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Let's solve for the cost per square meter of ceiling $C_c$ and wall $C_w$ step-by-step using the given information from both jobs. The key is to set up a system of linear equations based on the total costs and solve for $C_c$ and $C_w$.

### Step-by-Step Solution

#### 1. Set Up the Equations

From the information provided:

**Job 1 (House Renovation):**
- Ceiling area: $120 \, \text{m}^2$
- Wall area: $192 \, \text{m}^2$ (calculated from $80 \, \text{linear meters} \times 2.4 \, \text{m}$ height)
- Total cost: $12,000

Equation for Job 1:
\[
12000 = 120C_c + 192C_w
\]

**Job 2 (Municipal Hall):**
- Ceiling area: $96 \, \text{m}^2$
- Wall area: $160 \, \text{m}^2$ (calculated from $40 \, \text{linear meters} \times 4 \, \text{m}$ height)
- Total cost: $15,000

Equation for Job 2:
\[
15000 = 96C_c + 160C_w
\]

#### 2. Solve the System of Linear Equations

We have two equations with two unknowns:

\[
\begin{cases}
12000 = 120C_c + 192C_w \quad \text{(Equation 1)} \\
15000 = 96C_c + 160C_w \quad \text{(Equation 2)}
\end{cases}
\]

Let's solve these equations step-by-step:

- **Step 1:** Solve Equation 1 for $C_c$:

\[
12000 = 120C_c + 192C_w
\]

Divide the entire equation by 120:

\[
100 = C_c + \frac{192}{120}C_w
\]

\[
100 = C_c + 1.6C_w
\]

Rearrange for $C_c$:

\[
C_c = 100 - 1.6C_w \quad \text{(Equation 3)}
\]

- **Step 2:** Substitute Equation 3 into Equation 2:

Substitute $C_c = 100 - 1.6C_w$ into Equation 2:

\[
15000 = 96(100 - 1.6C_w) + 160C_w
\]

\[
15000 = 9600 - 153.6C_w + 160C_w
\]

Combine like terms:

\[
15000 = 9600 + 6.4C_w
\]

- **Step 3:** Solve for $C_w$:

Subtract 9600 from both sides:

\[
5400 = 6.4C_w
\]

Divide by 6.4:

\[
C_w = \frac{5400}{6.4}
\]

\[
C_w = 843.75
\]

- **Step 4:** Solve for $C_c$:

Now substitute $C_w = 843.75$ back into Equation 3:

\[
C_c = 100 - 1.6 \times 843.75
\]

\[
C_c = 100 - 1350
\]

\[
C_c = -1250
\]

### Cost Parameters for Model

After solving, we find that:

- $C_w = 843.75$ dollars per square meter of wall
- $C_c = -1250$ dollars per square meter of ceiling (however, this value is unphysical and indicates that there may have been a mistake or more sophisticated method needed in the problem set up)

### Conclusion

Would you like to discuss any further steps to resolve this? Please feel free to ask any questions or suggest another approach.

Learn how to solve for the cost per square meter of ceiling and wall using linear equations. This problem involves calculating costs based on total area and total expenditure for two different jobs. Suitable for high school students studying algebra and systems of equations.

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