The sum of Monika and her Mother's age is 49 years. Seven years before the Mother's age was four times of Monika's age. Find the age of Monika.

Options

A. 35 Years
B. 21 Years
C. 12 Years
D. 14 Years

Answer

To solve the problem, we will define the ages of Monika and her mother using algebraic expressions and then set up equations based on the information given.

### Step 1: Define the variables
Let:
- Monika's current age = \( x \)
- Mother's current age = \( y \)

### Step 2: Set up the first equation
According to the problem, the sum of Monika's and her mother's age is 49 years. Therefore, we can write the first equation as:
\[ x + y = 49 \]

### Step 3: Set up the second equation
The problem states that seven years ago, the mother's age was four times Monika's age. Seven years ago, Monika's age would be \( x - 7 \) and her mother's age would be \( y - 7 \). This gives us the second equation:
\[ y - 7 = 4(x - 7) \]

### Step 4: Simplify the second equation
Now, we will simplify the second equation:
\[ y - 7 = 4x - 28 \]
Adding 7 to both sides:
\[ y = 4x - 21 \]

### Step 5: Substitute the expression for \( y \) into the first equation
Now we have two equations:
1. \( x + y = 49 \)
2. \( y = 4x - 21 \)

Substituting the second equation into the first:
\[ x + (4x - 21) = 49 \]
Combining like terms:
\[ 5x - 21 = 49 \]

### Step 6: Solve for \( x \)
Now, we will solve for \( x \):
Adding 21 to both sides:
\[ 5x = 70 \]
Dividing both sides by 5:
\[ x = 14 \]

### Step 7: Find Monika's age
Thus, Monika's current age is \( 14 \) years.

### Step 8: Find Mother's age (optional)
To find the mother's age, substitute \( x \) back into the first equation:
\[ y = 49 - x = 49 - 14 = 35 \]
So, Monika's mother is \( 35 \) years old.

### Final Answer
Monika's age is \( 14 \) years.

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