To determine where the Pretty Pizza Company should open a new pizza place, we need to calculate the ratio of pizza places per person for both the north and south sides of town.
North Side of Town:
- Population per block: 225 people
- Number of blocks: 15 blocks
- Total population: \(225 , \text{people/block} \times 15 , \text{blocks} = 3375 , \text{people}\)
- Existing pizza places: 36
Now, calculate the current ratio of pizza places to people: \[ \text{Pizza places per person} = \frac{36 , \text{pizza places}}{3375 , \text{people}} \approx 0.01067 \]
If they open a new pizza place, the number of pizza places will be 37: \[ \text{New pizza places per person} = \frac{37 , \text{pizza places}}{3375 , \text{people}} \approx 0.01096 \] This ratio is greater than 0.01, so opening on the north side is not advisable.
South Side of Town:
- Population per block: 275 people
- Number of blocks: 22 blocks
- Total population: \(275 , \text{people/block} \times 22 , \text{blocks} = 6050 , \text{people}\)
- Existing pizza places: 37
Now, calculate the current ratio of pizza places to people: \[ \text{Pizza places per person} = \frac{37 , \text{pizza places}}{6050 , \text{people}} \approx 0.0061 \]
If they open a new pizza place, the new total will be 38: \[ \text{New pizza places per person} = \frac{38 , \text{pizza places}}{6050 , \text{people}} \approx 0.0063 \] This ratio is still less than 0.01.
Conclusion: The North side has a ratio higher than 0.01 after opening a new place, while the South side maintains a ratio below 0.01. Therefore, the Pretty Pizza Company should open a new pizza place on the south side of town.
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