A movie theater charges $9 for adults and $7 for senior citizens. On a day when 325 people paid admission, the total receipts were $2504. How many were senior citizens and how many were adults?

The movie theatre had 114 adults and 211 seniors in attendance, based on solving a system of linear equations with the given total number of attendees and revenue.

Explanation:

As per a system of linear equations, it can be determined how many senior citizens and adults attended the movie on a particular day when the total number of attendees was 325 and the total receipts were $2504, with the cost of admission being $9 for adults and $7 for seniors.

Let A be the number of adults and S be the number of seniors.
We have two equations based on the given information: A + S = 325 (total number of people) and 9A + 7S = 2504 (total revenue).
To solve for two unknowns, we can use the substitution method, elimination method, or matrix method. For simplicity, we will use the elimination method.
Multiply the first equation by 7 to align the senior's term with the second equation: 7A + 7S = 2275. Now, we have 7A + 7S = 2275 and 9A + 7S = 2504.
Subtract the transformed first equation from the second equation to eliminate the seniors' term: (9A + 7S) - (7A + 7S) = 2504 - 2275. This simplifies to 2A = 229, resulting in A = 114.5. Because the number of attendees must be a whole number, we round down to A = 114.
Substitute A = 114 into the first equation: 114 + S = 325, which gives us S = 211.
We find that there were 114 adults and 211 seniors.