6. A theater has 490 seats. Seats sell for $25 on the floor, $20 in the mezzanine, and $15 in the balcony. The number of seats on the floor equals the total number of
seats in the mezzanine and balcony. Suppose the theater takes in $10,520 from a
sold-out event. Which system of equations represents this situation?

There are 245 seats on the floor, 101 seats on the balcony and 144 seats in the mezzanine

Step-by-step explanation:

first equation: all sections added together equaling total number of seats. second equation: price of each type of seat multiplied by number of each seat, added together equals total sales. third equation: relates floor seats to addition of other two types

2

subtract f from both sides of third equation

3

first equation: add first equation from first step and equation from previous step

second equation: add second equation from first step and 25 times equation from previous step

4

subtract 40 times second equation in previous step from first.

5

plug m-value into first equation from third step

6

plug m and b values into first equation from first step

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8

the correct option is b

step-by-step explanation: