document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93718>Question 93718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 3 years, Alex will be 3 times as old as his sister Precy. A year ago, Alex was 7 times as old as Precy.How old are they now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68284 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=68284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be Alex's present age and P be Precy's present age.<BR>\n" );
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document.write( "If A is Alex's present age, then a year ago he was A-1 years old. And a year ago Precy was<BR>\n" );
document.write( "P -1 years old.<BR>\n" );
document.write( "At that time Alex's age equaled 7 times Precy's age. So in equation form, a year ago:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+1=7%28P-1%29 ALIGN=MIDDLE  ALT=\"A+-+1=7%28P-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can multiply out the right side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+1+=+7P+-+7 ALIGN=MIDDLE  ALT=\"A+-+1+=+7P+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then add +1 to both sides to get rid of the -1 on the left side and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+7P+-+6 ALIGN=MIDDLE  ALT=\"A+=+7P+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, subtract 7P from both sides and we get the standard form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+7P+=+-6 ALIGN=MIDDLE  ALT=\"A+-+7P+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is our first equation. Remember it.<BR>\n" );
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document.write( "If A is Alex's current age, then in 3 years his age will be A + 3. And if P is Precy's present<BR>\n" );
document.write( "age, then in 3 years she will be P + 3. We are told that at that time Alex's age will be <BR>\n" );
document.write( "3 times Precy's age. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+3+=+3%28P%2B3%29 ALIGN=MIDDLE  ALT=\"A+%2B+3+=+3%28P%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply our the right side and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+3+=+3P+%2B+9 ALIGN=MIDDLE  ALT=\"A+%2B+3+=+3P+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 3 on the left side by subtracting 3 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3P+%2B+6 ALIGN=MIDDLE  ALT=\"A+=+3P+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And finally, put this equation in standard form by subtracting 3P from both sides to<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+3P+=+6 ALIGN=MIDDLE  ALT=\"A+-+3P+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So now we have a set of equations as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-7P+=+-6 ALIGN=MIDDLE  ALT=\"A+-7P+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-3P+=+6 ALIGN=MIDDLE  ALT=\"A+-3P+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can eliminate A by subtracting the two equations vertically in columns to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4P+=+-12 ALIGN=MIDDLE  ALT=\"+-4P+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This can be solved for P by dividing both sides by -4 to get that P (Precy's present age)<BR>\n" );
document.write( "is +3.<BR>\n" );
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document.write( "That means that a year ago Precy was 2 and at that time Alex was 7 times as old as she. Therefore,<BR>\n" );
document.write( "a year ago Alex was 7*2 or 14 years old. But that was a year ago. That means that this<BR>\n" );
document.write( "year Alex is a year older so he is currently 15.<BR>\n" );
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document.write( "So we have that presently Alex is 15 and Precy is 3. <BR>\n" );
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document.write( "Three years from now Alex will be 18 and Precy will be 6.  So at that time Alex will be<BR>\n" );
document.write( "3 times as old as Precy. That checks so it appears that our answer is correct.<BR>\n" );
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document.write( "The answer is Alex is now 15 and Precy is now 3.<BR>\n" );
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document.write( "Hope this helps you to see your way through this problem.<BR>\n" );
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