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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?

Respuesta :

Answer:

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 equation that can be used to represent the information will be b + f + m = 490 and 15b + 25f + 20m = 10520.

Let the floor be represented by f.

Let the mezzanine be represented by m.

Let the balcony be represented by b.

Therefore, based on the information given, the equation to solve the question will be:

b + f + m = 490

15b + 25f + 20m = 10520

Therefore, the equation will be b + f + m = 490; 15b + 25f + 20m = 10520.

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