document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638396>Question 638396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John's age is 3 years more than twice Bill's age. Three years ago John was 4 times as old as Bill was then. How old is Bill now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #402170 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=402170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To make things easier, let's use the letter J to represent John's age, and the letter B to represent Bill's age.  The first sentence states that John is 3 years more than twice Bill's age.  In other words:\r<BR>\n" );
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document.write( "J = 2B + 3 \r<BR>\n" );
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document.write( "Now let's look at the second sentence, which states three years ago John was 4 times as old as Bill was then.  In other words:\r<BR>\n" );
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document.write( "J - 3 = 4(B - 3)\r<BR>\n" );
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document.write( "Now that we have our 2 equations (J=B+3 and J-3=4(B - 3)), we can solve.  Since we know John's age in terms of Bill, we will substitute 2B + 3 for our second equation:\r<BR>\n" );
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document.write( "2B + 3 - 3 = 4(B - 3)\r<BR>\n" );
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document.write( "The left side of our equation is now 2B and the right side is still 4(B - 3).  Using the distributive property, we will multiply the 4 by what's inside of the parenthesis:  4B - 12.  Our equation now looks like\r<BR>\n" );
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document.write( "2B = 4B - 12\r<BR>\n" );
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document.write( "We need to get the B's on one side of the equal sign, so we will subtract 2B from both sides, which gives us 0 = 2B - 12.  We will then add 12 to both sides, giving us 12 = 2B.  To get the B by itself, we will divide both sides by two, which will give us Bill's age:  6 = B. So, Bill is 6 years old.  \r<BR>\n" );
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document.write( "To find out John's age, replace the B in the first equation with 6:\r<BR>\n" );
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document.write( "J = 2(6) + 3\r<BR>\n" );
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document.write( "J = 12 + 3\r<BR>\n" );
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document.write( "Therefore, John is 15\r<BR>\n" );
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document.write( "Final Answer:  John is 15 and Bill is 6<BR>\n" );
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