document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136546>Question 1136546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person invested ​$7200 for 1​ year, part at 6​%, part at 10​%, and the remainder at 13​%.<BR>\n" );
document.write( "The total annual income from these investments was ​$787. <BR>\n" );
document.write( "The amount of money invested at 13​% was ​$200 more than the amounts invested at 6​% <BR>\n" );
document.write( "and 10​% combined. Find the amount invested at each rate.\r<BR>\n" );
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document.write( "The person invested $​[    ] at 6​%,<BR>\n" );
document.write( "$[    ] at 10​%, and $​[    ] at 13​%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754323 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "The solution is in 3 steps.\r<BR>\n" );
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document.write( "1.  One part of the condition says that the total amount is $7200.\r\n" );
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document.write( "    The other part of the condition says that the amount invested at 13% is 200 more than the combined amount invested at 6% and 10%.\r\n" );
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document.write( "    It implies immediately via simple logic, that the combined amount invested at 6% and 10% is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287200-200%29%2F2 ALIGN=MIDDLE  ALT=\"%287200-200%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3500 dollars\r\n" );
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document.write( "    and the amount invested at 13% is  3500+200 = 3700 dollars.\r\n" );
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document.write( "2.  It implies that the interest produced by the amount at 13% is\r\n" );
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document.write( "        0.13*3700 = 481 dollars\r\n" );
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document.write( "    and the combined interest of two other accounts is  787 - 481 = 306 dollars.\r\n" );
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document.write( "3.  Let x be the amount invested at 10%.\r\n" );
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document.write( "    Then the amount invested at 6% is ((3500-x) dollars.\r\n" );
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document.write( "     The combined interest equation for these two accounts is\r\n" );
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document.write( "         0.10*x + 0.06*(3500-x) = 306.\r\n" );
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document.write( "     The solution to this equation is\r\n" );
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document.write( "         x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28306+-+0.06%2A3500%29%2F%28010-0.06%29 ALIGN=MIDDLE  ALT=\"%28306+-+0.06%2A3500%29%2F%28010-0.06%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2400.\r\n" );
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document.write( "<U>Answer</U>.  $3700 invested at 13%;  $2400 invested at 10%,  and  (3500-2400) = 1100 dollars invested at 6%.\r\n" );
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document.write( "<U>CHECK</U>.   0.13*3700 + 0.10*2400 + 0.06*1100 = 787 dollars as the total interest.    ! Correct !\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "I'd like to make couple of comments to this solution.\r<BR>\n" );
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document.write( "The method of solution was to reduce the problem from 3 unknowns to only two unknowns.\r<BR>\n" );
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document.write( "Then the problem for two unknown investments was solved using single equation for only one unknown.\r<BR>\n" );
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document.write( "The method of reducing such problems from 3 unknowns to only two is very well known.\r<BR>\n" );
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document.write( "See the lesson \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/How-to-algebreze-and-to-solve-this-problem-on-2-eqns-in-2-unknwns.lesson>HOW TO algebreze and solve this problem on 2 equations in 2 unknowns</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "On solution of investment problems for two accounts see the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-investment.lesson>Using systems of equations to solve problems on investment</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic \"<U>Systems of two linear equations in two unknowns</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( "If you think that I hid from you the reducing step from 3 unknowns to 2 unknowns,\r<BR>\n" );
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document.write( "then I will present this step here EXPLICITLY.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    Let  A  be the amount invested at 13%  and  B  be  the combined amount invested ar 6% and 10%.\r\n" );
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document.write( "    We are given that \r\n" );
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document.write( "        A + B = 7200\r\n" );
document.write( "        A - B =  200\r\n" );
document.write( "  ----------------------   Add these two equations. You will get\r\n" );
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document.write( "      2A      = 7400  ==============>  A = 7400/2 = 3700  dollars.\r\n" );
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document.write( "     Then  B = 7200 - 3700 = 3500  dollars, exactly as I stated in the core text.\r\n" );
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document.write( "     Using logical arguments,  take off $200 from $7200 - then you will get a total of $7000, consisting of two equal parts \"reduced A\" and \"B\",\r\n" );
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document.write( "      so \"B\"  is 7000/2 = 3500 dollars and \"A\" is 3500+200 = 3700.\r\n" );
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document.write( "Thus, now you have all the parts of the solution \"in place\".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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