To determine the best option for visiting the amusement park based on your plans, let's analyze the costs for both scenarios.
-
Cost per Visit:
- If you pay $28 per visit, for 3 visits, the cost would be: \[ 3 \times 28 = 84 \]
- Membership option: $90 membership + (3 visits × $15 per visit): \[ 90 + (3 \times 15) = 90 + 45 = 135 \]
- Best option for 3 visits: Pay per visit ($84) is better than the membership ($135).
-
For 8 visits:
- Cost without membership: \[ 8 \times 28 = 224 \]
- Cost with membership: \[ 90 + (8 \times 15) = 90 + 120 = 210 \]
- Best option for 8 visits: Membership ($210) is better than the pay per visit option ($224).
-
Budget of $150:
- If you choose to pay per visit:
\[
x \times 28 \leq 150 \implies x \leq \frac{150}{28} \approx 5.36 \implies 5 \text{ visits}
\]
- Cost for 5 visits with pay per visit: \[ 5 \times 28 = 140 \]
- Cost with membership:
\[
90 + (x \times 15) \leq 150 \implies 15x \leq 60 \implies x \leq 4
\]
- Cost for 4 visits with membership: \[ 90 + (4 \times 15) = 90 + 60 = 150 \]
- Best option with a budget of $150: Membership is equal to your budget for 4 visits, while pay per visit gives you 5 visits at $140, which is better.
- If you choose to pay per visit:
\[
x \times 28 \leq 150 \implies x \leq \frac{150}{28} \approx 5.36 \implies 5 \text{ visits}
\]
-
Break-even point:
- Let \( x \) be the number of visits at which both costs are equal: \[ 28x = 90 + 15x \] \[ 28x - 15x = 90 \] \[ 13x = 90 \] \[ x \approx \frac{90}{13} \approx 6.92 \]
- Therefore, the break-even point is approximately 7 visits.
Summary:
- For 3 visits, best option: Pay per visit ($84).
- For 8 visits, best option: Membership ($210).
- For a budget of $150, best option: Pay per visit for 5 visits ($140) vs membership for 4 visits ($150).
- The break-even point is approximately 7 visits.