A minor league baseball park has 6800 seats. Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200. If the number of bleacher seats is 2 times the number of box seats, how many seats of each type are there?Box seats: Grandstand seats: Bleacher seats:

Step-by-step explanation:

Let us represent

The number of Box seats = x

The number of grandstand seats = y

The number of bleacher seats cost = z

A minor league baseball park has 6800 seats.

Hence,

x + y + z = 6800

Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200.

Hence:

$19 × x + $9 × y + $4 × z = $61200

19x + 9y + 4 z = 61200

If the number of bleacher seats is 2 times the number of box seats

z = 2x

Hence we substitute

x + y + z = 6800

x + y + 2x = 6800

3x + y = 6800 Equation 3

y = 6800 - 3x

For Equation 2, substituting 2x for z

19x + 9y + 4z = 61200

19x + 9y + 4(2x) = 61200

19x + 9y + 8x = 61200

27x + 9y = 61200 Equation 4

Combining Equation 3 and 4

3x + y = 6800 Equation 3

27x + 9y = 61200 Equation 4

Note that:

y = 6800 - 3x

We substitute the above in Equation 4

27x + 9(6800 - 3x) = 61200

27x + 61200 - 27x = 61200

Box seats: Grandstand seats: Bleacher seats:

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