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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?
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pay per visit
buy a membership
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1 answer

To determine which option is best based on the scenarios provided, we can calculate the total cost for each option:

  1. Cost per visit: $28 per visit

    • Total cost for visiting 3 times: \( 3 \times 28 = 84 \)
    • Total cost for visiting 8 times: \( 8 \times 28 = 224 \)

  2. Monthly membership: $90 + $15 per visit

    • Total cost for visiting 3 times: \( 90 + (3 \times 15) = 90 + 45 = 135 \)
    • Total cost for visiting 8 times: \( 90 + (8 \times 15) = 90 + 120 = 210 \)

  3. Budgeted amount: $150

    • Total cost for visiting 3 times: $84 (pay per visit) vs. $135 (membership) → Best option: pay per visit
    • Total cost for visiting 8 times: $224 (pay per visit) vs. $210 (membership) → Best option: buy a membership

  4. Break-even point:

    • For the cost of both options to be equal:
      • Cost per visit: \( 28x \) (where \( x \) is the number of visits)
      • Membership cost: \( 90 + 15x \)
      • Set them equal:
        \( 28x = 90 + 15x \)
        \( 13x = 90 \)
        \( x \approx 6.92 \), which we can round to approximately 7 visits (since you can't visit a fraction of a time).

Based on the calculations:

  • For 3 visits: pay per visit is best (responses: pay per visit)
  • For 8 visits: buy a membership is best (responses: buy a membership)
  • With $150 budget: pay per visit is best (responses: pay per visit)
  • Break-even point is approximately 7 visits (responses: 7)

Now, let's proceed to complete the responses:

  • 3 visits: pay per visit
  • 8 visits: buy a membership
  • $150 budget: pay per visit
  • Break-even point: 7 visits