Let's break down the problem step-by-step:
1. We know Anderson earns [tex]$6 per hour.
2. According to the problem, Anderson earns $[/tex]1 more than half of Carey's hourly rate. We need to express this relationship in the form of an equation.
3. Let [tex]\( c \)[/tex] represent Carey's hourly rate.
4. Half of Carey's hourly rate would be [tex]\(\frac{1}{2}c\)[/tex].
5. According to the problem, Anderson's hourly rate is [tex]\(1\)[/tex] dollar more than half of Carey's hourly rate. Mathematically, we can express Anderson's earnings as:
[tex]\[
\frac{1}{2}c + 1
\][/tex]
6. Since Anderson earns $6, we can set up the equation as follows:
[tex]\[
\frac{1}{2}c + 1 = 6
\][/tex]
7. The equation that corresponds to this relationship is:
[tex]\[
\frac{1}{2}c + 1 = 6
\][/tex]
Therefore, the correct equation to solve for Carey's hourly rate [tex]\( c \)[/tex] is:
[tex]\[
\boxed{\frac{1}{2}c + 1 = 6}
\][/tex]
