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Let's solve the problem step by step.

We are told that 49 tiles are needed to tile the floor of a **7 ft by 7 ft** room. We want to find out how many tiles are needed to tile the floor of a **31 ft by 31 ft** room.

### Step 1: Determine the area of the 7 ft by 7 ft room
The area is calculated using the formula for the area of a square:
\[
\text{Area of the 7 ft by 7 ft room} = 7 \times 7 = 49 \text{ square feet}
\]

### Step 2: Determine the area of the 31 ft by 31 ft room
Similarly, the area of the larger room is:
\[
\text{Area of the 31 ft by 31 ft room} = 31 \times 31 = 961 \text{ square feet}
\]

### Step 3: Calculate how many square feet each tile covers
Since we know that 49 tiles are needed to cover 49 square feet, we can conclude that each tile covers **1 square foot**.

### Step 4: Determine the number of tiles needed for the 31 ft by 31 ft room
To tile the 961 square feet in the larger room, and since each tile covers 1 square foot:
\[
\text{Number of tiles} = 961 \text{ tiles}
\]

Thus, **961 tiles** are needed to tile the 31 ft by 31 ft room.

Let me know if you want further clarification or details! Here are a few related questions:

1. How would the result change if the tile size were not 1 square foot?
2. What is the formula for finding the area of a rectangular room?
3. How many tiles would be needed for a room with dimensions 15 ft by 15 ft?
4. If each tile was 0.5 ft by 0.5 ft, how would the total number of tiles change?
5. How would you calculate the number of tiles for a circular room?

**Tip:** When calculating areas and tile counts, always make sure to check the dimensions of both the room and the tiles to avoid miscalculations.

Suppose you're tiling the floor of a 7 ft by 7 ft room, and find that 49 tiles will be needed. How many tiles will be needed to tile the floor of a 31 ft by 31 ft room? Round to two decimals if needed.

Learn how to determine the number of tiles needed to cover a 31 ft by 31 ft room, given that a 7 ft by 7 ft room requires 49 tiles. This problem explains the relationship between the areas of squares and the number of tiles needed. Suitable for students in Grades 6-8.

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