document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=612823>Question 612823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Select the set of equations that represents the following situation: Mary invested one amount at 5% simple interest, and a second amount at 4% interest, earning $21.32 in one year. If she had switched the amounts, she would have earned $25.84. What were the two amounts?<BR>\n" );
document.write( "0.05x + 0.04y = 25.84; 0.05x + 0.04y = 21.32<BR>\n" );
document.write( "       5x + 4y = 21.32; 5y + 4x = 25.84<BR>\n" );
document.write( "       0.05x + 0.04y = 21.32; 0.05y + 0.04x = 25.84<BR>\n" );
document.write( "       5x + 4y = 25.84; 5x + 4y = 21.32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385732 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=385732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your original equation is .05x + .04y = 21.32<BR>\n" );
document.write( "your switched equation is .05y + .04x = 25.84<BR>\n" );
document.write( "you can change your switched equation around to read .04x + .05y = 25.84 and it will mean the same thing.<BR>\n" );
document.write( "you have 2 equations to solve simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( ".05x + .04y = 21.32<BR>\n" );
document.write( ".04x + .05y = 25.84<BR>\n" );
document.write( "multiply the first equation by 4 and multiply the second equation by 5 to get:<BR>\n" );
document.write( ".2x + .16y = 85.28<BR>\n" );
document.write( ".2x + .25y = 129.2<BR>\n" );
document.write( "subtract the first equation from he second equation to get:<BR>\n" );
document.write( ".09y = 43.92<BR>\n" );
document.write( "divide both sides of this equation by .09 to get:<BR>\n" );
document.write( "y = 488<BR>\n" );
document.write( "substitute for y in either equation to get:<BR>\n" );
document.write( "x = 36<BR>\n" );
document.write( "you have x = 36 and y = 488<BR>\n" );
document.write( "from your first original equation, you get:<BR>\n" );
document.write( ".05(36) + .04(488) = 1.8 + 19.52 = 21.32<BR>\n" );
document.write( "from your second original equation, you get:<BR>\n" );
document.write( ".04(36) + .05(488) = 1.44 + 24.4 = 25.84<BR>\n" );
document.write( "it checks out so your answer is:<BR>\n" );
document.write( "x = 36<BR>\n" );
document.write( "y = 488\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );