In a school, `25/54` of the students are girls and the rest are boys. If the number of boys is 2030, find the number of girls.

Answer

To find the number of girls in the school, we can follow these steps:

### Step 1: Define the total number of students
Let the total number of students in the school be represented by \( x \).

### Step 2: Express the number of girls
According to the problem, the fraction of students who are girls is \( \frac{25}{54} \). Therefore, the number of girls can be expressed as:
\[ \text{Number of girls} = \frac{25}{54} \times x = \frac{25x}{54} \]

### Step 3: Express the number of boys
The problem states that the rest of the students are boys. If the number of boys is given as 2030, we can express the number of boys as:
\[ \text{Number of boys} = x - \text{Number of girls} \]
Substituting the expression for the number of girls:
\[ \text{Number of boys} = x - \frac{25x}{54} \]

### Step 4: Set up the equation
Since we know the number of boys is 2030, we can set up the equation:
\[ 2030 = x - \frac{25x}{54} \]

### Step 5: Simplify the equation
To simplify the equation, we can express \( x \) in terms of a common denominator:
\[ 2030 = \frac{54x}{54} - \frac{25x}{54} \]
This simplifies to:
\[ 2030 = \frac{54x - 25x}{54} = \frac{29x}{54} \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides by 54:
\[ 2030 \times 54 = 29x \]
Calculating the left side:
\[ 109620 = 29x \]
Now, divide both sides by 29:
\[ x = \frac{109620}{29} = 3780 \]

### Step 7: Calculate the number of girls
Now that we have the total number of students \( x = 3780 \), we can find the number of girls:
\[ \text{Number of girls} = \frac{25}{54} \times 3780 \]
Calculating this gives:
\[ \text{Number of girls} = \frac{25 \times 3780}{54} \]
First, calculate \( 25 \times 3780 = 94500 \), then divide by 54:
\[ \text{Number of girls} = \frac{94500}{54} = 1750 \]

### Final Answer
The number of girls in the school is **1750**.

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