document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=545043>Question 545043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening, I have an age application problem that I need assistance with. I will greatly appreciate your help. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages are 41, then how old is sue? What I have done so far with this problem: L+S+J=41 <BR>\n" );
document.write( "L(6+s)+S+J(5+L)=41 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #355400 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=355400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your first equation is correct. That is:<BR>\n" );
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document.write( "L + S + J = 41<BR>\n" );
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document.write( "You are told that Leah is 6 years older than Sue. This means if you add 6 years to Sue's age, the sum will equal Leah's age. So you can say:<BR>\n" );
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document.write( "L = S + 6<BR>\n" );
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document.write( "Now you can return to your first equation and substitute S + 6 for its equal, which is L. When you make that substitution the first equation becomes:<BR>\n" );
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document.write( "S + 6 + S + J = 41<BR>\n" );
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document.write( "Simplify this by adding the two S terms. Then subtract 6 from both sides to get rid of the 6 on the left side. These two simplifications make the equation become:<BR>\n" );
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document.write( "2S + J = 35<BR>\n" );
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document.write( "You are also told that John is 5 years older than Leah. This means that if you add 5 years to Leah's age, the sum will equal John's age. So you can say:<BR>\n" );
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document.write( "J = L + 5<BR>\n" );
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document.write( "But you know that L = S + 6. So in this equation for J, you can substitute S + 6 for L to get:<BR>\n" );
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document.write( "J = S + 6 + 5 <BR>\n" );
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document.write( "and by adding 6 + 5, you make the equation:<BR>\n" );
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document.write( "J = S + 11<BR>\n" );
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document.write( "Return to the equation 2S + J = 35 and substitute S + 11 for J to get:<BR>\n" );
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document.write( "2S + S + 11 = 35<BR>\n" );
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document.write( "Combine the 2 terms containing S and then subtract 11 from both sides to get rid of the 11 on the left side. These two simplifications make the equation become:<BR>\n" );
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document.write( "3S = 24<BR>\n" );
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document.write( "Solve for S by dividing both sides of this equation by 3 to get that S (Sue's age) is:<BR>\n" );
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document.write( "S = 24/3 = 8<BR>\n" );
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document.write( "Sue is 8 years old.<BR>\n" );
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document.write( "That means that Leah's age (she's 6 years older than Sue) is 8 + 6 = 14. And John is 5 years older than Leah so John is 14 + 5 = 19. Just as a check, let's add these three ages to see if the total is 41 as it should be:<BR>\n" );
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document.write( "8 + 14 + 19 = 22 + 19 = 41<BR>\n" );
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document.write( "That is correct.<BR>\n" );
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document.write( "So you can have confidence that Sue is 8 years old and that is the answer that the problem asked you to find.<BR>\n" );
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document.write( "Hope this helps you to understand how the problem can be solved. You were very close with your second equation, but you had to find L and J in terms of S to get to the answer.<BR>\n" );
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document.write( "Your second equation should have been:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28L%29%286%2BS%29%2BS%2Bcross%28J%29%285%2Bcross%28L%29%286+%2B+S%29%29=41 ALIGN=MIDDLE  ALT=\"cross%28L%29%286%2BS%29%2BS%2Bcross%28J%29%285%2Bcross%28L%29%286+%2B+S%29%29=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that you could have substituted 6 + S for L in one more place. Then it would have worked out for you because your equation would be:<BR>\n" );
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document.write( "(6 + S) + S + 5 + (6 + S) = 41<BR>\n" );
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document.write( "And combining the S terms would simplify this equation to:<BR>\n" );
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document.write( "3S + 6 + 5 + 6 = 41 <BR>\n" );
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document.write( "and combining the constants on the left side would give:<BR>\n" );
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document.write( "3S + 17 = 41<BR>\n" );
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document.write( "Subtracting 17 from both sides:<BR>\n" );
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document.write( "3S = 24<BR>\n" );
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document.write( "and by dividing both sides by 3 again results in:<BR>\n" );
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document.write( "S = 24/3 = 8<BR>\n" );
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