document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205323>Question 1205323</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 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847957 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ## Setting up the Linear Model\r<BR>\n" );
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document.write( "**Let's denote:**<BR>\n" );
document.write( "* **G:** Amount invested in Gading Mutual Deposit<BR>\n" );
document.write( "* **M:** Amount invested in Maju Makmur Bar Gold<BR>\n" );
document.write( "* **I:** Amount invested in Indah Certificate Deposit<BR>\n" );
document.write( "* **S:** Amount invested in Selamat Maju Bar Gold\r<BR>\n" );
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document.write( "**Based on the given information, we can set up the following system of linear equations:**\r<BR>\n" );
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document.write( "1.  **Total Investment:** G + M + I + S = 450000<BR>\n" );
document.write( "2.  **Total Annual Return:** 0.09G + 0.06M + 0.10I + 0.15S = 0.08 * 450000<BR>\n" );
document.write( "3.  **Indah and Selamat Maju Investment:** I + S = (1/3) * 450000\r<BR>\n" );
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document.write( "## Solving the System Using Elimination Method\r<BR>\n" );
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document.write( "**Step 1: Simplify the Equations**<BR>\n" );
document.write( "* Equation 2: 9G + 6M + 10I + 15S = 360000<BR>\n" );
document.write( "* Equation 3: I + S = 150000\r<BR>\n" );
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document.write( "**Step 2: Eliminate a Variable**<BR>\n" );
document.write( "* Let's eliminate S. From Equation 3, we can express S as:<BR>\n" );
document.write( "  * S = 150000 - I<BR>\n" );
document.write( "* Substitute S in Equations 1 and 2:<BR>\n" );
document.write( "  * Equation 1: G + M + I + (150000 - I) = 450000<BR>\n" );
document.write( "    => G + M + 150000 = 450000<BR>\n" );
document.write( "  * Equation 2: 9G + 6M + 10I + 15(150000 - I) = 360000<BR>\n" );
document.write( "    => 9G + 6M - 5I = -750000\r<BR>\n" );
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document.write( "**Step 3: Simplify the Equations Further**<BR>\n" );
document.write( "* Equation 1: G + M = 300000<BR>\n" );
document.write( "* Equation 2: 9G + 6M - 5I = -750000\r<BR>\n" );
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document.write( "**Step 4: Eliminate Another Variable**<BR>\n" );
document.write( "* Let's eliminate M. Multiply Equation 1 by -6 and add it to Equation 2:<BR>\n" );
document.write( "  * -6G - 6M = -1800000<BR>\n" );
document.write( "  * 9G + 6M - 5I = -750000<BR>\n" );
document.write( "  * -------------------------<BR>\n" );
document.write( "  * 3G - 5I = -2550000\r<BR>\n" );
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document.write( "**Step 5: Solve for G and I**<BR>\n" );
document.write( "* From Equation 1, we can express M as:<BR>\n" );
document.write( "  * M = 300000 - G<BR>\n" );
document.write( "* Substitute M in the simplified Equation 2:<BR>\n" );
document.write( "  * 3G - 5I = -2550000<BR>\n" );
document.write( "  * 3G - 5(150000 - G) = -2550000<BR>\n" );
document.write( "  * 8G = 1200000<BR>\n" );
document.write( "  * G = 150000<BR>\n" );
document.write( "* Substitute G in M = 300000 - G:<BR>\n" );
document.write( "  * M = 300000 - 150000 = 150000<BR>\n" );
document.write( "* Substitute G in I + S = 150000:<BR>\n" );
document.write( "  * I + S = 150000<BR>\n" );
document.write( "  * I + (150000 - I) = 150000<BR>\n" );
document.write( "  * S = 0\r<BR>\n" );
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document.write( "Therefore, the investments are:<BR>\n" );
document.write( "* Gading Mutual Deposit: RM150,000<BR>\n" );
document.write( "* Maju Makmur Bar Gold: RM150,000<BR>\n" );
document.write( "* Indah Certificate Deposit: RM150,000<BR>\n" );
document.write( "* Selamat Maju Bar Gold: RM0<BR>\n" );
document.write( " </SPAN>\n" );
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