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A kitchen has a tabletop that is a rectangle 24 inches long and 18 inches wide. Isabel, an interior designer, wants to cover the tabletop in small tiles. She knows the area each bag of tiles covers, but only in square centimeters.

(a) Find the area of the tabletop in square centimeters. Do not round intermediate computations and round your final answer to two decimal places. Use the table of conversion facts as needed.

[tex]\[
\text{Area} = \text{______} \, \text{cm}^2
\][/tex]

(b) The designer wants to cover the tabletop with tiles. She doesn't have any to begin with, and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm[tex]\(^2\)[/tex]. How many whole bags of tiles does the designer need to buy to completely cover the tabletop?

[tex]\[
\text{Bags needed} = \text{______} \, \text{bags}
\][/tex]

(c) If each bag of tiles costs \[tex]$3.76, how much will she need to spend on tile? Write your answer to the nearest cent.

\[
\text{Total cost} = \$\text{______}
\][/tex]

Conversion facts for length:

- 1 inch = 2.54 cm
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 mile = 5280 feet

Note: [tex]\(\approx\)[/tex] means "is approximately equal to." For this problem, treat [tex]\(\approx\)[/tex] as if it were [tex]\(=\)[/tex].

Answer :

Sure, let's work through the problem step-by-step:

### Part (a): Find the area of the tabletop in square centimeters.

1. Determine the dimensions in inches:
- Length: 24 inches
- Width: 18 inches

2. Calculate the area in square inches:
[tex]\[
\text{Area in square inches} = \text{Length} \times \text{Width} = 24 \times 18 = 432 \text{ square inches}
\][/tex]

3. Convert the area from square inches to square centimeters:
- Conversion factor: 1 inch = 2.54 centimeters
- Therefore, 1 square inch = [tex]\( (2.54)^2 \)[/tex] square centimeters ≈ 6.4516 square centimeters

4. Perform the conversion:
[tex]\[
\text{Area in square centimeters} = 432 \times 6.4516 \approx 2787.09 \text{ square centimeters}
\][/tex]

So, the area of the tabletop is approximately 2787.09 square centimeters.

### Part (b): Determine how many whole bags of tiles are needed.

1. Each bag covers 260 square centimeters.

2. Calculate the number of bags needed:
[tex]\[
\text{Bags needed} = \frac{\text{Area in square centimeters}}{\text{Coverage per bag}} = \frac{2787.09}{260} \approx 10.72
\][/tex]

3. Since Isabel can't buy a partial bag, round up to the nearest whole number:
- Bags needed: 11

Therefore, Isabel needs to buy 11 bags of tiles.

### Part (c): Calculate the cost to buy the tiles.

1. Each bag of tiles costs [tex]$3.76.

2. Calculate the total cost:
\[
\text{Total cost} = \text{Bags needed} \times \text{Cost per bag} = 11 \times 3.76 = 41.36
\]

So, Isabel will need to spend $[/tex]41.36 on tile.

These steps outline how to determine the area Isabel needs to cover, how many bags of tiles she'll need, and the total cost of those tiles.

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Rewritten by : Barada