document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283717>Question 283717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lydia, Sarah, and Denise collected campain buttons.  Lydia had 20 more buttons than Sarah. Denise had 3 times as many buttons as Sarah.  If the total number of campaign buttons the 3 girls had was 120, how many buttons did Lydia have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205901 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=205901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L = number of buttons collected by Lydia<BR>\n" );
document.write( "S = number of buttons collected by Sarah<BR>\n" );
document.write( "D = number of buttons collected by Denise<BR>\n" );
document.write( "L + S  + D = 120  :: Total given.<BR>\n" );
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document.write( "L = S + 20  :: Lydia has 20 more than Sarah<BR>\n" );
document.write( "D = 3S  :: Denise had 3 times as many as Sarah<BR>\n" );
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document.write( "Question:  How many did Lydia have?<BR>\n" );
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document.write( "We have 3 unknowns, so we need 3 equations...<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "We need to redefine the variables to use fewer than 3 unknowns.<BR>\n" );
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document.write( "Looking back, the problem was stated in terms of Sarah's buttons.<BR>\n" );
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document.write( "L = S+20<BR>\n" );
document.write( "D = 3S<BR>\n" );
document.write( "and<BR>\n" );
document.write( "S = S  of course<BR>\n" );
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document.write( "L + D + S = 120  :: given<BR>\n" );
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document.write( "substituting...<BR>\n" );
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document.write( "(S+20) + 3S + S = 120<BR>\n" );
document.write( "5S = 100<BR>\n" );
document.write( "S = 20<BR>\n" );
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document.write( "Substituting this value<BR>\n" );
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document.write( "L = S + 20<BR>\n" );
document.write( "L = 20 + 20 = 40<BR>\n" );
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document.write( "D = 3S<BR>\n" );
document.write( "D = 3(20) = 60<BR>\n" );
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document.write( "Checking, does L+S+D = 120?<BR>\n" );
document.write( "20 + 40 +60 = 120<BR>\n" );
document.write( "Yes!<BR>\n" );
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document.write( "Rechecking the question, it only asks how many Lydia has.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Lydia has 40 buttons.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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