document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118137>Question 118137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Betty's present age is twice Roni's present age. Two years ago, Betty was three times as old as Roni was then. 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 #86248 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=86248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let B represent Betty's present age and R represent Roni's present age.<BR>\n" );
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document.write( "The problem tells you that Betty's present age is 2 times Roni's present age. In equation form<BR>\n" );
document.write( "this is:<BR>\n" );
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document.write( "B = 2R<BR>\n" );
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document.write( "Two years ago how old was Betty? Take Betty's present age B and subtract 2 to get B - 2. And<BR>\n" );
document.write( "two years ago how old was Roni? Take Roni's present age R and subtract 2 to get R - 2. The problem <BR>\n" );
document.write( "then tells you that Betty's age 2 years ago (B - 2) was three times Roni's age at that time<BR>\n" );
document.write( "or ... 3 times (R - 2). In equation form this is:<BR>\n" );
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document.write( "B - 2 = 3(R - 2)<BR>\n" );
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document.write( "Multiply out the right side by multiplying 3 times each of the terms in the parentheses, and<BR>\n" );
document.write( "when you do that multiplication, the equation becomes:<BR>\n" );
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document.write( "B - 2 = 3R - 6<BR>\n" );
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document.write( "Get rid of the -2 on the left side by adding +2 to both sides. That addition makes the<BR>\n" );
document.write( "equation become:<BR>\n" );
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document.write( "B = 3R - 4<BR>\n" );
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document.write( "Next, get rid of the 3R on the right side by subtracting 3R from both sides to change the<BR>\n" );
document.write( "equation to:<BR>\n" );
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document.write( "B - 3R = -4<BR>\n" );
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document.write( "Recall that the very first equation above told you that B equaled 2R. So you can substitute<BR>\n" );
document.write( "2R for B in the equation directly above to change it to:<BR>\n" );
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document.write( "2R - 3R = -4<BR>\n" );
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document.write( "Combining the two terms on the left side leads to:<BR>\n" );
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document.write( "-R = -4<BR>\n" );
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document.write( "Multiply both sides of this equation by -1 and you end up with:<BR>\n" );
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document.write( "R = 4<BR>\n" );
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document.write( "So Roni's present age (R) is 4 years old. And since Betty's present age is equal to 2 times R,<BR>\n" );
document.write( "then Betty is presently 2 times 4 or 8 years old.<BR>\n" );
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document.write( "Check. Two years ago Betty would have been 8 - 2 or 6 years old and Roni would have been<BR>\n" );
document.write( "4 - 2 or 2 years old. And at that time Betty's age (6) was actually 3 times Roni's age (2).<BR>\n" );
document.write( "So the answers check ... Betty is now 8 and Roni is now 4.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to do it.<BR>\n" );
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document.write( "Happy 2008!!!!<BR>\n" );
document.write( ". </SPAN>\n" );
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