document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173233>Question 1173233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey can you please help me with this word problem ASAP?  Five times my age augmented by twice my sisters age is equal to sixty-four. Likewise, triple her age decreased by twice my age is equal to one. How old were each of us last year?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798425 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=798425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = your age.<BR>\n" );
document.write( "let y = your sister's age.\r<BR>\n" );
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document.write( "5 times your age plus 2 times your sister's age = 64<BR>\n" );
document.write( "the equation for that is 5x + 2y = 64\r<BR>\n" );
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document.write( "3 times her age minus 2 times your age = 1<BR>\n" );
document.write( "the equation for that is 3y - 2x = 1\r<BR>\n" );
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document.write( "solve for x in the first equation as shown below.<BR>\n" );
document.write( "start with 5x + 2y = 64.<BR>\n" );
document.write( "subtract 2y from both sides of the equation to get:<BR>\n" );
document.write( "5x = 64 - 2y<BR>\n" );
document.write( "divide both sides of the equation by 5 to get:<BR>\n" );
document.write( "x = (64 - 2y) / 5\r<BR>\n" );
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document.write( "replace x in the second equation with this to get:<BR>\n" );
document.write( "3y - 2x = 1 becomes:<BR>\n" );
document.write( "3y - 2 * (64 - 2y) / 5 = 1<BR>\n" );
document.write( "multiply both sides of this equation by 5 to get:<BR>\n" );
document.write( "15y - 2 * (64 - 2y) = 5<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "15y - 128 + 4y = 5<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "19y - 128 = 5<BR>\n" );
document.write( "add 237 to both sides of this equation to get:<BR>\n" );
document.write( "19y = 133<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 133/19 = 7\r<BR>\n" );
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document.write( "replace y with 7 in the equation of 5x + 2y = 64 to get:<BR>\n" );
document.write( "5x + 14 = 64<BR>\n" );
document.write( "subtract 14 from both sides of the equation to get:<BR>\n" );
document.write( "5x = 50<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 50/5 = 10\r<BR>\n" );
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document.write( "you have x = 10 and y = 7\r<BR>\n" );
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document.write( "confirm by replacing x and y in both original equations to get:<BR>\n" );
document.write( "5x + 2y = 64 becomes 5 * 10 + 2 * 7 = 64 which becomes 50 + 14 = 64 which becomes 64 = 64 which is true.<BR>\n" );
document.write( "3y - 2x = 1 becomes 3 * 7 - 2 * 10 = 1 which becomes 21 - 20 = 1 which becomes 1 = 1 which is true.\r<BR>\n" );
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document.write( "you were 10 years old and she was 7 years old this year.\r<BR>\n" );
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document.write( "your solution is that you were 9 years old and she was 6 years old last year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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