The Crestview High School student body is made up only of freshmen , sophomores , juniors, and seniors . 25% of the students are freshmen , 35% are sophomores , and 20% are juniors . If no student can be considered to be in two classes, and there are 150 seniors , how many students make up the Crestview High School student body ?

Options

A. 230
B. 500
C. 600
D. 750

Answer

To solve the problem, we need to find the total number of students in the Crestview High School student body. We will denote the total number of students as \( X \).

### Step 1: Determine the percentages of each class
From the problem, we know:
- 25% are Freshmen
- 35% are Sophomores
- 20% are Juniors

### Step 2: Calculate the percentage of Seniors
Since the total percentage must equal 100%, we can find the percentage of Seniors by subtracting the percentages of the other classes from 100%:

\[ \text{Percentage of Seniors} = 100\% - (25\% + 35\% + 20\%) \]

Calculating this gives:

\[ \text{Percentage of Seniors} = 100\% - 80\% = 20\% \]

### Step 3: Set up the equation for the number of Seniors
We know that 20% of the total number of students \( X \) are Seniors. Therefore, we can express the number of Seniors mathematically:

\[ \text{Number of Seniors} = 20\% \text{ of } X = \frac{20}{100} \times X = \frac{1}{5}X \]

### Step 4: Set the equation equal to the known number of Seniors
According to the problem, there are 150 Seniors. Thus, we can set up the equation:

\[ \frac{1}{5}X = 150 \]

### Step 5: Solve for \( X \)
To find \( X \), we can multiply both sides of the equation by 5:

\[ X = 150 \times 5 \]

Calculating this gives:

\[ X = 750 \]

### Conclusion
The total number of students in the Crestview High School student body is \( 750 \).

---