In a certain mathematics class, the part of the class that are members of the math club is 50% of the rest of that class. The total number of math club members in this class is what percent of the entire class?

Options

A. `20%`
B. `25%`
C. `33(1)/(3)%`
D. `50%`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Total Number of Students
Let the total number of students in the mathematics class be \( T = 100 \).

### Step 2: Define the Number of Math Club Members
Let the number of students who are members of the math club be \( x \).

### Step 3: Calculate the Number of Students Not in the Math Club
The number of students who are not in the math club can be calculated as:
\[ \text{Number of students not in the math club} = T - x = 100 - x \]

### Step 4: Set Up the Equation Based on the Given Information
According to the problem, the number of math club members \( x \) is 50% of the rest of the class (students not in the math club):
\[ x = 0.5 \times (100 - x) \]

### Step 5: Solve the Equation
Now, we can solve the equation:
\[ x = 0.5 \times (100 - x) \]
Multiplying both sides by 2 to eliminate the fraction:
\[ 2x = 100 - x \]
Now, add \( x \) to both sides:
\[ 2x + x = 100 \]
This simplifies to:
\[ 3x = 100 \]
Now, divide both sides by 3:
\[ x = \frac{100}{3} \]

### Step 6: Calculate the Percentage of Math Club Members in the Class
To find what percent of the entire class the number of math club members is, we use the formula:
\[ \text{Percentage} = \left( \frac{x}{T} \right) \times 100\% \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{\frac{100}{3}}{100} \right) \times 100\% = \frac{100}{3} \% \]
This simplifies to:
\[ \text{Percentage} = 33 \frac{1}{3} \% \]

### Final Answer
The total number of math club members in this class is \( 33 \frac{1}{3} \% \) of the entire class.

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