A movie theater has a seating capacity of 153. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1100, How many children, students, and adults attended? Children Attended= ? Students Attended= ? Adults Attended=? PLEASE ANSWER ASAP

x (children) = 58

y (students) = 66

z (adults) = 29

Step-by-step explanation:

Step 1: Write system of equations

x + y + z = 153

5x + 7y + 12z = 1100

1/2x = z

The best way to solve the systems of equations is to use an augmented matrix:

Top row: [1 1 1 | 153]

Middle row: [5 7 12 | 1100]

Bottom row: [1/2 0 -1 | 0]

And then put it in RREF form:

Top row: [1 0 0 | 58]

Middle row: [0 1 0 | 66]

Bottom row: [0 0 1 | 29]