Question

9 points) A rock concert brought in $432,500 on the sale of 9,500 tickets. If the tickets sold for $35 and $55

ach, how many of each type of ticket were sold? Solve this problem using matrix inverses.

Answer 1

To determine how many of each type of ticket were sold, matrix inverses are used on the set of linear equations derived from the total number of tickets sold and the total revenue earned. By representing the system as matrices and performing matrix operations, the solution for the number of $35 and $55 tickets can be found.

Step-by-step explanation:

To solve the problem using matrix inverses, let's denote the number of $35 tickets as x and the number of $55 tickets as y. We have two equations based on the given information:

1. The total number of tickets sold is 9,500, so x + y = 9,500.
2. The total revenue from the sales is $432,500, so 35x + 55y = 432,500.

These two equations can be represented in matrix form as:

[1 1; 35 55] [x; y] = [9,500; 432,500].

To find values for x and y, we can calculate the inverse of the coefficient matrix and multiply it by the constant matrix:

[x; y] = inverse([1 1; 35 55]) * [9,500; 432,500]

After calculating the inverse and performing the matrix multiplication, we will get the exact numbers of each type of ticket sold.