High School

A movie theater charges $7.00 for adults and $4.00 for senior citizens. On a day when 315 people paid for admission, the total receipts were $1572.

How many people who paid were adults?

How many were senior citizens?

Answer :

Final answer:

By setting up and solving a system of linear equations, we find that 168 adults and 147 senior citizens attended the movie theater on the day in question.

Explanation:

This is a problem-solving question using systems of linear equations. Let 'a' represent adults and 's' represent senior citizens. You have two linear equations from this scenario:

  1. The sum of adults and senior citizens equals the total number of people: a + s = 315
  2. The combined price of adult tickets and senior tickets equals total receipts: 7a + 4s = 1572

Next, we want to solve these equations for either 'a' or 's'. It would be easier to solve the second equation for 'a' in this case and then substitute it into the first equation. Here's how:

  1. Solve the second equation for 'a': a = (1572 - 4s)/7
  2. Substitute the above expression into the first equation: s + (1572 - 4s)/7 = 315
  3. Solving this yields: s = 147 (senior citizens)
  4. Substitute s = 147 into the first equation gives: a = 315 - 147 = 168 (adults)

Therefore, 168 adults and 147 senior citizens attended the movie theater on that day.

Learn more about Linear Equations here:

https://brainly.com/question/32634451

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