Question

antonio is comparing the crowdedness at three different sports events.

which 2 ways could antonio find the least crowded event?

choose 2 answers:

a find the least people per square meter.
b find the most people per square meter.
c find the least square meters per person.
d find the most square meters per person.

Explanation:

Define crowdedness and unit rates

Using the Ratios and Rates and Unit Rates knowledge points, we analyze how crowdedness is measured. Crowdedness represents how packed a space is with people. We can express this relationship using two different unit rates:

1. People per square meter: \(\frac{\text{People}}{\text{Area}}\)
2. Square meters per person: \(\frac{\text{Area}}{\text{People}}\)

Analyze people per square meter

The rate \(\frac{\text{People}}{\text{Area}}\) measures how many people occupy each single square meter of space.

• A higher value means more people are packed into the same space (more crowded).
• A lower value means fewer people occupy that space (less crowded).
• Therefore, finding the least people per square meter identifies the least crowded event. This matches option A.

Analyze square meters per person

The rate \(\frac{\text{Area}}{\text{People}}\) measures the amount of personal space available to each individual.

• A lower value means each person has very little space (more crowded).
• A higher value means each person has a larger amount of space to themselves (less crowded).
• Therefore, finding the most square meters per person identifies the least crowded event. This matches option D.

Answer:

• (A) Find the least people per square meter. (Correct answer)
• (B) Find the most people per square meter.
• (C) Find the least square meters per person.
• (D) Find the most square meters per person. (Correct answer)