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?
A. $c(x)=3 x+3$
B. $c(x)=6 x+3$
C. $c(x)=7 x+3$
D. $c(x)=8 x+3
Answer (2)
Define the hourly fee as h and set up the equation 3 h + 3 = 21 based on the given information.
Solve for h by subtracting 3 from both sides and then dividing by 3, resulting in h = 6 .
Formulate the cost function c ( x ) as the hourly fee times the number of hours plus the rental fee: c ( x ) = 6 x + 3 .
The equation representing the cost of ice skating is c ( x ) = 6 x + 3 .
Explanation
Problem Analysis Let's analyze the problem. We know that the ice skating rink charges an hourly fee for skating, and there's a fixed cost of $3 for renting skates. Gillian skated for 3 hours, rented skates, and paid a total of $21. We need to determine the equation that represents the total cost, c ( x ) , as a function of the number of hours, x , of skating.
Setting up the Equation Let h be the hourly fee for skating. The total cost for Gillian can be represented as the sum of the skate rental fee and the cost of skating for 3 hours. So, we can write the equation:
3 h + 3 = 21
Isolating the Hourly Fee Now, let's solve for h . First, subtract 3 from both sides of the equation:
3 h = 21 − 3
3 h = 18
Calculating the Hourly Fee Next, divide both sides by 3 to find the hourly fee:
h = 3 18
h = 6
Formulating the Cost Function Now that we know the hourly fee is $6, we can write the cost function c ( x ) as the hourly fee multiplied by the number of hours, plus the skate rental fee:
c ( x ) = 6 x + 3
Final Answer Therefore, the equation that represents the cost of ice skating as a function of the number of hours of skating is c ( x ) = 6 x + 3 .
Examples
Imagine you're planning a birthday party at the ice skating rink. Knowing the cost function c ( x ) = 6 x + 3 helps you calculate the total cost based on how long the party will last. For example, if the party lasts for 2 hours, the cost would be $c(2) = 6(2) + 3 = 12 + 3 = $15. This helps in budgeting and making informed decisions about the duration of the party.
The equation representing the cost of ice skating as a function of the number of hours skated is c ( x ) = 6 x + 3 . This indicates that the hourly fee for skating is $6, with an added $3 for skate rental. The answer is option B: c ( x ) = 6 x + 3 .
;
