Question 1193315: Please help me with the homework.
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.
1.1. calculate the total monthly expenses for the body corporate.
1.2. calculate the amount each owner must pay towards the monthly expenses.
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.
1.3.1. what is the total wage of the gardener per year?
1.3.2. what is the ratio of the gardener' s total wage to the average annual maintenance?
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! ### **Given Information:**
- Floor areas:
- Flat 1: \(200 \, \text{m}^2\)
- Flat 2: \(350 \, \text{m}^2\)
- Flat 3: \(350 \, \text{m}^2\)
- Flat 4: \(450 \, \text{m}^2\)
- Monthly expenses:
- Water: ₱680
- Refuse removal: ₱330
- Sewerage: ₱480
- Annual expenses:
- Rates and taxes: ₱44,600
- Maintenance: ₱24,000
- Gardener wage: ₱300 per day, works once a week. Annual bonus: ₱3,000.
---
### **1.1 Total monthly expenses for the body corporate**
1. **Monthly expenses:**
- Water: ₱680
- Refuse removal: ₱330
- Sewerage: ₱480
Total monthly operational expenses:
\[
680 + 330 + 480 = ₱1,490
\]
2. **Annual expenses converted to monthly:**
- Rates and taxes:
\[
\frac{44,600}{12} = ₱3,716.67
\]
- Maintenance:
\[
\frac{24,000}{12} = ₱2,000
\]
3. **Total monthly expenses:**
\[
₱1,490 + ₱3,716.67 + ₱2,000 = ₱7,206.67
\]
---
### **1.2 Amount each owner must pay towards monthly expenses**
1. **Total floor area:**
\[
200 + 350 + 350 + 450 = 1,350 \, \text{m}^2
\]
2. **Proportion of floor area:**
- Flat 1: \( \frac{200}{1350} \)
- Flat 2: \( \frac{350}{1350} \)
- Flat 3: \( \frac{350}{1350} \)
- Flat 4: \( \frac{450}{1350} \)
3. **Monthly share for each owner:**
Multiply the proportion by the total monthly expense (\(₱7,206.67\)):
- Flat 1:
\[
\frac{200}{1350} \times 7,206.67 = ₱1,067.00
\]
- Flat 2:
\[
\frac{350}{1350} \times 7,206.67 = ₱1,868.33
\]
- Flat 3:
Same as Flat 2, ₱1,868.33.
- Flat 4:
\[
\frac{450}{1350} \times 7,206.67 = ₱2,403.00
\]
---
### **1.3 Gardener's wage and its ratio to maintenance**
#### **1.3.1 Total annual wage for the gardener**
1. **Weekly pay:**
Gardener works once a week, earning ₱300 per day:
\[
₱300 \times 52 = ₱15,600
\]
2. **Add annual bonus:**
\[
₱15,600 + ₱3,000 = ₱18,600
\]
#### **1.3.2 Ratio of gardener's wage to annual maintenance**
1. Gardener's total wage:
\[
₱18,600
\]
2. Annual maintenance:
\[
₱24,000
\]
3. Ratio:
\[
\frac{18,600}{24,000} = 0.775 \, \text{or} \, 77.5\%
\]
---
### **Final Answers:**
1.1 Total monthly expenses: ₱7,206.67
1.2 Monthly payments by owners:
- Flat 1: ₱1,067.00
- Flat 2: ₱1,868.33
- Flat 3: ₱1,868.33
- Flat 4: ₱2,403.00
1.3.1 Gardener's total annual wage: ₱18,600
1.3.2 Ratio of gardener's wage to annual maintenance: 77.5%
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