Matrices and System of Equations

Question

A local venue is selling tickets to a show. They are selling $10 and $15 tickets, each with different seating. If the venue sells 1,000 tickets and collects a total of $12,200 from sales, how many of each type of ticket did they sell? Show all work.

Answer 1

Hi Commenwealth A.,

Let x = the number of tickets sold at $10

Let y = the number of tickets sold at $15

The number of tickets sold for $10 [(x)*$10] plus the number of tickets sold for $20 [(y)*$15] equals the total amount collected from ticket sales [$12,200]:

(x)*$10 + (y)*$15 = $12,200; [10x + 15y = 12,200]

The total number of tickets sold [x + y] is 1000

x + y = 1000

The matrix is:

|10 15 12200|

|1 1 1000 |

I bet you can solve it from here.

Ans.

|1 0 560|

|0 1 440|

I hope this helps, Joe.