Question

A museum charges $4 for a group of 4 or fewer people. A group of more than 4 people must, in addition to the $4, pay $2 per person for the number of people above 4. The maximum group size is 10.

Answer 1

To determine the total cost for a group visiting the museum based on the number of people in the group, we can break it down into two scenarios:

1. **For a group of 4 or fewer people:**
- The cost is a flat rate of $4.

2. **For a group of more than 4 people (from 5 to 10):**
- The base cost is $4.
- Additionally, there is a charge of $2 for each person above 4.

We can express the total cost for a group of \( n \) people (where \( n \) is the number of people in the group) as follows:

- If \( n \leq 4 \):
\[
\text{Total cost} = 4
\]

- If \( n > 4 \):
\[
\text{Total cost} = 4 + 2 \times (n - 4)
\]
This formula accounts for the base cost of $4 and adds $2 for each person beyond 4.

Let's simplify the formula for \( n > 4 \):
\[
\text{Total cost} = 4 + 2n - 8 = 2n - 4
\]

Now, we can summarize the total cost based on different group sizes:

- For \( n = 1, 2, 3, 4 \):
\[
\text{Total cost} = 4
\]

- For \( n = 5 \):
\[
\text{Total cost} = 2(5) - 4 = 10 - 4 = 6
\]

- For \( n = 6 \):
\[
\text{Total cost} = 2(6) - 4 = 12 - 4 = 8
\]

- For \( n = 7 \):
\[
\text{Total cost} = 2(7) - 4 = 14 - 4 = 10
\]

- For \( n = 8 \):
\[
\text{Total cost} = 2(8) - 4 = 16 - 4 = 12
\]

- For \( n = 9 \):
\[
\text{Total cost} = 2(9) - 4 = 18 - 4 = 14
\]

- For \( n = 10 \):
\[
\text{Total cost} = 2(10) - 4 = 20 - 4 = 16
\]

In summary, the total cost based on group size is:

- \( n = 1, 2, 3, 4 \): $4
- \( n = 5 \): $6
- \( n = 6 \): $8
- \( n = 7 \): $10
- \( n = 8 \): $12
- \( n = 9 \): $14
- \( n = 10 \): $16