A student gets 66 marks more in French than what she got in German. Her German marks are 28% of the sum of her French and German marks. What are her French marks?

Options

A. 108
B. 72
C. 120
D. 84

Answer

To solve the problem step by step, let's denote the marks obtained by the student in German as \( X \). According to the problem, the marks in French would then be \( X + 66 \).

### Step 1: Set up the equations
We know that the German marks \( X \) are 28% of the sum of French and German marks. The sum of French and German marks can be expressed as:
\[ \text{French marks} + \text{German marks} = (X + 66) + X = 2X + 66 \]
Thus, we can write the equation:
\[ X = 0.28 \times (2X + 66) \]

### Step 2: Expand the equation
Now, let's expand the equation:
\[ X = 0.28 \times (2X + 66) \]
This simplifies to:
\[ X = 0.56X + 18.48 \]

### Step 3: Rearrange the equation
Next, we rearrange the equation to isolate \( X \):
\[ X - 0.56X = 18.48 \]
This simplifies to:
\[ 0.44X = 18.48 \]

### Step 4: Solve for \( X \)
Now, we can solve for \( X \):
\[ X = \frac{18.48}{0.44} \]
Calculating this gives:
\[ X = 42 \]

### Step 5: Calculate French marks
Now that we have \( X \), we can find the French marks:
\[ \text{French marks} = X + 66 = 42 + 66 = 108 \]

### Final Answer
The French marks are \( \boxed{108} \).

---