Question

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?

Answer 1

To determine which option is best in each scenario, we can calculate the total cost for both options based on the number of visits:

1. **Single Visit Cost:** $28 per visit.
2. **Monthly Membership Cost:** $90 + $15 per visit after purchasing the membership.

Let's define the total cost expressions for both options:

- **Cost for single visits:** \( C_{\text{single}} = 28 \times n \)
- **Cost for membership visits:** \( C_{\text{membership}} = 90 + 15 \times n \)

Where \( n \) is the number of visits.

Now let's evaluate each scenario:

1. **You have plans to attend 3 times this summer:**
- Single cost: \( C_{\text{single}} = 28 \times 3 = 84 \)
- Membership cost: \( C_{\text{membership}} = 90 + 15 \times 3 = 90 + 45 = 135 \)

**Best option:** **Single visits ($84)**

2. **You think you will visit probably about 8 times this summer:**
- Single cost: \( C_{\text{single}} = 28 \times 8 = 224 \)
- Membership cost: \( C_{\text{membership}} = 90 + 15 \times 8 = 90 + 120 = 210 \)

**Best option:** **Membership ($210)**

3. **You have budgeted $150 for visiting the park this summer:**
- Single cost: \( C_{\text{single}} = 28 \times 5 = 140 \)
- Membership cost: \( C_{\text{membership}} = 90 + 15 \times 4 = 90 + 60 = 150 \)

**Best option:** **Membership ($150)**

4. **How many visits would be approximately the break-even point where both options would cost about the same?**
Set both cost expressions equal to each other:

\[
28n = 90 + 15n
\]

\[
28n - 15n = 90
\]

\[
13n = 90
\]

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

**Break-even visits:** Approximately **7 visits**

So here are the consolidated answers:

- **3 visits:** Best option is **Single visits ($84)**
- **8 visits:** Best option is **Membership ($210)**
- **Budget of $150:** Best option is **Membership ($150)**
- **Break-even point:** **Approximately 7 visits**