document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079941>Question 1079941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: Cathy won $10,000 in the lottery. She wants to put some in an accessible savings account, and the rest to a long-term investment. She has been considering a savings account which has been paying an annual percentage rate of 2.64%, and a mutual fund which has been paying an APR of 8.9%. At the end of 1 year, Cathy hopes to earn $750. How much money must she invest in each type of acct.?<BR>\n" );
document.write( "a. Model situation algebraically. <BR>\n" );
document.write( "b. Determine solution algebraically and graphically. <BR>\n" );
document.write( "c. Is there any way Cathy can invest the money to earn $1,000 in interest in one year? Explain how you arrived at your conclusion.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I started by defining my variables, s=Savings account, m=Mutual fund. Then, I tried modeling it algebraically like so: $750=2.64s+8.9m. I tried different numbers for each variable to get to $750, but it's not seeming to work, and I am stumped on how to solve this any further on a, b, or c. 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 #694169 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=694169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to solve 2 equations simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "s + m = 10,000<BR>\n" );
document.write( ".0264s + .089m = 750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "decimal equivalent = percent / 100.<BR>\n" );
document.write( "2.64% = .0264<BR>\n" );
document.write( "8.9% = .089\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we'll solve by elimination.<BR>\n" );
document.write( "you could also solve by substitution or by graphing.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'll do elimination and then show you the graphical solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your 2 equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "s + m = 10,000<BR>\n" );
document.write( ".0264s + .089m = 750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the first equation by .0264 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".0264s + .0264m = 264<BR>\n" );
document.write( ".0264s + .089m = 750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract the first equation from the second to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".0626m = 486\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve form to get m = 486 / .0626 = 7763.578275\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "s is equal to 10,000 - 7763.578275 = 2236.421725\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "s + m = 10,000<BR>\n" );
document.write( ".0264s + .089m = 750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solution looks good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graphical solution is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/050602.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you let x = amount invested in savings and y = amount invested in mutual funds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equations to graph are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".0264 * x + .089y = 750<BR>\n" );
document.write( "x + y = 10,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for y in both equations to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = (750 - .0264x) / .089<BR>\n" );
document.write( "y = 10000 - x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the intersection of the lines of these 2 equations should be your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution is shown in (x,y) format where x represents the investment in the savings account and y represents the investment in the mutual fund account.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it does not appear that she can earn 1000 interest in one year with .0264 interest on the savings and .089 interest on the mutual fund.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the problem is that, even if she invested all the money in the mutual fund account, the best she could get was 890 in interest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );