To find Carey's hourly rate, let [tex]\( c \)[/tex] represent Carey's hourly rate in dollars.
According to the problem:
1. Anderson earns [tex]$6 per hour.
2. Anderson earns $[/tex]1 more than half of Carey's hourly rate.
We can translate the second piece of information into an equation. The phrase "half of Carey's hourly rate" is represented as [tex]\( \frac{1}{2}c \)[/tex], and "Anderson earns [tex]$1 more than this" is represented mathematically as \( \frac{1}{2}c + 1 \).
Since we know Anderson earns $[/tex]6 per hour, we can set up the equation as follows:
[tex]\[ \frac{1}{2}c + 1 = 6 \][/tex]
Thus, the equation that can be used to solve for Carey's hourly rate is:
[tex]\[ \boxed{\frac{1}{2}c + 1 = 6} \][/tex]
To solve for [tex]\( c \)[/tex]:
1. Subtract 1 from both sides of the equation to isolate the term involving [tex]\( c \)[/tex]:
[tex]\[ \frac{1}{2}c = 5 \][/tex]
2. Multiply both sides of the equation by 2 to solve for [tex]\( c \)[/tex]:
[tex]\[ c = 10 \][/tex]
So, Carey's hourly rate is $10 per hour, and the correct equation to determine this is:
[tex]\[ \frac{1}{2}c + 1 = 6 \][/tex]
