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:

The answer is 7. If you add everything together that she bought except the 12.75 for the shirts and subtract it from the 134.25 then you have the total that she spent on the shirts so then you divide that number by 12.75 to get the total number of shirts which will be 7.