William H. answered • 04/20/20

Patient and Effective SAT Math and English Tutor

The question does not tell us whether the sections of the stadium are all the same size. So, we could have forty-nine sections each holding a maximum of one person each and a fiftieth section holding a maximum of 125,00 people – (1 * 49 people) = 124,951 people.

Since each section can hold from 0 people to the maximum number of people, we need to use an inequality to express the number of people possible in a given section. For a one-person section, the range of values is between 0 and 1. Using x to mean the number of people in the section, we express this as:

x ≤ 1, x ≥ 0.

We added the condition x >= 0 because we cannot have a negative number of people in a section.

For the large section, the number of people can be as low as 0 and as large as 124,951, so:

x ≤ 124,951, x ≥ 0

What is all the stadium sections are equal? If we assume, indeed, that all sections hold the same amount of people, the maximum number of people in each section is 125,000 people/50 sections = 2500 people/section. The minimum number possible in a section is 0. So, using x to mean the number of people in a section:

x ≤ 2500, x ≥ 0.

Can there be 600 people in each section? Since the inequality is true for any number of people less than 2500, and 600 is less than 2500, it is possible for there to be 600 people in each section.

Remember, we have assumed here that all the stadium sections are equal. Also, remember that the question says that the *capacity* of the stadium is 125,000, not that there are 125,00 in the stadium. With 600 people in each section, there would be 50 sections * 600 people/section = 30,000 people.