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QuestionDemarco tiles a floor with a scale where each square is 2ft2 \mathrm{ft}. He uses 12ft\frac{1}{2} \mathrm{ft} tiles. How many?

Studdy Solution

STEP 1

Assumptions1. The scale drawing uses unit squares where each side length represents ft. . Demarco uses square tiles that are1/ ft wide.
3. The area of the bathroom floor in the scale drawing is (4 x)(3 x) =48 square feet.
4. Each tile has an area of1/4 square foot, so it takes4 tiles to cover each square foot.

STEP 2

First, we need to calculate the total area of the bathroom floor in square feet. This is given by the product of the side lengths of the scale drawing, each multiplied by the scale factor.
Areafloor=(4×2)(×2)Area_{floor} = (4 \times2)( \times2)

STEP 3

Now, plug in the given values to calculate the area of the floor.
Areafloor=(×2)(3×2)=48 square feetArea_{floor} = ( \times2)(3 \times2) =48\, square\, feet

STEP 4

Next, we need to find out how many tiles are needed to cover one square foot. Since each tile has an area of1/4 square foot, we can calculate this by dividing one square foot by the area of each tile.
Tilesper square foot=1 square footAreatileTiles_{per\, square\, foot} = \frac{1\, square\, foot}{Area_{tile}}

STEP 5

Plug in the given value for the area of each tile to calculate the number of tiles per square foot.
Tilesper square foot=1 square foot1/4 square footTiles_{per\, square\, foot} = \frac{1\, square\, foot}{1/4\, square\, foot}

STEP 6

Calculate the number of tiles needed to cover one square foot.
Tilesper square foot=1 square foot1/4 square foot=4 tilesTiles_{per\, square\, foot} = \frac{1\, square\, foot}{1/4\, square\, foot} =4\, tiles

STEP 7

Now that we have the number of tiles needed to cover one square foot, we can find out how many tiles are needed to cover the entire floor. This is given by the product of the area of the floor and the number of tiles per square foot.
Total tiles=Areafloor×Tilesper square footTotal\, tiles = Area_{floor} \times Tiles_{per\, square\, foot}

STEP 8

Plug in the values for the area of the floor and the number of tiles per square foot to calculate the total number of tiles.
Total tiles=48 square feet×4 tilesTotal\, tiles =48\, square\, feet \times4\, tiles

STEP 9

Calculate the total number of tiles needed.
Total tiles=48 square feet×4 tiles=192 tilesTotal\, tiles =48\, square\, feet \times4\, tiles =192\, tilesDemarco needs192 tiles to cover the bathroom floor.

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