A girl is `28` years younger than her father. The sum of their ages is `50` years. Find the ages of the girl and her father.

Options

A. `11, 39`
B. `12, 40`
C. `13, 34`
D. `14, 44`

Answer

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

### Step 1: Define the Variables
Let the girl's age be represented by \( x \).

### Step 2: Express the Father's Age
Since the girl is 28 years younger than her father, we can express her father's age as:
\[ \text{Father's age} = x + 28 \]

### Step 3: Set Up the Equation
According to the problem, the sum of their ages is 50 years. Therefore, we can set up the following equation:
\[ x + (x + 28) = 50 \]

### Step 4: Simplify the Equation
Now, we simplify the equation:
\[ x + x + 28 = 50 \]
This simplifies to:
\[ 2x + 28 = 50 \]

### Step 5: Isolate the Variable
Next, we need to isolate \( x \). We can do this by subtracting 28 from both sides:
\[ 2x = 50 - 28 \]
\[ 2x = 22 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{22}{2} \]
\[ x = 11 \]

### Step 7: Find the Father's Age
Now that we have the girl's age, we can find the father's age:
\[ \text{Father's age} = x + 28 = 11 + 28 = 39 \]

### Conclusion
The girl's age is \( 11 \) years, and her father's age is \( 39 \) years.

### Summary of the Solution
- Girl's age: \( 11 \) years
- Father's age: \( 39 \) years

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