document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201076>Question 1201076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate a system of equations for the situation below and solve.\r<BR>\n" );
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document.write( "Michael Perez deposited a total of $2000 with two savings institutions. Bank A pays interest at the rate of 5%/year, whereas Bank B pays interest at the rate of 7%/year. If Michael earned a total of $108 in interest during a single year, how much did he deposit in each institution?<BR>\n" );
document.write( "Bank A    	$ <BR>\n" );
document.write( "Bank B    	$ <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835329 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=835329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a setup for solving the problem using a single equation; you asked for a solution using a system of equations.<br><BR>\n" );
document.write( "Let x = amount invested at 5%<BR>\n" );
document.write( "Let y = amount invested at 7%<br><BR>\n" );
document.write( "(1) The total invested is $2000: x+y = 2000<BR>\n" );
document.write( "(2) The total interest is $108: .05x+.07y = 108<br><BR>\n" );
document.write( "One solution method is to solve the first equation for either x or y and substitute in the second equation:<br><BR>\n" );
document.write( "y = 2000-x<BR>\n" );
document.write( ".05x+.07(2000-x) = 108<br><BR>\n" );
document.write( "That gives you a single equation in a single variable, like the one shown in the response from the other tutor.<br><BR>\n" );
document.write( "The other standard algebraic method for solving a system of two equations is elimination.  Here is one possible way to do that<br><BR>\n" );
document.write( "x+y = 2000  (the first equation, as it is)<BR>\n" );
document.write( "x+1.4y = 2160  (the second equation, multiplied by 20 -- because 20*(.05) = 1)<BR>\n" );
document.write( "0.4y = 160<BR>\n" );
document.write( "y = 160/0.4 = 400<br><BR>\n" );
document.write( "y = $400 was invested at 7%, so $2000-$400 = $1600 was invested at 5%<br><BR>\n" );
document.write( "ANSWER: $1600 at bank A, $400 at bank B<br><BR>\n" );
document.write( "NOTE:  Solving a problem with formal algebra using a single variable (and therefore a single equation) almost always makes the actual solution easier and faster.  However, a beginning algebra student should understand how to set up and solve the problem using two variables, as this assignment asks you to do.<br><BR>\n" );
document.write( "Second NOTE: If formal algebra is not required, here is a quick and easy way to solve this kind of \"2-part mixture\" problem.<br><BR>\n" );
document.write( "(1) If all $2000 were invested at 5%, the interest would be $100; if all were invested at 7%, the interest would be $140.<BR>\n" );
document.write( "(2) The actual interest, $108, is $8/$40 = 1/5 of the way from $100 to $140.<BR>\n" );
document.write( "(3) That means 1/5 of the total was invested at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 1/5 of $2000, or $400, was invested at 7%; the other $1600 at 5%.<br><BR>\n" );
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