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A minor league baseball park has 7000 seats. Box seats cost$6, grandstand seats cost $4, and bleacher seats cost $2. When all seats are sold, the total revenue is $26,400. If the number of box seats is one-third the number of bleacher seats, how many seats of each type are there?

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Let x be the number of box seats, then the number of bleacher seats is 3x.

Let g be the number of grandstand seats.

x + g +3x = 7000 seats, or 4x + g = 7000

6x + 4g +2(3x) = 26400, or 12x + 4g = 26400, or 3x + g = 6600 or

g = 6600 -3x

substituting for g,  4x + 6600 -3x = 7000 gives x = 400 box seats

and then g = 6600 - 3(400) = 5400 grandstand seats

and 3x = 1200 bleacher seats.

Check: 400 + 5400 + 1200 = 7000 seats

400($6) + 5400($4) +1200($2) = $26400


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