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For each hour he babysits, Anderson earns [tex] \$1 [/tex] more than half of Carey's hourly rate. Anderson earns [tex] \$6 [/tex] per hour. Which equation can be used to solve for Carey's hourly rate, [tex] c [/tex]?

A. [tex] \frac{1}{2} c + 1 = 6 [/tex]

B. [tex] \frac{1}{2} c - 1 = 6 [/tex]

C. [tex] \frac{1}{2} c + 6 = 1 [/tex]

D. [tex] \frac{1}{2} c - 6 = 1 [/tex]


Sagot :

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]