You have been given R32 300.you need to pay a site manager,a procurement manager and a civil engineer.do the cost proposal by including their cost per hour,total hours and total salary earned if the project is 40 days.Split the 32 300 between the 3 managers so that no money is left and all is spent paying them

To allocate the R32,300 among the site manager, procurement manager, and civil engineer for a project lasting 40 days, we need to follow these steps:

1. **Define the daily working hours** for each manager.
2. **Determine their hourly rates**.
3. **Allocate the total budget of R32,300** proportionally between the three managers.

For simplicity, I'll assume that each manager works **8 hours per day** for the **40 days**, which totals to **320 hours** (40 days * 8 hours/day) per manager.

Next, let's define variables to represent their hourly rates:

- Let \( r_1 \) be the hourly rate of the **site manager**.
- Let \( r_2 \) be the hourly rate of the **procurement manager**.
- Let \( r_3 \) be the hourly rate of the **civil engineer**.

Each manager works 320 hours over the course of the project, so the total salary earned by each is:

- **Site manager**: \( 320 \times r_1 \)
- **Procurement manager**: \( 320 \times r_2 \)
- **Civil engineer**: \( 320 \times r_3 \)

The total budget of R32,300 must be distributed between these three, so the equation is:

\[
320r_1 + 320r_2 + 320r_3 = 32,300
\]

We can simplify this equation by dividing through by 320:

\[
r_1 + r_2 + r_3 = 101.56
\]

This means the sum of the hourly rates for all three managers should equal **R101.56**.

### Step 1: Allocate Hourly Rates
You can decide how to split the rates depending on the importance of each role. For example, let's assume:

- **Site Manager** earns R40/hour,
- **Procurement Manager** earns R30/hour,
- **Civil Engineer** earns R31.56/hour.

These values satisfy the equation:

\[
40 + 30 + 31.56 = 101.56
\]

### Step 2: Calculate Total Salaries

Now, let's calculate the total salary for each manager:

1. **Site Manager**:  
   \( 320 \times 40 = 12,800 \)  
   Total salary: R12,800

2. **Procurement Manager**:  
   \( 320 \times 30 = 9,600 \)  
   Total salary: R9,600

3. **Civil Engineer**:  
   \( 320 \times 31.56 = 10,100.80 \)  
   Total salary: R10,100.80

### Final Allocation:

- **Site Manager**: R12,800
- **Procurement Manager**: R9,600
- **Civil Engineer**: R10,100.80

Total: R32,300 (which perfectly matches the budget).

---

Let me know if you want more details or clarifications!  
Here are five related questions to expand on this:

1. What happens if the working hours per day change for one of the managers?
2. How can we adjust the hourly rate if the total project budget increases to R40,000?
3. What if the civil engineer worked overtime for 10 extra hours in total?
4. How do the total salaries change if the project duration is extended to 45 days?
5. What method can we use to account for additional expenses like overtime?

**Tip**: When managing a budget, always account for potential changes in project scope that could impact both time and costs.

You have been given R32 300. You need to pay a site manager, a procurement manager, and a civil engineer. Do the cost proposal by including their cost per hour, total hours, and total salary earned if the project is 40 days. Split the R32,300 between the 3 managers so that no money is left and all is spent paying them.

Learn how to allocate a project budget of R32,300 between a site manager, procurement manager, and civil engineer for a 40-day project. This solution covers key algebraic concepts such as proportional distribution and solving linear equations to ensure the budget is fully utilized across the three roles. Suitable for Grades 10-12.

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