document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=578502>Question 578502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A, B, & C have equal incomes from investments. A has invested $2000 less than B and $2500 more than C . The rate of interest received by A is 1 per cent more than that received by B and 2 per cent less than that received by C. How much has A invested? Pls. help me solve this. I've been working on it for 2 hours now and still can't come up with the equation and the answer. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370691 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=370691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A, B, & C have equal incomes from investments. <BR>\n" );
document.write( "A has invested $2000 less than B and $2500 more than C .<BR>\n" );
document.write( " The rate of interest received by A is 1 per cent more than that received by B<BR>\n" );
document.write( " and 2 per cent less than that received by C.<BR>\n" );
document.write( " How much has A invested?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You're right, this is a doozy<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let A, B, C = amt of each investment<BR>\n" );
document.write( "Let a, b, c = interest rate of each in decimal form<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Given that incomes are equal:<BR>\n" );
document.write( "aA = bB = cC<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Get B and C in terms of A, and get b & c in terms of a<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" A has invested $2000 less than B.\"<BR>\n" );
document.write( "A = B-2000<BR>\n" );
document.write( "or<BR>\n" );
document.write( "B = (A+2000)<BR>\n" );
document.write( "and <BR>\n" );
document.write( "\"$2500 more than C\" <BR>\n" );
document.write( "A = C+2500<BR>\n" );
document.write( "or<BR>\n" );
document.write( "C = (A-2500)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" The rate of interest received by A is 1 per cent more than that received by B\"<BR>\n" );
document.write( "a = b+.01<BR>\n" );
document.write( "or <BR>\n" );
document.write( "b =(a-.01)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"and 2 per cent less than that received by C.\"<BR>\n" );
document.write( "a = c-.02<BR>\n" );
document.write( "or<BR>\n" );
document.write( "c = (a+.02)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We know<BR>\n" );
document.write( "aA = bB<BR>\n" );
document.write( "replace b with (a-.01) and B with (A+2000)<BR>\n" );
document.write( "aA = (a-.01)(A+2000)<BR>\n" );
document.write( "FOIL the right<BR>\n" );
document.write( "aA = aA + 2000a - .01A - 20<BR>\n" );
document.write( "Subtract aA from both sides, add 20 to each side<BR>\n" );
document.write( "2000a - .01A = 20<BR>\n" );
document.write( ":<BR>\n" );
document.write( "aA = cC<BR>\n" );
document.write( "replace c with (a+.02) and C with (A-2500)<BR>\n" );
document.write( "aA = (a+.02)(A-2500)<BR>\n" );
document.write( "FOIL the right<BR>\n" );
document.write( "aA = aA - 2500a + .02A - 50<BR>\n" );
document.write( "Subtract aA from both sides, add 50 to each side<BR>\n" );
document.write( "-2500a + .02A = 50<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination with these two equation, multiply the 1st on by 2, add to the 2nd<BR>\n" );
document.write( "4000a - .02A = 40<BR>\n" );
document.write( "-2500a +.20A = 50<BR>\n" );
document.write( "-------------------adding eliminates A, find a<BR>\n" );
document.write( "1500a = 90<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2F1500 ALIGN=MIDDLE  ALT=\"90%2F1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = .06, so 6% is the int rate of the A investment<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = .06 - .01<BR>\n" );
document.write( "b = .05, 5% is the int rate of the B investment<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = .06 +.02<BR>\n" );
document.write( "c = .08, 8% is the int rate of the C investment<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Remember aA = bB<BR>\n" );
document.write( ".06A = .05B<BR>\n" );
document.write( "Replace B with (B+2000)<BR>\n" );
document.write( ".06A = .05(A+2000)<BR>\n" );
document.write( ".06A = .05A + 100<BR>\n" );
document.write( ".06A - .05A = 100<BR>\n" );
document.write( ".01A = 100<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F.01 ALIGN=MIDDLE  ALT=\"100%2F.01\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = $10,000 investment which is what they want <BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check this by finding the actual interest from B & C, confirming that they are all equal. I did this and found each had a return of $600, but don't take my word for it.   C\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );