Mr. Scott rented a bicycle for 6 hours on Saturday and then several more hours on Sunday. It cost $4 per hour to rent the bicycle, and he paid a total of $48. For how many hours did Mr. Scott rent the bicycle on Sunday?
Choose two answers: one for the equation that models this situation and one for the correct answer.
A. Answer: 6 hours
B. Equation: [tex]4(6+x)=48[/tex]
C. Answer: 4 hours
D. Equation: [tex]6(4+x)=48[/tex]
Answer (1)
Set up the equation representing the total cost: 4 ( 6 + x ) = 48 , where x is the number of hours on Sunday.
Divide both sides of the equation by 4 to simplify: 6 + x = 12 .
Subtract 6 from both sides to solve for x: x = 6 .
Mr. Scott rented the bicycle for 6 hours on Sunday: 6 h o u rs .
Explanation
Problem Analysis Let's analyze the problem. Mr. Scott rented a bicycle for 6 hours on Saturday and an unknown number of hours on Sunday. We'll call the number of hours on Sunday 'x'. The rental cost is $4 per hour, and the total cost was $48. Our goal is to find the value of x, which represents the number of hours Mr. Scott rented the bicycle on Sunday, and to identify the correct equation that models this situation.
Setting up the Equation We know that the total number of hours Mr. Scott rented the bicycle is the sum of the hours on Saturday and Sunday, which is 6 + x. Since the rental cost is $4 per hour, the total cost can be represented as 4 multiplied by the total number of hours: 4 ( 6 + x ) . We are given that the total cost was $48, so we can set up the equation: 4 ( 6 + x ) = 48 .
Solving for x Now, let's solve the equation 4 ( 6 + x ) = 48 for x. First, we divide both sides of the equation by 4: 4 4 ( 6 + x ) = 4 48 6 + x = 12
Finding the Value of x Next, we subtract 6 from both sides of the equation to isolate x: 6 + x − 6 = 12 − 6 x = 6 Therefore, Mr. Scott rented the bicycle for 6 hours on Sunday.
Final Answer The equation that models the situation is 4 ( 6 + x ) = 48 , and the number of hours Mr. Scott rented the bicycle on Sunday is 6. Therefore, the correct answers are:Equation: 4 ( 6 + x ) = 48 Answer: 6 hours
Examples
Imagine you're planning a weekend activity and need to rent equipment. This problem demonstrates how to calculate the total cost based on hourly rates and how to determine the number of hours you can use the equipment given a budget. For example, if you have a budget of $48 and the rental cost is $4 per hour, you can use the equation 4 ( 6 + x ) = 48 to determine how many additional hours (x) you can rent the equipment on Sunday after renting it for 6 hours on Saturday. Understanding these calculations helps you manage your budget and plan your activities effectively.
