Johan is 20 years older than Brian 12 years ago, johan was twice as old as Brian. How old Brian?

Answer

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

### Step 1: Define the variables
Let Brian's current age be represented as \( x \).

### Step 2: Express Johan's age in terms of Brian's age
Since Johan is 20 years older than Brian, we can express Johan's age as:
\[ \text{Johan's age} = x + 20 \]

### Step 3: Set up the equation based on the information given
According to the problem, 12 years ago, Johan was twice as old as Brian. We need to express their ages 12 years ago:
- Brian's age 12 years ago: \( x - 12 \)
- Johan's age 12 years ago: \( (x + 20) - 12 = x + 8 \)

Now we can set up the equation based on the information that Johan was twice as old as Brian 12 years ago:
\[ x + 8 = 2(x - 12) \]

### Step 4: Simplify the equation
Now, we will simplify the equation:
\[ x + 8 = 2x - 24 \]

### Step 5: Rearrange the equation to solve for \( x \)
To isolate \( x \), we will move all terms involving \( x \) to one side and constant terms to the other side:
\[ x + 8 + 24 = 2x \]
\[ 32 = 2x - x \]
\[ 32 = x \]

### Step 6: Conclusion
Thus, Brian's current age is:
\[ x = 32 \]

### Final Answer
Brian is 32 years old.

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