Kendra is 13 years old, and her age is half of Justin's age. We can represent Justin's age with the variable \( a \).
Since Kendra's age is half of Justin's, we can write the equation as:
\[ 13 = \frac{1}{2}a \]
To isolate \( a \), we can multiply both sides of the equation by 2:
\[ 2 \times 13 = a \]
This simplifies to:
\[ a = 26 \]
Now, looking at the options you provided:
- \( 13a = 2 \) - This does not represent the relationship correctly.
- \( 2a = 13 \) - This is the inverse of what we need (it would imply that if you double Justin's age, you get Kendra's age, which is incorrect).
- \( a + \frac{1}{2} = 13 \) - This does not represent the situation correctly.
- \( \frac{1}{2}a = 13 \) - This is actually a rearranged form of the initial relationship and is correct.
Therefore, the correct equation that represents Justin's age \( a \) is:
\[ \frac{1}{2}a = 13 \]
So, the correct answer is the fourth option: \( \frac{1}{2}a = 13 \).
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