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Chris is making a tabletop from some leftover tiles. He has 9 tiles that measure 3 1/8 inches long and 2 3/4 inches wide. What is the greatest area he can cover with these tiles?

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Answer: The length of each tile is 3 1/8 inches and the width is 2 3/4 inches. To find the area of one tile, we need to multiply the length and width:

Area of one tile = (3 1/8) x (2 3/4)

= (25/8) x (11/4)

= 275/32

Therefore, the area of 9 tiles is:

Area of 9 tiles = 9 x (275/32)

= 2475/32

= 77.34 (rounded to two decimal places)

Since Chris cannot use a fraction of a tile, he can cover the greatest area by arranging the tiles in a rectangle with as close to equal length and width as possible. Let x be the length of the rectangle and y be the width. Then:

x = (number of tiles in length) x (length of one tile)

= 3 x 3 1/8

= 9 3/8

y = (number of tiles in width) x (width of one tile)

= 3 x 2 3/4

= 8 1/4

The area of the rectangle is:

Area of rectangle = x * y

= (9 3/8) * (8 1/4)

= 77.34 (rounded to two decimal places)

Therefore, the greatest area Chris can cover with these tiles is 77.34 square inches, using all 9 tiles arranged in a rectangle.

Explanation:

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