In a school, `(5)/(8)` of the students are boys. If there are `240` girls, find the number of boys in the school.

Options

A. `450`
B. `480`
C. `400`
D. `460`

Answer

To solve the problem step by step, we need to find the number of boys in a school where \( \frac{5}{8} \) of the students are boys and there are 240 girls.

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

### Step 2: Express the number of boys in terms of \( x \)
According to the problem, the number of boys is \( \frac{5}{8} \) of the total number of students. Therefore, the number of boys can be expressed as:
\[ \text{Number of boys} = \frac{5}{8} x \]

### Step 3: Express the number of girls
We are given that there are 240 girls in the school.

### Step 4: Set up the equation for total students
The total number of students is the sum of the number of boys and the number of girls. Thus, we can write the equation:
\[ \frac{5}{8} x + 240 = x \]

### Step 5: Rearrange the equation
To isolate \( x \), we can subtract \( \frac{5}{8} x \) from both sides:
\[ 240 = x - \frac{5}{8} x \]

### Step 6: Simplify the equation
The right side can be simplified. We can express \( x \) as \( \frac{8}{8} x \):
\[ 240 = \frac{8}{8} x - \frac{5}{8} x = \frac{3}{8} x \]

### Step 7: Solve for \( x \)
To find \( x \), multiply both sides by \( \frac{8}{3} \):
\[ x = 240 \times \frac{8}{3} \]
Calculating the right side:
\[ x = 240 \times \frac{8}{3} = 240 \times 2.67 = 640 \]
So, the total number of students is \( 640 \).

### Step 8: Find the number of boys
Now that we have the total number of students, we can find the number of boys:
\[ \text{Number of boys} = \frac{5}{8} \times 640 \]
Calculating this:
\[ \text{Number of boys} = 400 \]

### Conclusion
Thus, the number of boys in the school is \( 400 \).

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