Question

a kitchen has a tabletop that is a rectangle 24 in long and 18 in wide. latoya 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 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.
(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 260 cm². how many whole bags of tiles does the designer need to buy to completely cover the tabletop?
(c) if each bag of tiles costs $3.76, 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:

Step1: Convert length and width to centimeters

Length: \(24\ \text{in}\times2.54\ \text{cm/in}=60.96\ \text{cm}\)
Width: \(18\ \text{in}\times2.54\ \text{cm/in}=45.72\ \text{cm}\)

Step2: Calculate area of the rectangle

Area formula \(A = l\times w\), so \(A=60.96\times45.72\)

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Step3: Find number of bags

Number of bags \(n=\frac{2787.09}{260}\approx10.72\). Since we can't buy partial bags, \(n = 11\)

Step4: Calculate total cost

Total cost \(C=11\times3.76 = 41.36\)

Answer:

(a) \(2787.09\)
(b) \(11\)
(c) \(41.36\)