To determine which equation represents Justin's age, we can first analyze the relationships presented in the problem.
We know:
- Kendra’s age is 13 years.
- Kendra’s age is half the age of Justin.
From the information above, we can establish the relationship between Kendra's age (K) and Justin's age (J):
\[ K = \frac{1}{2} J \]
Since Kendra is 13 years old, we can substitute this value into the equation:
\[ 13 = \frac{1}{2} J \]
To eliminate the fraction, we can multiply both sides of the equation by 2:
\[ 2 \times 13 = J \]
This simplifies to:
\[ J = 26 \]
Thus, Justin's age is 26 years. Now, if we want to express this relationship in an equation format like the ones given in the responses, we can rearrange the equation for Justin’s age to:
\[ 2a = 26 \]
However, none of the provided responses directly use 26 as a representation. Instead, let’s express it in terms of Kendra's age:
If we take \( a \) to represent Justin's age, \( a = 2 \times 13 \). This would yield
So if we let the equation represent Justin's age directly relative to Kendra's age, we rewrite it to accommodate logic:
Given the original options:
- \( 13a = 2 \) → Incorrect
- \( a + 12 = 13 \) → Incorrect
- \( 12a = 13 \) → Incorrect
- \( 2a = 13 \) → Incorrect, as it corresponds to Kendra's age not representing Justin's correctly in relation to her age.
Thus, none of the options correctly represent Justin's age from Kendra being 13 years old. All are incorrect, and the right formulation is \( J = 2 \times K \) meaning \( 2 \times 13 \) deriving Justin's age directly.
The resulting proper equation when \( a = J \) would indeed lead us to \( J = 26 \), unlisted in any options presented.