document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165486>Question 165486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%,<BR>\n" );
document.write( "then how much did she invest at each rate?\r<BR>\n" );
document.write( "\n" );
document.write( "I need some help I am not sure how to work this problem out. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121976 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> B = bonus = 33000<BR>\n" );
document.write( "BI = bonus interest = 970.<BR>\n" );
document.write( "X = amount of money invested at .04 interest rate.<BR>\n" );
document.write( "Y = amount of money invested at .0225 interest rate.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(.04*X) + (.0225)*Y = 970 (equation 1)<BR>\n" );
document.write( "you have 1 equation with 2 unknowns so you can't solve directly.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "X + Y = 33000 (equation 2)<BR>\n" );
document.write( "subtract X from both sides of equation.<BR>\n" );
document.write( "Y = 33000 - X<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can replace Y with (33000-X) in equation 1.<BR>\n" );
document.write( "it becomes:<BR>\n" );
document.write( "(.04*X) + (.0225)*(33000-X) = 970<BR>\n" );
document.write( "now you have 1 equation with 1 unknown so you can solve for X directly.<BR>\n" );
document.write( "remove parentheses:<BR>\n" );
document.write( ".04*X + .0225*33000 - .0225*X = 970<BR>\n" );
document.write( "perform indicated operations:<BR>\n" );
document.write( ".04*X + 742.5 - .0225*X = 970<BR>\n" );
document.write( ".0175*X + 742.5 = 970<BR>\n" );
document.write( "subtract 742.5 from both sides of equation.<BR>\n" );
document.write( ".0175*X = 970 - 742.5 = 227.5<BR>\n" );
document.write( "divide both sides of equation by .0175.<BR>\n" );
document.write( "X = 13000.<BR>\n" );
document.write( "Y = 33000 - 13000 = 20000<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "she invested 13000 at .04 interest rate (4%) = 520 interest.<BR>\n" );
document.write( "she invested 20000 at .0225 interest rate (2.25%) = 450 interest.<BR>\n" );
document.write( "total interest = 970.<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );