Answer:
To determine when Ramona will be half her father's age, we need to set up an equation based on their ages and the passage of time.
Let \( t \) be the number of years from now until Ramona is half her father's age.
Currently, Ramona is 12 and her father is 38.
In \( t \) years, Ramona's age will be \( 12 + t \) and her father's age will be \( 38 + t \).
We need to find \( t \) such that:
\[ 12 + t = \frac{1}{2} (38 + t) \]
To solve for \( t \), follow these steps:
1. Multiply both sides by 2 to eliminate the fraction:
\[ 2(12 + t) = 38 + t \]
2. Distribute and simplify:
\[ 24 + 2t = 38 + t \]
3. Subtract \( t \) from both sides:
\[ 24 + t = 38 \]
4. Subtract 24 from both sides:
\[ t = 14 \]
So, in 14 years, Ramona will be half her father's age.
To find her father's age at that time:
\[ 38 + 14 = 52 \]
Therefore, Ramona's father will be 52 years old when Ramona is half his age.
