Question
The Mom & Pop Coffee Shop wants to open new locations, either downtown or uptown. They open a new location wherever the ratio of existing coffee shops per person is less than 0.010. The population density of the 20-city-block downtown area is 225 people per city block, but there are already 48 coffee shops in the area. The population of the 30-block uptown area is 125 people per block, and there are 16 coffee shops around.
Should Mom & Pop open a new coffee shop? If not, why not? If so, wehre should they open a shop and why?
Question 5 options:
They should open a shop in the downtown area because the ratio of coffee shops per person is 0.011, which is less than 0.010.
They can open the coffee shop wherever they want.
They should not open a coffee shop because there are already 48 coffee shops downtown and 16 coffee shops uptown.
They should open a shop in the uptown area because the ratio of coffee shops per person is 0.004, which is less than 0.010.
Should Mom & Pop open a new coffee shop? If not, why not? If so, wehre should they open a shop and why?
Question 5 options:
They should open a shop in the downtown area because the ratio of coffee shops per person is 0.011, which is less than 0.010.
They can open the coffee shop wherever they want.
They should not open a coffee shop because there are already 48 coffee shops downtown and 16 coffee shops uptown.
They should open a shop in the uptown area because the ratio of coffee shops per person is 0.004, which is less than 0.010.
Answers
GPT-4o mini
To determine whether Mom & Pop Coffee Shop should open a new location and where, we need to calculate the ratio of existing coffee shops per person in both the downtown and uptown areas and compare them to the threshold of 0.010.
### Downtown Area:
- **Population density:** 225 people per block
- **Blocks in downtown:** 20 blocks
- **Total population in downtown = Population density × Number of blocks = 225 people/block × 20 blocks = 4500 people**
- **Number of existing coffee shops in downtown:** 48
**Ratio of coffee shops per person in downtown = Number of coffee shops / Total population = 48 / 4500 = 0.01067**
### Uptown Area:
- **Population density:** 125 people per block
- **Blocks in uptown:** 30 blocks
- **Total population in uptown = Population density × Number of blocks = 125 people/block × 30 blocks = 3750 people**
- **Number of existing coffee shops in uptown:** 16
**Ratio of coffee shops per person in uptown = Number of coffee shops / Total population = 16 / 3750 = 0.00427**
### Conclusion:
- **Downtown ratio:** 0.01067 (not less than 0.010, so they should not open a shop here)
- **Uptown ratio:** 0.00427 (less than 0.010, so they can open a shop here)
**Final Decision: They should open a shop in the uptown area because the ratio of coffee shops per person is 0.004, which is less than 0.010.**
Thus, the correct answer is:
"They should open a shop in the uptown area because the ratio of coffee shops per person is 0.004, which is less than 0.010."
### Downtown Area:
- **Population density:** 225 people per block
- **Blocks in downtown:** 20 blocks
- **Total population in downtown = Population density × Number of blocks = 225 people/block × 20 blocks = 4500 people**
- **Number of existing coffee shops in downtown:** 48
**Ratio of coffee shops per person in downtown = Number of coffee shops / Total population = 48 / 4500 = 0.01067**
### Uptown Area:
- **Population density:** 125 people per block
- **Blocks in uptown:** 30 blocks
- **Total population in uptown = Population density × Number of blocks = 125 people/block × 30 blocks = 3750 people**
- **Number of existing coffee shops in uptown:** 16
**Ratio of coffee shops per person in uptown = Number of coffee shops / Total population = 16 / 3750 = 0.00427**
### Conclusion:
- **Downtown ratio:** 0.01067 (not less than 0.010, so they should not open a shop here)
- **Uptown ratio:** 0.00427 (less than 0.010, so they can open a shop here)
**Final Decision: They should open a shop in the uptown area because the ratio of coffee shops per person is 0.004, which is less than 0.010.**
Thus, the correct answer is:
"They should open a shop in the uptown area because the ratio of coffee shops per person is 0.004, which is less than 0.010."