A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?

Answer

To solve the problem step by step, we will set up an equation based on the information given.

### Step 1: Define the variables
Let \( X \) be the number of years from now when the son's age will be half the man's age.

### Step 2: Write the expressions for their ages in \( X \) years
- The man's current age is 42 years. In \( X \) years, he will be \( 42 + X \) years old.
- The son's current age is 12 years. In \( X \) years, he will be \( 12 + X \) years old.

### Step 3: Set up the equation
According to the problem, we want to find when the son's age will be half the man's age. This gives us the equation:
\[ 12 + X = \frac{1}{2}(42 + X) \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 2:
\[ 2(12 + X) = 42 + X \]
This simplifies to:
\[ 24 + 2X = 42 + X \]

### Step 5: Rearrange the equation
Now, we will rearrange the equation to isolate \( X \):
\[ 2X - X = 42 - 24 \]
This simplifies to:
\[ X = 18 \]

### Step 6: Conclusion
Thus, the son will be half the age of the man in **18 years**.