document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130>Question 130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ralph is four times as old as Frank. In 20 years, Ralph will be twice as old as Frank. How old are ralph and Frank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104 by </B><A HREF=/tutors/aboutme.mpl?userid=terrtwo><B>terrtwo(10)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=terrtwo><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=104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we use R for Ralph and F for Frank, the initial relationship between their ages is R = 4F\r<BR>\n" );
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document.write( "Ralph's age in twenty years will be R + 20, or his age now plus 20 years.\r<BR>\n" );
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document.write( "Frank's age will likewise be F + 20 in twenty years\r<BR>\n" );
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document.write( "Therefore the second equation we can write is \r<BR>\n" );
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document.write( "--> (R + 20) = 2(F + 20)\r<BR>\n" );
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document.write( "If we then substitute 4F for R in the second equation <BR>\n" );
document.write( "--> (4F + 20) = 2(F + 20)\r<BR>\n" );
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document.write( "We then distribute the 2:\r<BR>\n" );
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document.write( "--> 4F + 20 = 2F + 40<BR>\n" );
document.write( "Subtract 20 from both sides;\r<BR>\n" );
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document.write( "--> 4F + 20 - 20 = 2F + 40 - 20 <BR>\n" );
document.write( "--> 4F = 2F + 20\r<BR>\n" );
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document.write( "Subtract 2F from both sides\r<BR>\n" );
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document.write( "--> 4F - 2F = 2F + 20 - 2F<BR>\n" );
document.write( "--> 2F = 20\r<BR>\n" );
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document.write( "Divide both sides by 2;\r<BR>\n" );
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document.write( "--> 2F/2 = 20/2<BR>\n" );
document.write( "--> F = 10\r<BR>\n" );
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document.write( "When we substitute 10 for F back into the original equation (R = 4F);\r<BR>\n" );
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document.write( "--> R = 4*10 = 40\r<BR>\n" );
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document.write( "Hence Frank is now 10 and Ralph is 40<BR>\n" );
document.write( "Twenty years from now, Frank will be 30 and Ralph will be 60, or twice Frank's age\r<BR>\n" );
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document.write( "So the answer is F = 10 and R = 40 </SPAN>\n" );
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