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 \\)

Explanation:

Step1: Determine the fixed and variable costs

The skate rental is a fixed cost of $3 (doesn't depend on hours). Let the hourly fee be $m$. The total cost $c(x)$ is fixed cost plus (hourly fee × hours), so $c(x)=mx + 3$.

Step2: Find the hourly fee $m$

Gillian skated 3 hours and paid $21. Substitute $x = 3$, $c(3)=21$ into $c(x)=mx + 3$:
$21=m(3)+3$
Subtract 3: $18 = 3m$
Divide by 3: $m = 6$

Step3: Write the cost function

Substitute $m = 6$ into $c(x)=mx + 3$: $c(x)=6x + 3$

Answer:

B. $c(x) = 6x + 3$