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An amusement park that you are excited to try is $28 per visit.

You have the option to purchase a monthly membership for $90 and then pay $15 for each visit.

(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
You have plans to attend 3 times this summer. Which option is best?
You think you will visit probably about 8 times this summer. Which option is best?
You have budgeted $150 for visiting the park this summer. Which option is best?
How many visits would be approximately the break even point where both options would cost about the same?

Pay per visit
Buy a membership
2
5
7
11

1 answer

To determine the best option and break-even point, we can calculate the costs for both visiting options based on the number of visits.

  1. Cost for Pay per Visit: \[ \text{Cost} = \text{Price per visit} \times \text{Number of visits} = 28 \times \text{Number of visits} \]

  2. Cost for Membership: \[ \text{Cost} = \text{Membership fee} + (\text{Price per visit after membership} \times \text{Number of visits}) = 90 + 15 \times \text{Number of visits} \]

Now we can analyze the specific scenarios:

Scenario 1: Planning to attend 3 times

  • Pay per visit: \[ 28 \times 3 = 84 \]

  • Membership: \[ 90 + 15 \times 3 = 90 + 45 = 135 \]

Best option: Pay per visit (84 < 135)

Scenario 2: Planning to attend 8 times

  • Pay per visit: \[ 28 \times 8 = 224 \]

  • Membership: \[ 90 + 15 \times 8 = 90 + 120 = 210 \]

Best option: Buy a membership (210 < 224)

Scenario 3: Budgeted $150

  • Pay per visit (x visits): \[ 28 \times x \] We want this to be less than or equal to 150.
    \[ 28x \leq 150 \Rightarrow x \leq \frac{150}{28} \approx 5.36 \]

    So, if you go 5 times: \[ 28 \times 5 = 140 \]

  • Membership: \[ 90 + 15x \leq 150 \Rightarrow 15x \leq 60 \Rightarrow x \leq 4 \]

Best option: Pay per visit (140 < 150, while membership would only allow 4 visits).

Break-even point

Set the costs equal to find the break-even point: \[ 28x = 90 + 15x \] \[ 28x - 15x = 90 \] \[ 13x = 90 \] \[ x = \frac{90}{13} \approx 6.92 \]

Thus, rounding up, the break-even point is about 7 visits.

Summary of Responses

  • You have plans to attend 3 times this summer: Pay per visit
  • You think you will visit probably about 8 times this summer: Buy a membership
  • You have budgeted $150 for visiting the park this summer: Pay per visit
  • How many visits would be approximately the break-even point: 7