Expert: Sherry Wallin - 9/22/2010

Question
a theatre has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. At a show of full attendance, the number of adults was half the number of children adn students combined. The total reciept for the show was $5600. How many children attended the show?

I only need 3 matrix equtions, the rest i can do on my own...so far i have some but i dont know if they are right.... 4x+6y+8z=5600 and .5x+.5y-1z+900

Answer
Monica~

One of the first things you will want to do is define your variables:

Let x = # of childrens tickets
let y = # of student tickets
let z = # of adult tickets

x + y + z = 900
4x + 6y + 8z = 5600
z = (1/2)(x + y) -> (1/2)x + (1/2)y - z = 0

thus the matrix would be:

1  1  1  900
4  6  8  5600
.5 .5 -1  0

Now solve the matrix.

Math Prof