Ginas bathroom needs new tile. At the tile store 4 cm x 4 cm squares cost 19 cents each, 8 cm x 8 cm squares cost 73 cents each, and 16 cm x 16 cm squares cost $2.89 each, The bathroom, is 8 ft x 12 ft. Which tile would be the cheapest for Gina to buy?
Let's assume that the cut-off parts of tiles are discarded.
8ft x 12ft = 243.84cm x 365.76cm
So, using the 4cm tiles, Gina will need 60.96x91.44, or
61x92 = 5612 tiles, for a cost of $1066.28
Now find the costs of the other sizes, and compare.
8ft. * 12in/ft * 2.54cm/in. = 243.64 cm.
12ft * 12in/ft * 2.54cm/in = 365.76 cm.
Ab = 243.84 * 365.76 = 89,187 cm^2. = Area of bathroom.
4cm * 4cm Tiles.
Ab/At = 89,187/16 = 5575 Tiles.
Cost = 5575 * 0.19 = $1059.10.
8cm * 8 cm Tiles:
Ab/At = 89,187/64 = 1394 Tiles.
Cost = 1394 * 0.73 =
16cm * 16cm Tiles:
To determine which tile would be the cheapest for Gina to buy, we need to calculate the cost per square foot for each tile option. Here are the steps:
1. Convert the dimensions of the bathroom from feet to centimeters:
- 8 ft x 12 ft = 96 inches x 144 inches
- 1 ft = 30.48 cm (approximately)
- 96 inches x 30.48 cm = 2929.28 cm
- 144 inches x 30.48 cm = 4389.12 cm
2. Calculate the total number of tiles required for each option:
For 4 cm x 4 cm squares:
- Divide the total area of the bathroom by the tile area to find the total number of tiles needed.
- Area of each tile = 4 cm x 4 cm = 16 cm²
- Total number of tiles = (2929.28 cm x 4389.12 cm) / 16 cm²
For 8 cm x 8 cm squares:
- Area of each tile = 8 cm x 8 cm = 64 cm²
- Total number of tiles = (2929.28 cm x 4389.12 cm) / 64 cm²
For 16 cm x 16 cm squares:
- Area of each tile = 16 cm x 16 cm = 256 cm²
- Total number of tiles = (2929.28 cm x 4389.12 cm) / 256 cm²
3. Calculate the cost for each option:
- For 4 cm x 4 cm squares: Total number of tiles x 0.19 (cents)
- For 8 cm x 8 cm squares: Total number of tiles x 0.73 (cents)
- For 16 cm x 16 cm squares: Total number of tiles x 2.89 (dollars)
4. Compare the costs of each option and determine which one is the cheapest.
Now, you can follow these steps to calculate the cost per square foot for each tile option and find out which one would be the cheapest for Gina to buy.