In a collage art class, 76 students are painting a mural on one wall of the campus amphitheater. The wall has been divided into 23 sections, and each section will be painted by a group of either 2 or 4 students. How many more sections will be painted by a group of 4 students than by a group of 2 students?

Options

A. `6`
B. `7`
C. `8`
D. `9`

Explanation

To solve the problem step by step, we will define the variables, set up the equations based on the information given, and then solve those equations.

### Step 1: Define the Variables
Let:
- \( T \) = the number of sections painted by a group of 2 students
- \( F \) = the number of sections painted by a group of 4 students

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of sections is 23:
\[ T + F = 23 \quad \text{(Equation 1)} \]
2. The total number of students is 76:
\[ 2T + 4F = 76 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We will solve these two equations simultaneously.

**From Equation 1**, we can express \( T \) in terms of \( F \):
\[ T = 23 - F \]

**Substituting \( T \) in Equation 2**:
\[ 2(23 - F) + 4F = 76 \]
Expanding this:
\[ 46 - 2F + 4F = 76 \]
Combining like terms:
\[ 46 + 2F = 76 \]
Subtracting 46 from both sides:
\[ 2F = 30 \]
Dividing by 2:
\[ F = 15 \]

### Step 4: Find \( T \)
Now, substitute \( F \) back into Equation 1 to find \( T \):
\[ T = 23 - F = 23 - 15 = 8 \]

### Step 5: Calculate the Difference
The question asks how many more sections will be painted by a group of 4 students than by a group of 2 students:
\[ F - T = 15 - 8 = 7 \]

### Conclusion
Thus, the number of more sections painted by a group of 4 students than by a group of 2 students is **7**.

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