Let's address the problem step-by-step:
1. Anderson earns [tex]\( \$6 \)[/tex] per hour from babysitting.
2. Anderson's hourly earning is [tex]\( \$1 \)[/tex] more than half of Carey's hourly rate ([tex]\( c \)[/tex]).
To find the relationship between Anderson's hourly rate and Carey's hourly rate, we set up the following equation:
[tex]\[
\text{Anderson's hourly rate} = \frac{1}{2} \text{Carey's hourly rate} + 1
\][/tex]
Substitute Anderson's hourly rate (\$6) into the equation:
[tex]\[
6 = \frac{1}{2} c + 1
\][/tex]
This equation correctly represents the relationship stated in the problem. Thus, the correct equation to solve for Carey's hourly rate [tex]\( c \)[/tex] is:
[tex]\[
\boxed{\frac{1}{2} c + 1 = 6}
\][/tex]
No further calculations are required, as the question only asks for the equation that can be used to solve for Carey's hourly rate. The other provided equations do not fit the described relationship.
