document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193315>Question 1193315</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me with the homework.<BR>\n" );
document.write( "Four apartments belong to three owners. Each apartment has a representative in the body corporate that runs the affairs of this block of flats. They decide the owners will pay a share that is in proportion to the floor area of their apartments. The floor areas are as follows: flat 1=200m,flat 2&3=350m,flat 4= 450m. Monthly and annual expensive are as follows: monthly water bill is 680, monthly refuse removal is 330, monthly sewerage is 480, rate and taxes is 44600, annual maintenance is 24000.<BR>\n" );
document.write( "1.1. calculate the total monthly expenses for the body corporate.<BR>\n" );
document.write( "1.2. calculate the amount each owner must pay towards the monthly expenses.<BR>\n" );
document.write( "1.3. The committee decide to pay the gardener who works once a week out of maintenance money 300 per Day and give him an annual bonus of 3000.<BR>\n" );
document.write( "1.3.1. what is the total wage of the gardener per year?<BR>\n" );
document.write( "1.3.2. what is the ratio of the gardener' s total wage to the average annual maintenance? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848668 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ### **Given Information:**\r<BR>\n" );
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document.write( "- Floor areas:<BR>\n" );
document.write( "  - Flat 1: \(200 \, \text{m}^2\)<BR>\n" );
document.write( "  - Flat 2: \(350 \, \text{m}^2\)<BR>\n" );
document.write( "  - Flat 3: \(350 \, \text{m}^2\)<BR>\n" );
document.write( "  - Flat 4: \(450 \, \text{m}^2\)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "- Monthly expenses:<BR>\n" );
document.write( "  - Water: ₱680<BR>\n" );
document.write( "  - Refuse removal: ₱330<BR>\n" );
document.write( "  - Sewerage: ₱480<BR>\n" );
document.write( "  <BR>\n" );
document.write( "- Annual expenses:<BR>\n" );
document.write( "  - Rates and taxes: ₱44,600<BR>\n" );
document.write( "  - Maintenance: ₱24,000<BR>\n" );
document.write( "  <BR>\n" );
document.write( "- Gardener wage: ₱300 per day, works once a week. Annual bonus: ₱3,000.\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### **1.1 Total monthly expenses for the body corporate**\r<BR>\n" );
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document.write( "1. **Monthly expenses:**<BR>\n" );
document.write( "   - Water: ₱680<BR>\n" );
document.write( "   - Refuse removal: ₱330<BR>\n" );
document.write( "   - Sewerage: ₱480\r<BR>\n" );
document.write( "\n" );
document.write( "   Total monthly operational expenses:<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   680 + 330 + 480 = ₱1,490<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "2. **Annual expenses converted to monthly:**<BR>\n" );
document.write( "   - Rates and taxes:<BR>\n" );
document.write( "     \[<BR>\n" );
document.write( "     \frac{44,600}{12} = ₱3,716.67<BR>\n" );
document.write( "     \]<BR>\n" );
document.write( "   - Maintenance:<BR>\n" );
document.write( "     \[<BR>\n" );
document.write( "     \frac{24,000}{12} = ₱2,000<BR>\n" );
document.write( "     \]\r<BR>\n" );
document.write( "\n" );
document.write( "3. **Total monthly expenses:**<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   ₱1,490 + ₱3,716.67 + ₱2,000 = ₱7,206.67<BR>\n" );
document.write( "   \]\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
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document.write( "### **1.2 Amount each owner must pay towards monthly expenses**\r<BR>\n" );
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document.write( "1. **Total floor area:**<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   200 + 350 + 350 + 450 = 1,350 \, \text{m}^2<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "2. **Proportion of floor area:**<BR>\n" );
document.write( "   - Flat 1: \( \frac{200}{1350} \)<BR>\n" );
document.write( "   - Flat 2: \( \frac{350}{1350} \)<BR>\n" );
document.write( "   - Flat 3: \( \frac{350}{1350} \)<BR>\n" );
document.write( "   - Flat 4: \( \frac{450}{1350} \)\r<BR>\n" );
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document.write( "3. **Monthly share for each owner:**<BR>\n" );
document.write( "   Multiply the proportion by the total monthly expense (\(₱7,206.67\)):\r<BR>\n" );
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document.write( "   - Flat 1:<BR>\n" );
document.write( "     \[<BR>\n" );
document.write( "     \frac{200}{1350} \times 7,206.67 = ₱1,067.00<BR>\n" );
document.write( "     \]<BR>\n" );
document.write( "   - Flat 2:<BR>\n" );
document.write( "     \[<BR>\n" );
document.write( "     \frac{350}{1350} \times 7,206.67 = ₱1,868.33<BR>\n" );
document.write( "     \]<BR>\n" );
document.write( "   - Flat 3:<BR>\n" );
document.write( "     Same as Flat 2, ₱1,868.33.<BR>\n" );
document.write( "   - Flat 4:<BR>\n" );
document.write( "     \[<BR>\n" );
document.write( "     \frac{450}{1350} \times 7,206.67 = ₱2,403.00<BR>\n" );
document.write( "     \]\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
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document.write( "### **1.3 Gardener's wage and its ratio to maintenance**\r<BR>\n" );
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document.write( "#### **1.3.1 Total annual wage for the gardener**\r<BR>\n" );
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document.write( "1. **Weekly pay:**<BR>\n" );
document.write( "   Gardener works once a week, earning ₱300 per day:<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   ₱300 \times 52 = ₱15,600<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "2. **Add annual bonus:**<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   ₱15,600 + ₱3,000 = ₱18,600<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "#### **1.3.2 Ratio of gardener's wage to annual maintenance**\r<BR>\n" );
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document.write( "1. Gardener's total wage:<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   ₱18,600<BR>\n" );
document.write( "   \]<BR>\n" );
document.write( "2. Annual maintenance:<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   ₱24,000<BR>\n" );
document.write( "   \]<BR>\n" );
document.write( "3. Ratio:<BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   \frac{18,600}{24,000} = 0.775 \, \text{or} \, 77.5\%<BR>\n" );
document.write( "   \]\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "### **Final Answers:**<BR>\n" );
document.write( "1.1 Total monthly expenses: ₱7,206.67  <BR>\n" );
document.write( "1.2 Monthly payments by owners:  <BR>\n" );
document.write( "   - Flat 1: ₱1,067.00  <BR>\n" );
document.write( "   - Flat 2: ₱1,868.33  <BR>\n" );
document.write( "   - Flat 3: ₱1,868.33  <BR>\n" );
document.write( "   - Flat 4: ₱2,403.00  <BR>\n" );
document.write( "1.3.1 Gardener's total annual wage: ₱18,600  <BR>\n" );
document.write( "1.3.2 Ratio of gardener's wage to annual maintenance: 77.5%   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );