Question

A movie theater charges $ 9 for adults and $ 6 for seniors. On a particular day when 334 people paid an admission, the total receipts were $ 2551. Round your answers to the nearest integers.

How many who paid were adults?

Answer 1

To determine the number of adults who paid for admission, we set up a system of equations based on the given information and solved it, finding that approximately 182 adult tickets were sold.

Step-by-step explanation:

How to Solve the Mathematical Problem with a System of Equations

Let's solve the mathematical problem involving the total receipts of a movie theater and the number of adult and senior tickets sold. We are given two pieces of information:

• The total number of people who paid for admission is 334.
• The total amount of money collected from these 334 people is $2551.

To solve this problem, we'll use a system of linear equations. Let's denote the number of adult tickets as A and the number of senior tickets as S. We know that:

1. A + S = 334 (the total number of tickets sold)
2. 9A + 6S = $2551 (the total amount of money collected)

We can use substitution or elimination to solve this system. Let's go through the steps:

1. First, we can express S in terms of A from the first equation: S = 334 - A.
2. Next, we substitute S from the first equation into the second equation: 9A + 6(334 - A) = $2551.
3. Now let's solve for A: 9A + 2004 - 6A = $2551.
4. Combine like terms: 3A = $547.
5. Finally, divide both sides by 3 to find the number of adult tickets: A ≈ 182.33, which we round to the nearest integer, 182.

The solution is approximately 182 adult tickets were sold. Hence, we round our answer to the nearest integer, which gives us that 182 adults paid for admission.