document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=526175>Question 526175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jane's employer gave her a bonus of $1600. She decided to invest all the money, some at 5%, some at 7%, and some at 8%. She invested three times more money at 8% than she did at 5%. At the end of one year the total interest she earned was $115.<BR>\n" );
document.write( "a) solve the problem <BR>\n" );
document.write( "b) If you did not know that jane invested three times more money at 8% than she did at 5%, could you still solve the problem? Why or Why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #348554 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=348554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Jane's employer gave her a bonus of $1600.<BR>\n" );
document.write( " She decided to invest all the money, some at 5%, some at 7%, and some at 8%.<BR>\n" );
document.write( "She invested three times more money at 8% than she did at 5%.<BR>\n" );
document.write( " At the end of one year the total interest she earned was $115.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) Solve the problem<BR>\n" );
document.write( "Let a = amt invested at 5%<BR>\n" );
document.write( "Let b = amt invested at 7%<BR>\n" );
document.write( "Let c = amt invested at 8%<BR>\n" );
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document.write( "total amt invested<BR>\n" );
document.write( "a + b + c = 1600<BR>\n" );
document.write( ":<BR>\n" );
document.write( "total interest equation<BR>\n" );
document.write( ".05a + .07b + .08c = 115<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Equation for the statement:<BR>\n" );
document.write( "\"She invested three times more money at 8% than she did at 5%.\"<BR>\n" );
document.write( "c = 3a<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Replace c with 3a in the amt invested and the interest equation<BR>\n" );
document.write( "a + b + 3a = 1600<BR>\n" );
document.write( "4a + b = 1600<BR>\n" );
document.write( "arrange for substitution<BR>\n" );
document.write( "b = (-4a + 1600)<BR>\n" );
document.write( "and the interest equation<BR>\n" );
document.write( ".05a + .07b + .08(3a) = 115<BR>\n" );
document.write( ".05a + .07b + .24a = 115<BR>\n" );
document.write( ".29a + .07b = 115<BR>\n" );
document.write( "Replace b with (-4a+1600), find a<BR>\n" );
document.write( ".29a + .07(-4a+1600) = 115<BR>\n" );
document.write( ".29a - .28a + 112 = 115<BR>\n" );
document.write( ".01a = 115 - 112<BR>\n" );
document.write( ".01a = 3<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F.01 ALIGN=MIDDLE  ALT=\"3%2F.01\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = $300 invested at 5%<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = -4(300) + 1600<BR>\n" );
document.write( "b = -1200 + 1600<BR>\n" );
document.write( "b = $400 invested at 7%<BR>\n" );
document.write( ":<BR>\n" );
document.write( "and we know c = 3a, therefore<BR>\n" );
document.write( "c = 3(300)<BR>\n" );
document.write( "c = $900 invested at 8%<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solutions in the interest equation<BR>\n" );
document.write( ".05(300) + .07(400) + .08(900) = 0<BR>\n" );
document.write( "15 + 28 + 72 = 115 \r<BR>\n" );
document.write( "\n" );
document.write( "b) If you did not know that jane invested three times more money at 8% than she did at 5%, could you still solve the problem? Why or Why not?<BR>\n" );
document.write( ":<BR>\n" );
document.write( " No. Generally you need the same number of equations as there are unknowns<BR>\n" );
document.write( "If you did not know a = 3c, you would have only two equations, and three unknowns </SPAN>\n" );
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