document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151971>Question 1151971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One safe investment pays 7​% per​ year, and a more risky investment pays 14​% per year.\r<BR>\n" );
document.write( "\n" );
document.write( "a. How much must be invested in each account if an investor of ​$100,000 would like a return of ​$9,100 per​ year?<BR>\n" );
document.write( "b. Why might the investor use two accounts rather than put all the money in the 14​% ​investment?\r<BR>\n" );
document.write( "\n" );
document.write( "a. $__ is invested in the 7% account.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773863 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=773863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is an easy alternative to the standard algebraic method (shown by the other tutors) for solving \"mixture\" problems like this.<br><BR>\n" );
document.write( "(1) The $9,100 return on an investment of $100,000 is a rate of 9.1%.<BR>\n" );
document.write( "(2) That 9.1% is 3/10 of the way from 7% to 14%.<BR>\n" );
document.write( "(Think of starting at 7% on a number line and \"walking\" towards 14%, stopping when you get to 9.1%.  What fraction of the distance have you gone? 7% to 14% is a difference of 7%; 7% to 9.1% is a difference of 2.1%.  The fraction of the distance you have gone is 2.1/7 = 3/10.)<BR>\n" );
document.write( "(3) Since 9.1% is 3/10 of the way from 7% to 14%, 3/10 of the total was invested at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 3/10 of $100,000, or $30,000, at 14%; the other 7/10, or $70,000, at 7%.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".14(30,000)+.07(70,000) = 4200+4900 = 9100<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );