To determine which expression represents Jonah’s earnings correctly, let's break down the information given:
Jonah earned [tex]$5 more than half of Karen's salary. Let's denote Karen's salary by the variable \( k \).
To find half of Karen's salary, we calculate:
\[
\frac{1}{2} \times k = \frac{k}{2}
\]
Next, since Jonah earned $[/tex]5 more than this amount, we add $5 to half of Karen's salary. This gives us:
[tex]\[
\frac{k}{2} + 5
\][/tex]
Now let's go through each of the given options to see which one matches this expression:
1. [tex]\(\frac{1}{2}(k + 5)\)[/tex]:
- This represents half of Karen's salary plus 5 combined before taking half: [tex]\(\frac{1}{2} \times (k + 5)\)[/tex].
- Using distributive property: [tex]\(\frac{1}{2}k + \frac{1}{2} \times 5 = \frac{1}{2}k + 2.5\)[/tex]
- Clearly, this does not match [tex]\(\frac{k}{2} + 5\)[/tex]
2. [tex]\(\frac{1}{2} k + 5\)[/tex]:
- This matches [tex]\(\frac{k}{2} + 5\)[/tex] perfectly, which is the correct representation of Jonah's earnings.
3. [tex]\(\frac{1}{2} + k + 5\)[/tex]:
- This simplifies to [tex]\(0.5 + k + 5\)[/tex], which does not match [tex]\(\frac{k}{2} + 5\)[/tex]
4. [tex]\(\frac{1}{2} k > 5\)[/tex]:
- This is an inequality, not an expression for Jonah's earnings, and it doesn't represent the relationship given in the problem.
After evaluating all the options, we conclude that the correct expression representing Jonah's earnings is:
[tex]\[
\frac{1}{2}k + 5
\][/tex]
Therefore, the second option is the correct answer.
