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:
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For a group of 4 or fewer people:
- The cost is a flat rate of $4.
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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:
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If \( n \leq 4 \): \[ \text{Total cost} = 4 \]
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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:
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For \( n = 1, 2, 3, 4 \): \[ \text{Total cost} = 4 \]
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For \( n = 5 \): \[ \text{Total cost} = 2(5) - 4 = 10 - 4 = 6 \]
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For \( n = 6 \): \[ \text{Total cost} = 2(6) - 4 = 12 - 4 = 8 \]
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For \( n = 7 \): \[ \text{Total cost} = 2(7) - 4 = 14 - 4 = 10 \]
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For \( n = 8 \): \[ \text{Total cost} = 2(8) - 4 = 16 - 4 = 12 \]
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For \( n = 9 \): \[ \text{Total cost} = 2(9) - 4 = 18 - 4 = 14 \]
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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
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