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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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Answers:
Pay per visit
Buy a membership
2
5
7
11

3 answers

To determine which option is best for each scenario, we can calculate the cost for both options and compare them.

Option 1: Pay per visit

  • Cost per visit: $28
  • Cost for 3 visits: 3 x $28 = $84

Option 2: Buy a membership

  • Membership cost: $90 + 3 x $15 (for each visit)
  • Cost for 3 visits: $90 + $45 = $135

Best option for 3 visits: Pay per visit (since $84 < $135).

For 8 visits:

  • Pay per visit: 8 x $28 = $224
  • Membership: $90 + 8 x $15 = $90 + $120 = $210

Best option for 8 visits: Buy a membership (since $210 < $224).

For a budget of $150:

  • Pay per visit for 5 visits: 5 x $28 = $140
  • Membership cost with visits: $90 + 4 x $15 = $90 + $60 = $150

Best option for a budget of $150: Buy a membership (both cost the same, but you get 4 visits).

Break-even point:

To find the break-even point, we need to determine where the costs are the same.

Let \( x \) be the number of visits:

Pay per visit: \( 28x \)
Membership: \( 90 + 15x \)

Setting them equal:

\[ 28x = 90 + 15x \]

Subtracting \( 15x \) from both sides:

\[ 13x = 90 \]

Dividing by 13:

\[ x \approx 6.92 \]

The break-even point is approximately between 7 visits.

Summary Responses:

  1. 3 visits: Pay per visit
  2. 8 visits: Buy a membership
  3. Budget of $150: Buy a membership
  4. Break-even point: 7 visits
are you sure?

Let me double-check the calculations for clarity.

1. For 3 visits:

  • Pay per visit option:

    • \( 3 \times 28 = 84 \)

  • Membership option:

    • Cost of membership: \( 90 \)
    • Cost for 3 visits: \( 3 \times 15 = 45 \)
    • Total: \( 90 + 45 = 135 \)

Conclusion: Pay per visit ($84) is cheaper than membership ($135).

2. For 8 visits:

  • Pay per visit option:

    • \( 8 \times 28 = 224 \)

  • Membership option:

    • Cost of membership: \( 90 \)
    • Cost for 8 visits: \( 8 \times 15 = 120 \)
    • Total: \( 90 + 120 = 210 \)

Conclusion: Buy a membership ($210) is cheaper than pay per visit ($224).

3. For a budget of $150:

  • Pay per visit for 5 visits:

    • \( 5 \times 28 = 140 \)

  • Membership option with 4 visits:

    • Cost of membership: \( 90 \)
    • Cost for 4 visits: \( 4 \times 15 = 60 \)
    • Total: \( 90 + 60 = 150 \)

Conclusion: Both options can be valid; membership ($150) works with a budget while pay per visit is cheaper for 5 visits ($140).

4. Break-even point:

Set the equations equal:

Let \( x \) be the number of visits:

  • Pay per visit: \( 28x \)
  • Membership: \( 90 + 15x \)

Set them equal:

\[ 28x = 90 + 15x \]

Subtract \( 15x \) from both sides:

\[ 13x = 90 \]

Dividing by 13:

\[ x = \frac{90}{13} \approx 6.92 \]

This means at 7 visits, the costs will be nearly equal, but the membership may slightly edge out.

Final Confirmed Responses:

  1. 3 visits: Pay per visit
  2. 8 visits: Buy a membership
  3. Budget of $150: Buy a membership
  4. Break-even point: 7 visits

If you have any other specific concerns or questions, feel free to ask!