Kendra's age is half the age of Justin.Kendra is 13 years old.Which of the following equations represents Justin's age, a?

Question

2a=13, 1/2a=13, 13a=2, a+1/2=13

Answer 1

Kendra's age is 13, and according to the problem, Kendra's age is half the age of Justin. We can represent Justin's age as \( a \).

The relationship can be expressed in an equation as follows:

\[ \text{Kendra's age} = \frac{1}{2} \times \text{Justin's age} \]

Substituting in Kendra's age:

\[ 13 = \frac{1}{2} a \]

To eliminate the fraction, we can multiply both sides by 2:

\[ 2 \times 13 = a \] \[ a = 26 \]

Now, looking at the options given in the question, we can rearrange our derived equation \( 13 = \frac{1}{2} a \) to compare with the available choices. If we multiply both sides of this equation by 2, we get:

\[ 2 \times 13 = a \quad \text{or} \quad a = 26 \]

The original form of the equation is:

\[ 2a = 26 \]

None of the provided options match this format. However, from the options:

1. \( 2a = 13 \) (this is incorrect)
2. \( \frac{1}{2}a = 13 \) (this is actually correct but needs rearranging)
3. \( 13a = 2 \) (this is incorrect)
4. \( a + \frac{1}{2} = 13 \) (this is incorrect)

So the correct equation that represents Justin's age based on the problem is:

\[ \frac{1}{2}a = 13 \]

Therefore, the answer is:

\(\frac{1}{2}a = 13\) (this one fits).