Final answer:
To find when a toll pass is cheaper than paying per use, we compared the total costs of both options. The cost equality point is at 5 uses, but for the toll pass to become the cheaper option, it would require 6 uses.
Step-by-step explanation:
The student is asking about determining the number of uses required before purchasing a toll pass becomes more cost-effective than paying the per-use fee of a toll road. We'll approach this by setting up a cost comparison between the two options.
Without the toll pass, the cost of using the toll road is $5 per use. With the toll pass, there's an upfront cost of $15, and then each use costs $2. We need to find the point where the total cost of both options is the same, and any further use would make the toll pass the cheaper option.
Let's denote the number of uses with the variable n. Without the pass, the cost is 5n. With the pass, the cost is 15 + 2n. Setting these equal to each other gives us the equation:
5n = 15 + 2n
Solving for n, we get:
- Subtract 2n from both sides: 3n = 15
- Divide both sides by 3: n = 5
Thus, at 5 uses, the cost is the same for both options: $25. But the question asks for when the toll pass is cheaper, so we need one more use to make the toll pass the better deal. Therefore, the answer is 6 times (option B).