A room whose rectangular floor is 3.7 m by 1.6 m is to be covered by square tiles of length 150 mm and having a space of 2.5 cm between any two adjacent tiles and between each tile and the wall. Calculate the cost of tiling the floor if each tile costs ksh. 90.

To solve this problem, we need to calculate the total number of square tiles required to cover the floor of the room and then determine the cost of the tiles.

### Step 1: Convert dimensions to consistent units
The floor dimensions are given in meters, and the tile dimensions are given in millimeters and centimeters. Let's convert everything to meters for consistency:

- **Floor dimensions**:
  - Length: \( 3.7 \, \text{m} \)
  - Width: \( 1.6 \, \text{m} \)

- **Tile dimensions**:
  - Tile length: \( 150 \, \text{mm} = 0.15 \, \text{m} \)
  - Space between tiles: \( 2.5 \, \text{cm} = 0.025 \, \text{m} \)

### Step 2: Calculate the effective dimensions of each tile including the space
Each tile occupies an area larger than its actual size due to the space between tiles. The effective side length of one tile including the space is:

\[
\text{Effective tile length} = 0.15 \, \text{m} + 0.025 \, \text{m} = 0.175 \, \text{m}
\]

### Step 3: Determine the number of tiles needed
To find the number of tiles needed along the length and width of the room:

- **Number of tiles along the length**:
\[
\text{Number of tiles along length} = \frac{3.7 \, \text{m}}{0.175 \, \text{m}} \approx 21.14 \text{ tiles}
\]
We round up since a partial tile cannot be used. Therefore, we need 22 tiles along the length.

- **Number of tiles along the width**:
\[
\text{Number of tiles along width} = \frac{1.6 \, \text{m}}{0.175 \, \text{m}} \approx 9.14 \text{ tiles}
\]
Similarly, we round up to 10 tiles along the width.

### Step 4: Calculate the total number of tiles
\[
\text{Total number of tiles} = 22 \times 10 = 220 \, \text{tiles}
\]

### Step 5: Calculate the total cost of the tiles
Given that each tile costs Ksh. 90:

\[
\text{Total cost} = 220 \times 90 = \text{Ksh.} 19,800
\]

### Final Answer:
The cost of tiling the floor is **Ksh. 19,800**.

Would you like any further details or explanations?

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Here are 8 related questions you might be interested in:

1. How would the cost change if the tile size were different?
2. What if the space between the tiles was reduced to 1 cm?
3. How would you calculate the total area covered by the tiles including the gaps?
4. How does rounding affect the number of tiles needed?
5. What if the room had an irregular shape?
6. How would you estimate the cost if some tiles had to be cut to fit?
7. What would the cost be if the price per tile increased by 10%?
8. How can you account for wastage in your calculation?

**Tip:** Always ensure to convert all units to the same measurement system when solving problems involving dimensions and areas.

Learn how to calculate the cost of tiling a room with square tiles considering dimensions and tile spacing. This problem involves converting units, calculating area, and determining total cost. Suitable for students in Grades 7-9.

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