At City High School, the sophomore class has 60 numbers than the freshman class. The junior class has 50 fewer students than twice the students in the freshman class. The senior class is three times as large as the freshman class. If there are a total of 1,424 students at City High School, how many students are in the freshman class?

Options

A. `202`
B. `205`
C. `235`
D. `236`

Answer

To solve the problem, we need to set up equations based on the information provided about the number of students in each class at City High School.

### Step 1: Define Variables
Let:
- \( f \) = number of students in the freshman class
- \( p \) = number of students in the sophomore class
- \( j \) = number of students in the junior class
- \( s \) = number of students in the senior class

### Step 2: Set Up Equations Based on the Problem
From the problem statement, we can derive the following equations:
1. The sophomore class has 60 more students than the freshman class:
\[ p = f + 60 \]
2. The junior class has 50 fewer students than twice the number of students in the freshman class:
\[ j = 2f - 50 \]
3. The senior class is three times as large as the freshman class:
\[ s = 3f \]

### Step 3: Total Students Equation
The total number of students at City High School is given as 1,424. Therefore, we can write:
\[ p + f + j + s = 1424 \]

### Step 4: Substitute the Expressions for \( p \), \( j \), and \( s \)
Substituting the expressions we derived in Step 2 into the total students equation:
\[ (f + 60) + f + (2f - 50) + (3f) = 1424 \]

### Step 5: Simplify the Equation
Now, combine like terms:
\[ f + 60 + f + 2f - 50 + 3f = 1424 \]
This simplifies to:
\[ 7f + 10 = 1424 \]

### Step 6: Solve for \( f \)
Now, isolate \( f \):
\[ 7f = 1424 - 10 \]
\[ 7f = 1414 \]
\[ f = \frac{1414}{7} \]
\[ f = 202 \]

### Conclusion
The number of students in the freshman class is \( \boxed{202} \).