document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169808>Question 169808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem:<BR>\n" );
document.write( "Write a system of equations to solve the following problem. Be sure to identify what the variables represent. Then find the solution.\r<BR>\n" );
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document.write( "Ms. Jones purchased a total of $45,000 in stocks, bonds, and money market funds. The total she invested in bonds and money market funds was twice the amount she invested in stocks. The return rates on the stocks, bonds, and money market funds were 10.0%, 7.0%, and 7.5%, respectively. The total value of the return was $3,660. How much of each investment (stocks, bonds, and money market funds) did Ms. Jones purchase?\r<BR>\n" );
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document.write( "My attempt:\r<BR>\n" );
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document.write( "2x + 2x + x = 45000 (x = stocks with 2x = bonds and money market funds which are twice the amount of stocks)<BR>\n" );
document.write( "x(10%) + x(7%) + x(7.5%) =3600\r<BR>\n" );
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document.write( "Solving the first equation I get: 5x = 4500; x = 9000<BR>\n" );
document.write( "plug the value for x back into the equation and it adds up. ( 5 * 9000= 45000)<BR>\n" );
document.write( "Insert the values of x into the second equation and it does not add up.<BR>\n" );
document.write( "(9000 * 10%) + (18000 * 7%) + (18000 * 7.5) = 3510<BR>\n" );
document.write( "The answer is off by $150 (3660 - 3510 = 150)\r<BR>\n" );
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document.write( "Am I reading this word problem wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125201 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=125201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yep.\r<BR>\n" );
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document.write( "The total invested in bonds AND money market is twice the amound in stocks, so if x represents the amount invested in stocks, then 2x represents the amount invested in both bonds AND money market funds, therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2x=45000 ALIGN=MIDDLE  ALT=\"x%2B2x=45000\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the correct first equation.  Solving, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15000 ALIGN=MIDDLE  ALT=\"x=15000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the total invested in stocks was $15,000 and the total invested in bonds AND money market was $30,000.\r<BR>\n" );
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document.write( "That means that the total return with respect to stocks was 10% of 15,000 or $1500.  It also means that the total return with respect to bonds AND money market funds was $3,660 - $1,500 or $2,160.\r<BR>\n" );
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document.write( "Let's now say that the amount invested in bonds is b and the amount invested in the money market is m.\r<BR>\n" );
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document.write( "We know two things:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bm=30000 ALIGN=MIDDLE  ALT=\"b%2Bm=30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.07b%2B.075m=2160 ALIGN=MIDDLE  ALT=\".07b%2B.075m=2160\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rearranging the first equation we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=30000-b ALIGN=MIDDLE  ALT=\"m=30000-b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then substituting in the second equation we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.07b%2B.075%2830000-b%29=2160 ALIGN=MIDDLE  ALT=\".07b%2B.075%2830000-b%29=2160\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now simply solve for b and then subtract the value of b from 30000 to get m.\r<BR>\n" );
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document.write( "Hope that helps. </SPAN>\n" );
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