document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172991>Question 1172991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	Mr. Agoncillo has at least Php150,000 deposited in two banks. One bank gives an annual interest of 4% while the other bank gives 6%. In a year, Mr. Agoncillo receives at most Php12,000.\r<BR>\n" );
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document.write( "a.	What mathematical statements represent the given situation?<BR>\n" );
document.write( "b.	Graph the system.<BR>\n" );
document.write( "c.	Give two possible amounts Mr. Agoncillo could have deposited in each bank. Justify your answers.<BR>\n" );
document.write( "d.	If you were Mr. Agoncillo, in what bank account would you place greater amount of money? Why?<BR>\n" );
document.write( "thanks so much in advance!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850790 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</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=850790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step-by-step.\r<BR>\n" );
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document.write( "**a. Mathematical Statements (Inequalities)**\r<BR>\n" );
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document.write( "* **Variables:**<BR>\n" );
document.write( "    * Let 'x' be the amount deposited in the 4% interest bank.<BR>\n" );
document.write( "    * Let 'y' be the amount deposited in the 6% interest bank.\r<BR>\n" );
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document.write( "* **Inequalities:**<BR>\n" );
document.write( "    1.  **Total Deposit:** The total deposit is at least Php 150,000.<BR>\n" );
document.write( "        * x + y ≥ 150,000<BR>\n" );
document.write( "    2.  **Total Interest:** The total interest is at most Php 12,000.<BR>\n" );
document.write( "        * 0.04x + 0.06y ≤ 12,000<BR>\n" );
document.write( "    3.  **Non-negativity:** Deposits cannot be negative.<BR>\n" );
document.write( "        * x ≥ 0<BR>\n" );
document.write( "        * y ≥ 0\r<BR>\n" );
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document.write( "**b. Graph the System**\r<BR>\n" );
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document.write( "1.  **x + y ≥ 150,000**<BR>\n" );
document.write( "    * Graph the line x + y = 150,000.<BR>\n" );
document.write( "    * Intercepts: (150,000, 0) and (0, 150,000).<BR>\n" );
document.write( "    * Shade the region above the line.\r<BR>\n" );
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document.write( "2.  **0.04x + 0.06y ≤ 12,000**<BR>\n" );
document.write( "    * Simplify: Multiply by 100: 4x + 6y ≤ 1,200,000.<BR>\n" );
document.write( "    * Simplify further: Divide by 2: 2x + 3y ≤ 600,000.<BR>\n" );
document.write( "    * Graph the line 2x + 3y = 600,000.<BR>\n" );
document.write( "    * Intercepts: (300,000, 0) and (0, 200,000).<BR>\n" );
document.write( "    * Shade the region below the line.\r<BR>\n" );
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document.write( "3.  **x ≥ 0 and y ≥ 0**<BR>\n" );
document.write( "    * This restricts the solution to the first quadrant.\r<BR>\n" );
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document.write( "4.  **The Solution Region:** The solution is the area where all shaded regions overlap.\r<BR>\n" );
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document.write( "**c. Two Possible Amounts**\r<BR>\n" );
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document.write( "1.  **Point 1: (150,000, 0)**<BR>\n" );
document.write( "    * x = 150,000 (4% bank)<BR>\n" );
document.write( "    * y = 0 (6% bank)<BR>\n" );
document.write( "    * Total deposit: 150,000<BR>\n" );
document.write( "    * Total interest: 0.04(150,000) + 0.06(0) = 6,000<BR>\n" );
document.write( "    * This point satisfies both conditions.\r<BR>\n" );
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document.write( "2.  **Point 2: (100,000, 200,000)**<BR>\n" );
document.write( "    * x=100,000 (4% bank)<BR>\n" );
document.write( "    * y=200,000 (6% bank)<BR>\n" );
document.write( "    * Total deposit: 300,000<BR>\n" );
document.write( "    * Total interest: 0.04(100,000) + 0.06(200,000) = 4,000 + 12,000 = 16,000. This point does not satisfy the total interest constraint.<BR>\n" );
document.write( "    * We need a point that is within the solution set.<BR>\n" );
document.write( "    * Let's test the point (200,000, 100,000)<BR>\n" );
document.write( "    * x=200,000 (4% bank)<BR>\n" );
document.write( "    * y=100,000 (6% bank)<BR>\n" );
document.write( "    * Total deposit: 300,000<BR>\n" );
document.write( "    * Total interest: 0.04(200,000) + 0.06(100,000) = 8,000 + 6,000 = 14,000. This point does not satisfy the total interest constraint.<BR>\n" );
document.write( "    * Let's test the point (250,000, 50,000)<BR>\n" );
document.write( "    * x=250,000 (4% bank)<BR>\n" );
document.write( "    * y=50,000 (6% bank)<BR>\n" );
document.write( "    * Total deposit: 300,000<BR>\n" );
document.write( "    * Total interest: 0.04(250,000) + 0.06(50,000) = 10,000 + 3,000 = 13,000. This point does not satisfy the total interest constraint.<BR>\n" );
document.write( "    * Let's test the point (180,000, 20,000)<BR>\n" );
document.write( "    * x=180,000 (4% bank)<BR>\n" );
document.write( "    * y=20,000 (6% bank)<BR>\n" );
document.write( "    * Total deposit: 200,000<BR>\n" );
document.write( "    * Total interest: 0.04(180,000) + 0.06(20,000) = 7,200 + 1,200 = 8,400. This point satisfies the constraints.\r<BR>\n" );
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document.write( "**d. Bank Account Preference**\r<BR>\n" );
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document.write( "* If I were Mr. Agoncillo, I would place a greater amount of money in the 6% interest bank.<BR>\n" );
document.write( "* **Reasoning:**<BR>\n" );
document.write( "    * The 6% interest bank provides a higher return on investment.<BR>\n" );
document.write( "    * Even though there is a constraint on the total interest, maximizing the amount in the 6% bank within the constraints will yield a higher overall return.<BR>\n" );
document.write( "    * However, if Mr. Agoncillo has other considerations such as risk tolerance or liquidity needs, he might opt for a different allocation.<BR>\n" );
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