Question

A movie theater charges $8.00 for adults and $6.00 for senior citizens. On a day when people paid $318 for admission, the total receipts were $2112. How many who paid were adults? How many were seniors?

Answer 1

The number of adults who paid was 174, and the number of seniors was 29.

Step-by-step explanation:

Let x be the number of adults and y be the number of seniors.

The total revenue equation is 8x + 6y = 2112.

The total number of people equation is x + y = total number of people.

Given that the total number of people paid $318, x + y = 318.

Solve the system of equations:

8x + 6y = 2112 (Equation 1)

x + y = 318 (Equation 2)

Solve Equation 2 for x: x = 318 - y.

Substitute x into Equation 1: 8(318 - y) + 6y = 2112.

Solve for y to find the number of seniors.

Substitute y into x = 318 - y to find the number of adults.