12800 chocolates were distributed among the students of a class. Each student got twice as many chocolates as the number of students in the class. Calculate the number of students in the class.

Options

A. 30
B. 40
C. 60
D. 80

Answer

To solve the problem step-by-step, we start by defining the variables and setting up the equation based on the information given in the question.

### Step 1: Define the Variables
Let the number of students in the class be \( n \).

### Step 2: Determine the Chocolates per Student
According to the problem, each student receives twice as many chocolates as the number of students in the class. Therefore, the number of chocolates each student receives is:
\[ \text{Chocolates per student} = 2n \]

### Step 3: Calculate Total Chocolates Distributed
Since there are \( n \) students and each student receives \( 2n \) chocolates, the total number of chocolates distributed can be expressed as:
\[ \text{Total Chocolates} = n \times (2n) = 2n^2 \]

### Step 4: Set Up the Equation
We know from the problem statement that the total number of chocolates distributed is 12,800. Thus, we can set up the equation:
\[ 2n^2 = 12800 \]

### Step 5: Solve for \( n^2 \)
To isolate \( n^2 \), divide both sides of the equation by 2:
\[ n^2 = \frac{12800}{2} = 6400 \]

### Step 6: Solve for \( n \)
Now, take the square root of both sides to find \( n \):
\[ n = \sqrt{6400} = 80 \]

### Conclusion
The number of students in the class is \( n = 80 \).