To determine which equation represents Justin's age based on the information given, we know that Kendra's age is half that of Justin's age and that Kendra is 13 years old.
Let \( a \) represent Justin's age. Since Kendra's age is half Justin's age, we can express this relationship as: \[ \text{Kendra's age} = \frac{1}{2} \times \text{Justin's age} \] Substituting Kendra's age into the equation gives us: \[ 13 = \frac{1}{2} a \]
To isolate \( a \), we can multiply both sides by 2: \[ 2 \times 13 = a \] Thus, the equation simplifies to: \[ a = 26 \]
Now we can look at the given options. The correct representation of Justin's age based on our equation is: \[ a = 2 \times 13 \]
Since none of the options directly list this equation, we should look for the equation that derives from \( 13 = \frac{1}{2} a \): This can be rearranged as: \[ 2(13) = a \] which can be restated as: \[ a = 26 \]
Among the choices provided, the correct equation that represents this relationship is: \( 2a = 13 \) (this correctly leads to \( a = 26 \) when manipulated correctly).
So, the answer choice would be: None of the options provided seem to state Justin's age correctly. The closest relationship derived from the given statement is: \( a = 2 \times 13 \).