document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10096>Question 10096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five years ago , a father awas twice as old as his son. In 4 years'time the sum of their ages will be 78. Find their present ages. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5369 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ok, asked to find present ages, so define:\r<BR>\n" );
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document.write( "father currently = x<BR>\n" );
document.write( "son currently = y\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "five years ago, father was x-5<BR>\n" );
document.write( "five years ago, son was y-5\r<BR>\n" );
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document.write( "and,<BR>\n" );
document.write( "in 4 years time, father will be x+4<BR>\n" );
document.write( "in 4 years time, son will be y+4\r<BR>\n" );
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document.write( "Right then, we need 2 equations since we have 2 unknowns:\r<BR>\n" );
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document.write( "1. 5 years ago, father was twice as old as son:<BR>\n" );
document.write( "--> (x-5) = 2(y-5)<BR>\n" );
document.write( "--> x-5 = 2y-10<BR>\n" );
document.write( "--> x-2y = -5\r<BR>\n" );
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document.write( "2. in 4 years time, sum of ages = 78<BR>\n" );
document.write( "--> (x+4) + (y+4) = 78<BR>\n" );
document.write( "--> x+y +8 = 78<BR>\n" );
document.write( "--> x+y=70\r<BR>\n" );
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document.write( "So, now solve the 2 equations:\r<BR>\n" );
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document.write( "x-2y = -5<BR>\n" );
document.write( "x+y = 70\r<BR>\n" );
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document.write( "Subtract them to leave -3y = -75 --> y = 25, so son is now 25.\r<BR>\n" );
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document.write( "put this info into one of the 2 equations: pick either. I shall use x+y=70 --> means x must be 70-25, so father is now 45.\r<BR>\n" );
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document.write( "NOW, check!\r<BR>\n" );
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document.write( "5 years ago, ages were 40 and 20... CORRECT doubled age!<BR>\n" );
document.write( "4 years time, ages will be 49 and 29...add together to make 78!\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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