To represent the relationship between Kendra's age and Justin's age based on the information given, we need to clarify a few things.
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If Kendra's age is half of Justin's age, we can denote Kendra's age as \( K \) and Justin's age as \( J \).
The relationship can be expressed mathematically as: \[ K = \frac{1}{2} J \]
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We also know that Justin is 13 years old, so \( J = 13 \).
Now, substituting \( J \) into the equation gives us: \[ K = \frac{1}{2} \times 13 \]
Now, let's analyze the provided options to find the one that correctly represents Justin's age:
a. \( \frac{1}{2} = 13 \) (This is not correct.)
b. \( 2a = 13 \) (This suggests that \( a \) is half of 13, which represents Kendra's age, not Justin's.)
c. \( a + \frac{1}{2} = 13 \) (This doesn't relate to the age relationship correctly.)
d. \( 13a = 2 \) (This incorrectly suggests a relationship where \( a \) is a scaling factor rather than an age.)
None of the provided options represent Justin's age directly. However, if we interpret the age relationship correctly, based on the options given, none correctly represent Justin's age being 13 years old.
So, the best interpretation is that Kendra’s age (represented as \( a \)) is related to Justin's age (who is 13, hence \( J = 13 \)) through the equation \( K = \frac{1}{2} J \) or \( 2K = 13 \), but this specific relationship isn’t included in your options.
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