To find the number of 10" x 10" tiles needed to cover a floor measuring 18'10" x 24'2", let's break the problem down step by step:

Step 1: Convert all measurements to inches

• The tile dimensions are already given in inches: 10" x 10".
• The floor dimensions are given in feet and inches, so we convert everything to inches.
  • 18'10" (18 feet 10 inches):
    $18' \times 12 = 216"$ Add the 10 inches:
    $216" + 10" = 226"$
  • 24'2" (24 feet 2 inches):
    $24' \times 12 = 288"$ Add the 2 inches:
    $288" + 2" = 290"$

So, the floor dimensions in inches are 226" x 290".

Step 2: Adjust tile size for grout

The tiles are slightly smaller to allow for grout, so the actual tile dimensions are 9.75" x 9.75".

Step 3: Calculate the number of tiles required for each dimension

Now, divide the floor dimensions by the tile size:

• For the length (226"): $\frac{226"}{9.75"} \approx 23.18 \implies 24 \text{ tiles} \quad (\text{rounded up to the nearest whole number})$
• For the width (290"): $\frac{290"}{9.75"} \approx 29.74 \implies 30 \text{ tiles} \quad (\text{rounded up to the nearest whole number})$

Step 4: Calculate total number of tiles

Now multiply the number of tiles required for both dimensions: $24 \times 30 = 720 \text{ tiles}$

Final Answer:

You will need 720 tiles to cover the floor.

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the number of tiles change if the room dimensions were larger?
2. What would happen if the grout width changed?
3. How many tiles would be needed if the tiles were a different size, say 12" x 12"?
4. What if there were a feature in the floor, like a pillar, that reduced the total area?
5. How could we calculate the total cost of tiles if each tile had a price?

Tip: When rounding up for tiling, always account for extra tiles due to potential mistakes or future repairs.