There are 1550 boys and girls in a school. The number of girls exceeds the number of boys by 500. What is the percentage (to nearest integer) of girls in the school?

Options

A. `67%`
B. `66%`
C. `64%`
D. `65%`

Answer

To solve the problem step by step, we can follow these calculations:

1. **Define Variables**:
Let the number of boys be \( B \) and the number of girls be \( G \).

2. **Set Up Equations**:
According to the problem:
- The total number of boys and girls is 1550:
\[ B + G = 1550 \quad \text{(1)} \]
- The number of girls exceeds the number of boys by 500:
\[ G - B = 500 \quad \text{(2)} \]

3. **Add the Equations**:
To eliminate \( B \), we can add equations (1) and (2):
\[ (B + G) + (G - B) = 1550 + 500 \]
This simplifies to:
\[ 2G = 2050 \]

4. **Solve for Girls**:
Divide both sides by 2 to find \( G \):
\[ G = \frac{2050}{2} = 1025 \]

5. **Find the Percentage of Girls**:
To find the percentage of girls in the school, we use the formula:
\[ \text{Percentage of Girls} = \left( \frac{G}{\text{Total Students}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of Girls} = \left( \frac{1025}{1550} \right) \times 100 \]

6. **Calculate the Percentage**:
First, calculate \( \frac{1025}{1550} \):
\[ \frac{1025}{1550} \approx 0.66129 \]
Now multiply by 100:
\[ 0.66129 \times 100 \approx 66.129 \]

7. **Round to the Nearest Integer**:
Rounding 66.129 to the nearest integer gives us:
\[ 66\% \]

Thus, the percentage of girls in the school is **66%**.