document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205318>Question 1205318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Siti has RM450000 in her ASB. She wants to invest in Gading Mutual deposit, Maju<BR>\n" );
document.write( "Makmur bar gold, Indah certificate deposit and Selamat Maju bar gold which pay<BR>\n" );
document.write( "simple annual interest of 9%, 6%, 10% and 15%, respectively. Moreover, she wants<BR>\n" );
document.write( "to combine annual return of 8% and want to have only one-third of investment in<BR>\n" );
document.write( "Indah certificate deposit and Selamat Maju bar gold.<BR>\n" );
document.write( "a. Write the linear model system equation for the whole investment.<BR>\n" );
document.write( "c. Use elimination method to find each of the investment\r<BR>\n" );
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document.write( "3. Alia rows a boat upstream from one point on a river to another point 4 km away in 1.5 hours.<BR>\n" );
document.write( "The return trip, traveling with the current, takes only 45 min.<BR>\n" );
document.write( "a. Identify the variables involve in algebra.<BR>\n" );
document.write( "b. Find the speed of the current flowing by using back-substitution method </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842041 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "For the first problem....<br><BR>\n" );
document.write( "There is not enough information to find a unique solution.  Mathematically, an infinite number of possible answers is possible; in actuality, since the numbers have to be whole numbers, the number of solutions is finite, but still large.<br><BR>\n" );
document.write( "Write the equations in thousands of RM to make the numbers smaller and easier to work with.<br><BR>\n" );
document.write( "450 = total investment<BR>\n" );
document.write( "150 = total invested in Indah and Selamat (1/3 of the total)<BR>\n" );
document.write( "300 = total invested in Gading and Maju (the other 2/3 of the total)<BR>\n" );
document.write( "Let x = amount invested in Indah<BR>\n" );
document.write( "Then 150-x = amount invested in Selamat<BR>\n" );
document.write( "Let y = amount invested in Gading<BR>\n" );
document.write( "Then 300-y = amount invested in Maju<br><BR>\n" );
document.write( "The average return on the investments is 8%:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.09%28y%29%2B.06%28300-y%29%2B.10%28x%29%2B.15%28150-x%29=.08%28450%29 ALIGN=MIDDLE  ALT=\".09%28y%29%2B.06%28300-y%29%2B.10%28x%29%2B.15%28150-x%29=.08%28450%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.09y%2B18-.06y%2B.10x%2B22.5-.15x=36 ALIGN=MIDDLE  ALT=\".09y%2B18-.06y%2B.10x%2B22.5-.15x=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.09y-.06y%2B.10x-.15x=36-18-22.5 ALIGN=MIDDLE  ALT=\".09y-.06y%2B.10x-.15x=36-18-22.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.03y-.05x=-4.5 ALIGN=MIDDLE  ALT=\".03y-.05x=-4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05x-.03y=4.5 ALIGN=MIDDLE  ALT=\".05x-.03y=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-3y=450 ALIGN=MIDDLE  ALT=\"5x-3y=450\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With no restrictions, that linear equation in two variables has an infinite number of solutions.  If we limit the possible solutions to whole numbers of thousands (x and y non-negative integers), there are still a large number of solutions.<br><BR>\n" );
document.write( "One easily seen solution is x=90 and y=0, corresponding to 90000 invested in Indah, 60000 in Selamat, 0 in Gading, and 300000 in Maju.<br><BR>\n" );
document.write( "Checking that solution....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.09%280%29%2B.06%28300%29%2B.10%2890%29%2B.15%2860%29=0%2B18%2B9%2B9+=+36 ALIGN=MIDDLE  ALT=\".09%280%29%2B.06%28300%29%2B.10%2890%29%2B.15%2860%29=0%2B18%2B9%2B9+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "One other solution is x=120 and y=50, corresponding to 120000 invested in Indah,  30000 in Selamat, 50000 in Gading, and 250000 in Maju.<br><BR>\n" );
document.write( "Checking that solution....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.09%2850%29%2B.06%28250%29%2B.10%28120%29%2B.15%2830%29=4.5%2B15%2B12%2B4.5=36 ALIGN=MIDDLE  ALT=\".09%2850%29%2B.06%28250%29%2B.10%28120%29%2B.15%2830%29=4.5%2B15%2B12%2B4.5=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: There is not enough information to find a unique solution<br><BR>\n" );
document.write( "For the second problem....<br><BR>\n" );
document.write( "I don't know what your definition is of the \"back-substitution method\"; I will solve using what I think is the easiest method.<br><BR>\n" );
document.write( "The rate upstream, where the speed of the current is subtracting from the boat speed, is 4/1.5 = 8/3 mph.<br><BR>\n" );
document.write( "The rate downstream, where the speed of the current is adding to the boat speed, is 4/(3/4) = 16/3 mph.<br><BR>\n" );
document.write( "Informally, since the current speed subtracted from the boat speed is 8/3 mph and the current speed added to the boat speed is 16/3 mph, the boat speed is halfway between 8/3 and 16/3 mph, which is 12/3 mph, or 4 mph.  Then the current speed is the difference between 4 and 8/3, or between 4 and 16/3, which is 4/3.<br><BR>\n" );
document.write( "ANSWER: The speed of the current is 4/3 mph<br><BR>\n" );
document.write( "NOTE: An informal solution as shown above uses logical reasoning.  If required, a formal algebraic solution is relatively easy:<br><BR>\n" );
document.write( "b = boat speed<BR>\n" );
document.write( "c = current speed<br><BR>\n" );
document.write( "b+c = 16/3<BR>\n" );
document.write( "b-c = 8/3<br><BR>\n" );
document.write( "Subtract the second equation from the first, eliminating b:<br><BR>\n" );
document.write( "2c = 8/3<BR>\n" );
document.write( "c = 4/3<br><BR>\n" );
document.write( "ANSWER: the current speed is 4/3 mph<br><BR>\n" );
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