An accountant checks the reported earnings for a theater for three nightly performances against the number of tickets sold. Night Children Tickets Student Tickets General Admission Total Revenue
1 80 400 480 $9280
2 50 350 400 $7800
3 75 525 600 $10,500
a. Let x, y, and z represent the cost for children tickets, student tickets, and general admission tickets, respectively. Set up a system of equations to solve for x, y, and z.
b. Set up the augmented matrix for the system and solve the system. (Hint: To make the augmented matrix simpler to work with, consider dividing each linear equation by an appropriate constant.)
c. Explain why the auditor knows that there was an error in the record keeping.