document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199487>Question 1199487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Betsy, a recent retiree, requires $6000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6000 in interest per year.\r<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "The equation I seek should show the following:\r<BR>\n" );
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document.write( "Bonds + CD = Total\r<BR>\n" );
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document.write( "Let x = amount of money that should be invested in each account\r<BR>\n" );
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document.write( "Bonds = 0.07x\r<BR>\n" );
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document.write( "CD = 0.15(50,000 - x)\r<BR>\n" );
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document.write( "Here is my equation:\r<BR>\n" );
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document.write( "0.07x + 0.15(50,000 - x) = 6000\r<BR>\n" );
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document.write( "Is this the correct set up?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833406 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Your equation is fine; when you solve it correctly you will have what you need to answer the question.<br><BR>\n" );
document.write( "But you have not defined your variables and expressions correctly.<br><BR>\n" );
document.write( "Your equation clearly shows that you are using x for the amount invested at 7% and (50000-x) for the amount invested at 15%.  That is consistent with the given information.<br><BR>\n" );
document.write( "But your opening statement (presumably hastily and carelessly written) says that x is the amount invested in each account.  The given information certainly does not tell you that.<br><BR>\n" );
document.write( "For beginning algebra students especially, it is necessary to start your setup with clear and correct definitions of the variables and expressions you are going to use.  Even an experienced student, when working a long and involved problem, can get himself into trouble if he starts with sloppily written definitions which in fact are not correct and precise.<br><BR>\n" );
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document.write( "Added after response from student....<br><BR>\n" );
document.write( "Here is what you wrote in your post:<br><BR>\n" );
document.write( "(1) The equation I seek should show the following:<br><BR>\n" );
document.write( "(2) Bonds + CD = Total<br><BR>\n" );
document.write( "(3) Let x = amount of money that should be invested in each account<br><BR>\n" );
document.write( "(4) Bonds = 0.07x<br><BR>\n" );
document.write( "(5) CD = 0.15(50,000 - x)<br><BR>\n" );
document.write( "(6) Here is my equation:<br><BR>\n" );
document.write( "(7) 0.07x + 0.15(50,000 - x) = 6000<br><BR>\n" );
document.write( "(8) Is this the correct set up? <br><BR>\n" );
document.write( "It appears to me that you need to take the time to write out CLEAR AND PRECISE definitions of the expressions you are going to use.  In this case, you ended up with a (mostly) correct equation; but what you show before the equation is \"shorthand\" that doesn't tell what you REALLY mean.<br><BR>\n" );
document.write( "Using what you show in your work as an outline, your actual work should look something like this:<br><BR>\n" );
document.write( "(2) interest from bonds, plus interest from CD, equals total interest<BR>\n" );
document.write( "[NOT just \"bonds + CD = total\"]<br><BR>\n" );
document.write( "(3a) let x = amount invested in bonds<BR>\n" );
document.write( "(3b) then 50,000-x = amount invested in CD<br><BR>\n" );
document.write( "Your \"Let x = amount of money that should be invested in each account\" does NOT tell what you are really doing!<br><BR>\n" );
document.write( "(4) interest from bonds (15% of x): 0.15x<BR>\n" );
document.write( "[NOT just \"bonds = ...\"]<BR>\n" );
document.write( "(5) interest from CD (7% of (50,000-x)): .07(50000-x)<BR>\n" );
document.write( "[NOT just \"CD = ...\"]<br><BR>\n" );
document.write( "(Note that, as the other tutors who responded noted (and I overlooked), your work has the interest rates from the two investments switched.)<br><BR>\n" );
document.write( "(7) Now, using (4) and (5), you are ready to write the equation you said you were going to in (2), showing that the total interest should be $6000:<br><BR>\n" );
document.write( "0.15x + 0.07(50,000-x) = 6000<br><BR>\n" );
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