.write( "Kim is using a list of his friends' ages. He adds two of his friends' ages and gets 17. He multiplies the ages and gets 72. How old are his two friends?\r<BR>\n" );
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document.write( "I would appreciate your help. Thanks.<BR>\n" );
document.write( "-- Mary </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\">First question: <BR>\n" );
document.write( "Right now, Alan's mother is 4 times older than he is. In <BR>\n" );
document.write( "4 years, she will be 3 times older than he is. How old are <BR>\n" );
document.write( "Alan and his mother right now?<BR>\n" );
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document.write( "Let Alan's age be X<BR>\n" );
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document.write( ">>...Alan's mother is 4 times older than he is...<<<BR>\n" );
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document.write( "Mother's age = 4X<BR>\n" );
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document.write( ">>...In 4 years,...<<<BR>\n" );
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document.write( "` (Alan's age in 4 years) = X+4<BR>\n" );
document.write( "(Mother's age in 4 years) = 4X+4<BR>\n" );
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document.write( ">>...In 4 years, she will be 3 times older than he is...<<<BR>\n" );
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document.write( "(Mother's age in 4 years) = 3 times (Allen's age in 4 years)<BR>\n" );
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document.write( "` ` ` ` ` ` ` ` ` ` `4X+4 = 3(X+4)<BR>\n" );
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document.write( "Can you solve that?  Answer: X = 8, Mother's age = 4×8 = 32.<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( ">>...Right now, Alan's mother is 4 times older than he is...<< <BR>\n" );
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document.write( "That's true because he is 8 and she is 4 times 8 or 32.<BR>\n" );
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document.write( ">>...In 4 years, she will be 3 times older than he is...<<<BR>\n" );
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document.write( "That's true because he will be 12 and she will be 3 times<BR>\n" );
document.write( "12 or 36.<BR>\n" );
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document.write( "Second question: Kim is using a list of his friends' ages. <BR>\n" );
document.write( "He adds two of his friends' ages and gets 17. He multiplies <BR>\n" );
document.write( "the ages and gets 72. How old are his two friends?<BR>\n" );
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document.write( "Let x be one friend's age and y be the other friend's age:<BR>\n" );
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document.write( ">>...He adds two of his friends' ages and gets 17...<<<BR>\n" );
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document.write( "Translation:` x + y = 17<BR>\n" );
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document.write( ">>...He multiplies the ages and gets 72...<<<BR>\n" );
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document.write( "Translation:` ` `xy = 72<BR>\n" );
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document.write( "You have this system to solve<BR>\n" );
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document.write( "` ` ` ` ` ` ` x + y = 17<BR>\n" );
document.write( "` ` ` ` ` ` ` ` `xy = 72<BR>\n" );
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document.write( "Solve the first equation for y<BR>\n" );
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document.write( "` ` ` ` ` ` ` ` ` y = 17-x<BR>\n" );
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document.write( "Substitute 17-x for y in the second equation:<BR>\n" );
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document.write( "` ` ` ` ` ` ` ` ` xy = 72<BR>\n" );
document.write( "` ` ` ` ` ` `x(17-x) = 72<BR>\n" );
document.write( "` ` ` ` ` ` 17x - x² = 72<BR>\n" );
document.write( "` ` ` -x² + 17x - 72 = 0<BR>\n" );
document.write( "` ` ` `x² - 17x + 72 = 0<BR>\n" );
document.write( "` ` ` (x - 9)(x - 8) = 0      <BR>\n" );
document.write( "` ` ` x - 9 = 0 or x = 9<BR>\n" );
document.write( "` ` ` x - 8 = 0 or x = 8<BR>\n" );
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document.write( "`If x = 8, then y = 17-8 or 9<BR>\n" );
document.write( "`If x = 9, then y = 17-9 or 8<BR>\n" );
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document.write( "`Either way, one of them is 8 and the other 9.<BR>\n" );
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document.write( "`Edwin </SPAN>\n" );
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