To determine the equation that can be used to solve for Carey's hourly rate [tex]\(c\)[/tex], let's break down the details given in the problem.
1. Let [tex]\(c\)[/tex] be Carey's hourly rate.
2. Anderson earns [tex]\(\$6\)[/tex] per hour.
3. Anderson's earnings per hour are [tex]\(\$1\)[/tex] more than half of Carey's hourly rate.
To translate this into a mathematical equation, consider the following steps:
- Half of Carey's hourly rate is represented by [tex]\(\frac{1}{2}c\)[/tex].
- Anderson earns [tex]\(\$1\)[/tex] more than this amount, so we add 1 to [tex]\(\frac{1}{2}c\)[/tex].
Thus, Anderson’s hourly earnings can be expressed as:
[tex]\[
\frac{1}{2}c + 1
\][/tex]
We know from the problem statement that Anderson actually earns [tex]\(\$6\)[/tex] per hour. Therefore, we set the equation equal to 6:
[tex]\[
\frac{1}{2} c + 1 = 6
\][/tex]
So, the correct equation to solve for Carey's hourly rate [tex]\(c\)[/tex] is:
[tex]\[
\boxed{\frac{1}{2} c + 1 = 6}
\][/tex]
