Solving Ticket Sales Equations for a Football Game

Suppose you are selling tickets to a football game. Student tickets cost $4, while general admission tickets cost $7. After selling a total of 241 tickets, you collect a total of $1315. The question is, how many of each type of ticket did you sell?

Setting Up the Equations

To solve this problem, we will use algebraic methods to set up and solve a system of linear equations.

Let's denote the number of student tickets as x and the number of general admission tickets as y. Given the total price collected and the total number of tickets sold, we can write the following equations:

4x 7y 1315

x y 241

Solving for One Variable

The second equation, x y 241, can be rearranged to solve for one of the variables. Let's solve for y:

y 241 - x

Substituting and Simplifying

Now, substitute y 241 - x into the first equation:

4x 7(241 - x) 1315

Expand and simplify:

4x 1687 - 7x 1315

-3x 1687 1315

-3x 1315 - 1687

-3x -372

x 124

Finding the Other Variable

Now that we have the value of x, we can find the value of y by substituting x 124 back into the equation y 241 - x:

y 241 - 124

y 117

Conclusion

Therefore, the number of student tickets sold is 124, and the number of general admission tickets sold is 117. The solution can be verified by checking the total number of tickets (241) and the total revenue ($1315):

124 student tickets * $4 117 general admission tickets * $7 496 819 1315

Thus, the problem is solved and the solution is correct.