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18 cases

Math:

each tile is 5in X 5in = 25 square inches per tile

25 square inches per tile X 75 tiles per box = 1875 square inches per case

1875 square inches per case / 144 square inches per square foot = 13 square feet per case

225 square feet in the room / 13 square feet per case = 17.3 cases or 18 full cases.

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