Question

The ice skating rink charges an hourly fee for skating and $3 to rent skates for the day. Gillian rented skates and skated for 3 hours and was charged $21. Which equation represents the cost, c(x), of ice skating as a function of x, the number of hours of skating?

c(x) = 3x + 3
c(x) = 6x + 3
c(x) = 7x + 3
c(x) = 8x + 3

Answer 1

To determine the equation that represents the cost \( c(x) \) of ice skating, we need to understand the components of the cost.

1. There is a $3 fee to rent skates.
2. 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**