PHIL'S WIFE ROWENA, IS DECORATING A PORTION OF THE KITCHEN WALL BEHIND THE STOVE IN A MOSAIC MADE UP OF EQUAL NUMBERS OF BLACK,WHITE, AND RED TILES. THE SPACE MEASURES 6 FEET BY 2 FEET. THE MOSAIC TILES ARE 6 INCH SQUARES. HOW MANY RED TILES ARE REQUIRED?
To find out how many red tiles are required, we first need to determine the total number of tiles needed for the mosaic.
1. Start by calculating the total area of the space behind the stove:
Area = Length x Width
= 6 feet x 2 feet
= 12 square feet
2. Since the mosaic tiles are 6 inches square, we must convert the area to square inches. There are 12 inches in a foot, so:
Area (in square inches) = Area (in square feet) x Conversion Factor
= 12 square feet x 144 square inches/square foot
= 1728 square inches
3. Next, calculate the total number of tiles required. Since the mosaic is made up of equal numbers of black, white, and red tiles, we divide the total area by the area of each tile:
Total number of tiles = Total area / Area of each tile
4. The area of each tile is given as 6 inches x 6 inches = 36 square inches.
Total number of tiles = 1728 square inches / 36 square inches
= 48 tiles
5. Since the mosaic consists of equal numbers of black, white, and red tiles, one-third of the total tiles will be red.
Number of red tiles = Total number of tiles / 3
= 48 tiles / 3
= 16 red tiles
Therefore, 16 red tiles are required to complete the mosaic.