document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84801>Question 84801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! I am reviewing my Algebra for this year and I am having difficulty solving this one problem. I am not sure if I need to use three variables or if I should do something else. Here is the problem:<BR>\n" );
document.write( "Darrell has $2 less than five times as much money as Bob. Mary has as much money as Darrell and Bob together. If all three of them together have $80, how much money does Mary have?<BR>\n" );
document.write( "~There is my question. It would be incredibly helpful if you helped me solve this. Thank you once again.<BR>\n" );
document.write( "~ev10993@comcast.net </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61097 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=61097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have three unknowns: the amount of money Darrell has (call it D), the amount of money<BR>\n" );
document.write( "that Bob has (call it B), and the amount of money that Mary has (call it M). Since there are<BR>\n" );
document.write( "three unknowns, you can anticipate using three independent equations to solve for the unknowns.<BR>\n" );
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document.write( "Start with the fact that Darrell has $2 less than 5 times the amount of money that Bob has.<BR>\n" );
document.write( "You can translate this into 5 times the amount of money that Bob has take away $2 is equal<BR>\n" );
document.write( "to the amount of money that Darrell has. In equation form this can be written as:<BR>\n" );
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document.write( "D = 5*B - 2 <=== equation 1<BR>\n" );
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document.write( "Next you are told that Mary has as much money as Darrell and Bob combined. In equation<BR>\n" );
document.write( "form this is:<BR>\n" );
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document.write( "M = B + D  <=== equation 2<BR>\n" );
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document.write( "And finally you are told that if you add up all the money that these three have, the amount<BR>\n" );
document.write( "is $80. In equation form this is:<BR>\n" );
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document.write( "M + B + D = 80  <=== equation 3<BR>\n" );
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document.write( "Now what you need to do is to examine the equations and start substituting from one to<BR>\n" );
document.write( "the other. For example, from equation 1 you know what D is in terms of B. So you could <BR>\n" );
document.write( "substitute the right side of equation 1 into equation 3 in place of D. You could also<BR>\n" );
document.write( "substitute the right side of equation 1 for D in equation 2.  That would result in equation<BR>\n" );
document.write( "2 having M on the left side and only terms containing B on the right side. You could then<BR>\n" );
document.write( "substitute the right side of this \"new\" equation 2 into the \"new\" equation 3 and it would <BR>\n" );
document.write( "only then have only the unknown B. So you could solve for B and then work your way backward<BR>\n" );
document.write( "find M and D.<BR>\n" );
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document.write( "Let's work it a little differently.  Notice that equation 3 contains B + D. But from equation<BR>\n" );
document.write( "2 you know that B + D is equal to M.  So in equation 3 you can replace B + D with M and<BR>\n" );
document.write( "equation 3 then becomes:<BR>\n" );
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document.write( "M + M = 80<BR>\n" );
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document.write( "The left side adds up to 2M so the equation is:<BR>\n" );
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document.write( "2M = 80<BR>\n" );
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document.write( "and dividing both sides by 2 results in:<BR>\n" );
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document.write( "M = 40<BR>\n" );
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document.write( "So now you know that Mary has $40.<BR>\n" );
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document.write( "Return to equation 2 and substitute 40 for M. When you do, the equation becomes:<BR>\n" );
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document.write( "40 = B + D<BR>\n" );
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document.write( "Solve this equation for D by subtracting B from both sides to get:<BR>\n" );
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document.write( "D = 40 - B<BR>\n" );
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document.write( "You can now substitute the right side of this for D equation 1 to get:<BR>\n" );
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document.write( "40 - B = 5B - 2<BR>\n" );
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document.write( "Add B to both sides and this becomes:<BR>\n" );
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document.write( "40 = 6B - 2<BR>\n" );
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document.write( "Next add 2 to both sides:<BR>\n" );
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document.write( "42 = 6B<BR>\n" );
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document.write( "Finally, divide both sides by 6 to find B:<BR>\n" );
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document.write( "B = 42/6 = 7<BR>\n" );
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document.write( "Now you know that Bob has $7<BR>\n" );
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document.write( "From equation 3 you know that the sum of all the money is $80, and you have found that<BR>\n" );
document.write( "Mary has $40 and Bob has $7. Together Mary and Bob have $47 so Darrell must have the amount<BR>\n" );
document.write( "remaining that it takes to get to $80. Therefore, Darrell must have $33.<BR>\n" );
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document.write( "There are other ways you can manipulate the three equations to come up with this answer also,<BR>\n" );
document.write( "but this is one way that will work.<BR>\n" );
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document.write( "Hope this helps you. Good luck with your review.\r<BR>\n" );
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