Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,214 was collected on the sale of 1,234 tickets. How many of each type of ticket were sold?

Question

I need exact numbers

Answer 1

We want to solve this with a system of equations. This means we will write two equations with two variables each, enabling us to solve for both.

You want to begin by writing a let statement where you say:

Let x=number of adult tickets

Let y=number of student tickets.

Now we can use the information given in the problem to write equations. We know that the total tickets sold is 1,234, which means that x+y=1,234. At the same time, we can multiply the cost of each ticket by the number of tickets sold to find revenue collected. This leads us to say that 5x+1y=3214.

I'll let you try to solve the algebra/system of equations on your own, but you'll want to isolate the variable in one equation and plug it into the other. Good luck!

Answer 2

A + S = 1234

5A + 1S = 3214

substitute for S in the second equation: S = 1234 - A

Answer 3

Let the number of the adult tickets be x.

Let the number of the student tickets be y.

Equation 1: It is given that the total number of tickets (x + y) is 1234. Therefore, our first equation is

x + y = 1234

Equation 2: Each adult ticket costs $5. So, the total costs of all adult tickets is 5x. Similarly each student ticket costs $1. So, the total costs of all student tickets is y. It is given that the total cost for all tickets is $3,214. Therefore, our second equation is

5x + y = 3214

We solve by the method of elimination:

Subtracting equation 1 from equation 2, we get

5x + y - x - y = 3214 - 1234

4x = 1980

x = 495

Plug in x = 495 in equation 1:

495 + y = 1234

y = 739

Therefore, 495 adult tickets and 739 student tickets were sold.

Let me know if you have any questions :)