Question

tickets for the school play cost $5 for students and $8 for adults. on opening night, all 360 seats were filled, and the box office revenues were $2610. how many student and how many adult tickets were sold?

Answer 1

To determine the number of student and adult tickets sold, we set up a system of equations and solved for the variables. It was found that 90 student tickets and 270 adult tickets were sold.

Step-by-step explanation:

To solve how many student and how many adult tickets were sold for the school play, we need to set up a system of equations based on the given information. Let's use x to represent the number of student tickets sold and y to represent the number of adult tickets sold.

From the information given:

All 360 seats were filled, so x + y = 360.The box office revenues were $2610, meaning 5x + 8y = 2610.

Now we can solve this system of equations.

Step 1: Multiply the first equation by 5 to get a new equation, 5x + 5y = 1800.

Step 2: Subtract this new equation from the second revenue equation to find the number of adult tickets: 5x + 8y - (5x + 5y) = 2610 - 1800, which simplifies to 3y = 810.

Step 3: Divide by 3 to get y = 270. There were 270 adult tickets sold.

Step 4: Substitute y back into the first equation: x + 270 = 360 to get x = 90. There were 90 student tickets sold.

Thus, 90 student tickets and 270 adult tickets were sold on opening night.

Answer 2

To determine how many student and adult tickets were sold for the school play, we set up a system of equations based on the cost of tickets and the total revenue. By solving the system, we found that 90 student tickets and 270 adult tickets were sold.

Step-by-step explanation:

Solving a System of Equations

To find out how many student and adult tickets were sold for the school play, we can set up a system of linear equations. Let's define the following variables:

s = number of student tickets sold

a = number of adult tickets sold

According to the question, student tickets cost $5 and adult tickets cost $8. Also, all 360 seats were filled, and the total box office revenue was $2610.

We can write two equations based on this information:

The total number of tickets sold (students and adults) was 360, giving us the equation: s + a = 360

The total revenue was $2610, which gives us the equation: 5s + 8a = 2610

We can solve this system of equations using either substitution or elimination. Let's use the elimination method for this problem:

First, multiply the first equation by -5 to get -5s - 5a = -1800.

Next, add this new equation to the second equation to eliminate s and solve for a:
5s + 8a = 2610 + -5s - 5a = -1800 results in 3a = 810, so a = 270.

Substitute a = 270 into the first equation, s + a = 360, to find s:
s + 270 = 360, therefore s = 90.

Thus, 90 student tickets and 270 adult tickets were sold on opening night.