To determine the equation that represents the cost \( c(x) \) of ice skating, we need to understand the components of the cost.
- There is a $3 fee to rent skates.
- There is an hourly fee charged to skate for each hour.
Let \( x \) be the number of hours skated. The total cost \( c(x) \) can be expressed as:
\[ c(x) = (\text{hourly fee}) \times x + \text{skate rental fee} \]
From the information given, we know that Gillian skated for 3 hours and the total charge was $21, which can be expressed as:
\[ c(3) = 21 \]
Substituting the equation for \( c(x) \):
\[ c(3) = \text{Hourly fee} \times 3 + 3 = 21 \]
Let’s denote the hourly fee as \( y \). We can set up the equation:
\[ 3y + 3 = 21 \]
Subtracting 3 from both sides:
\[ 3y = 18 \]
Dividing by 3:
\[ y = 6 \]
So the hourly fee is $6. Now we can write the cost function:
\[ c(x) = 6x + 3 \]
Thus, the equation that represents the cost of ice skating as a function of \( x \) is:
\[ c(x) = 6x + 3 \]
Therefore, the correct choice is:
c(x) = 6x + 3
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