X is 36 years old and Y is 16 years old. In how many years will X be twice as old as Y? 

Options

A. 1 year
B. 2 years
C. 3 years
D. 4 years

Answer

To solve the problem step by step, we will determine in how many years X (who is currently 36 years old) will be twice as old as Y (who is currently 16 years old).

### Step 1: Define the ages after a certain number of years
Let the number of years after which X will be twice as old as Y be represented by \( x \).

- After \( x \) years, X's age will be \( 36 + x \).
- After \( x \) years, Y's age will be \( 16 + x \).

### Step 2: Set up the equation
According to the problem, we want to find when X's age will be twice Y's age. Therefore, we can set up the equation:

\[ 36 + x = 2(16 + x) \]

### Step 3: Expand the equation
Now, we will expand the right side of the equation:

\[ 36 + x = 32 + 2x \]

### Step 4: Rearrange the equation
Next, we will rearrange the equation to isolate \( x \). We will move all terms involving \( x \) to one side and constant terms to the other side:

\[ 36 - 32 = 2x - x \]

This simplifies to:

\[ 4 = x \]

### Step 5: Conclusion
Thus, the value of \( x \) is 4. This means that in 4 years, X will be twice as old as Y.

### Final Answer
In 4 years, X will be twice as old as Y.

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