To determine the equation that can be used to solve for Carey's hourly rate, [tex]\( c \)[/tex], we start by understanding the relationship between Anderson's and Carey's earnings.
According to the problem, Anderson earns \[tex]$6 per hour and this amount is \$[/tex]1 more than half of Carey's hourly rate. We need to translate this relationship into a mathematical equation.
Let's break it down step-by-step:
1. Carey's hourly rate is [tex]\( c \)[/tex].
2. Half of Carey's hourly rate is [tex]\(\frac{1}{2} c\)[/tex].
3. Anderson earns \[tex]$1 more than half of Carey's hourly rate. Therefore, we add 1 to half of Carey's rate:
\[
\frac{1}{2} c + 1
\]
4. According to the problem, Anderson's hourly rate is \$[/tex]6. Therefore, we set up the equation:
[tex]\[
\frac{1}{2} c + 1 = 6
\][/tex]
Among the given options, the equation that represents this relationship is:
[tex]\[
\frac{1}{2} c + 1 = 6
\][/tex]
Thus, the correct equation to solve for Carey's hourly rate, [tex]\(c\)[/tex], is:
[tex]\[
\boxed{\frac{1}{2} c + 1 = 6}
\][/tex]
