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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) 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?
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) 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?
Answers
GPT 3.5
To determine which option is best in each scenario, let's compare the total cost of each option.
1. For 3 visits:
- Option 1: 3 visits x $28/visit = $84
- Option 2: $90 (membership fee) + 3 visits x $15/visit = $90 + $45 = $135
In this case, Option 1 is the better choice as it costs less.
2. For 8 visits:
- Option 1: 8 visits x $28/visit = $224
- Option 2: $90 (membership fee) + 8 visits x $15/visit = $90 + $120 = $210
In this case, Option 2 is the better choice as it costs less.
3. Budget of $150:
- Option 1: The maximum number of visits within the budget is $150 / $28/visit ≈ 5 visits.
- Option 2: The maximum number of visits within the budget is ($150 - $90) / $15/visit ≈ 4 visits.
In this case, Option 2 is the better choice as it allows for more visits within the given budget.
4. Break-even point:
To find the approximate break-even point, let's determine the number of visits for both options to have a similar cost.
- Option 1: $90 (membership fee) + x visits x $15/visit = $28x
Simplifying, we get x ≈ 5.45 visits.
- Option 2: x visits x $15/visit = $90 + $28x
Simplifying, we get x ≈ 5.45 visits.
Therefore, at approximately 5-6 visits, both options would cost about the same.
In summary, the recommended option depends on the specific scenario:
- For 3 visits: Option 1 is best.
- For 8 visits: Option 2 is best.
- With a budget of $150: Option 2 is best.
- Break-even point: Both options cost about the same at approximately 5-6 visits.
1. For 3 visits:
- Option 1: 3 visits x $28/visit = $84
- Option 2: $90 (membership fee) + 3 visits x $15/visit = $90 + $45 = $135
In this case, Option 1 is the better choice as it costs less.
2. For 8 visits:
- Option 1: 8 visits x $28/visit = $224
- Option 2: $90 (membership fee) + 8 visits x $15/visit = $90 + $120 = $210
In this case, Option 2 is the better choice as it costs less.
3. Budget of $150:
- Option 1: The maximum number of visits within the budget is $150 / $28/visit ≈ 5 visits.
- Option 2: The maximum number of visits within the budget is ($150 - $90) / $15/visit ≈ 4 visits.
In this case, Option 2 is the better choice as it allows for more visits within the given budget.
4. Break-even point:
To find the approximate break-even point, let's determine the number of visits for both options to have a similar cost.
- Option 1: $90 (membership fee) + x visits x $15/visit = $28x
Simplifying, we get x ≈ 5.45 visits.
- Option 2: x visits x $15/visit = $90 + $28x
Simplifying, we get x ≈ 5.45 visits.
Therefore, at approximately 5-6 visits, both options would cost about the same.
In summary, the recommended option depends on the specific scenario:
- For 3 visits: Option 1 is best.
- For 8 visits: Option 2 is best.
- With a budget of $150: Option 2 is best.
- Break-even point: Both options cost about the same at approximately 5-6 visits.