Bratin is now 18 years old, whereas his cousin is 7 years old. After how many years will Bratin's age be 1.5 times that of his cousin?

Options

A. 15
B. 16
C. 13
D. 14

Answer

To solve the problem step by step, we need to determine after how many years Bratin's age will be 1.5 times that of his cousin's age.

### Step 1: Define the current ages
- Bratin's current age = 18 years
- Cousin's current age = 7 years

### Step 2: Let \( x \) be the number of years after which we want to find the relationship between their ages.
- After \( x \) years, Bratin's age will be \( 18 + x \).
- After \( x \) years, his cousin's age will be \( 7 + x \).

### Step 3: Set up the equation based on the problem statement
According to the problem, we want Bratin's age to be 1.5 times his cousin's age:
\[ 18 + x = 1.5 \times (7 + x) \]

### Step 4: Expand the equation
Now, we will expand the right-hand side:
\[ 18 + x = 1.5 \times 7 + 1.5 \times x \]
\[ 18 + x = 10.5 + 1.5x \]

### Step 5: Rearrange the equation
To isolate \( x \), we will rearrange the equation:
\[ 18 + x - 1.5x = 10.5 \]
\[ 18 - 10.5 = 1.5x - x \]
\[ 7.5 = 0.5x \]

### Step 6: Solve for \( x \)
Now, divide both sides by 0.5 to find \( x \):
\[ x = \frac{7.5}{0.5} = 15 \]

### Conclusion
Bratin's age will be 1.5 times that of his cousin's age after **15 years**.

---