Question

a kitchen has a tabletop that is a rectangle 56 cm long and 36 cm wide. melissa is an interior designer and wants to cover the tabletop in small tiles. she knows the area each bag of tiles covers, but only in square inches.
(a) find the area of the tabletop in square inches. do not round intermediate computations and round your final answer to two decimal places. use the table of conversion facts, as needed.
(b) the designer wants to cover the tabletop with tiles. she doesnt have any to begin with and she cant buy partial bags of tiles. each bag of tiles covers 55 in². how many whole bags of tiles does the designer need to buy to completely cover the tabletop?
(c) if each bag of tiles costs $2.63, how much will she need to spend on tile? write your answer to the nearest cent.
conversion facts for length
1 inch (in) = 2.54 centimeters (cm)
1 foot (ft) = 30.48 centimeters (cm)
1 yard (yd) ≈ 0.91 meters (m)
1 mile (mi) ≈ 1.61 kilometers (km)
note that ≈ means \is approximately equal to\. for this problem, treat ≈ as if it were =.

Explanation:

Part (a)

Step1: Convert length and width to inches

First, we need to convert the length and width from centimeters to inches. We know that \(1\) inch \( = 2.54\) cm. So, for the length: \(56\) cm \(=\frac{56}{2.54}\) inches. For the width: \(36\) cm \(=\frac{36}{2.54}\) inches.
\[
\text{Length in inches} = \frac{56}{2.54} \approx 22.0472 \text{ inches}
\]
\[
\text{Width in inches} = \frac{36}{2.54} \approx 14.1732 \text{ inches}
\]

Step2: Calculate the area of the rectangle

The area of a rectangle is given by \(A=\text{length}\times\text{width}\). So, we multiply the length and width in inches.
\[
A = 22.0472\times14.1732\approx 312.49 \text{ square inches}
\]

Step1: Determine the number of bags needed

We know the area of the tabletop from part (a) is approximately \(312.49\) square inches, and each bag covers \(55\) square inches. We divide the total area by the area per bag: \(\frac{312.49}{55}\approx 5.68\). But since we can't buy a partial bag, we need to round up to the next whole number.
\[
\text{Number of bags} = \lceil\frac{312.49}{55}
ceil=\lceil5.68
ceil = 6
\]

Step1: Calculate the total cost

Each bag costs \(\$2.63\) and we need \(6\) bags. So, we multiply the cost per bag by the number of bags: \(2.63\times6\).
\[
\text{Total cost} = 2.63\times6 = 15.78
\]

Answer:

\(312.49\) square inches

Part (b)