Problem
A kitchen has a tabletop that is a rectangle $56 \mathrm{~cm}$ long and $36 \mathrm{~cm}$ wide. Jessica 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. \[ \square_{\text {in }}{ }^{2} \] (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 $55 \mathrm{in}^{2}$. How many whole bags of tiles does the designer need to buy to completely cover the tabletop? bags (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. \begin{tabular}{|c|} \hline Conversion facts for length \\ \hline 1 inch $(\mathrm{in})=2.54$ centimeters $(\mathrm{cm})$ \\ 1 foot $(\mathrm{ft})=30.48$ centimeters $(\mathrm{cm})$ \\ 1 yard $(\mathrm{yd}) \approx 0.91$ meters $(\mathrm{m})$ \\ 1 mile $(\mathrm{mi}) \approx 1.61$ kilometers $(\mathrm{km})$ \end{tabular} Note that $\approx$ means "is approximately equal to". For this problem, treat $\approx$ as if it were $=$.
Solution
Step 1 ：\(\text{Length in inches} = \frac{56 \text{ cm}}{2.54} = 22.05 \text{ inches}\)
Step 2 ：\(\text{Width in inches} = \frac{36 \text{ cm}}{2.54} = 14.17 \text{ inches}\)
Step 3 ：\(\text{Area} = 22.05 \text{ inches} \times 14.17 \text{ inches} = 312.59 \text{ square inches}\)
Step 4 ：\(\text{Number of bags} = \frac{312.59 \text{ square inches}}{55 \text{ square inches}} = 5.68 \text{ bags}\)
Step 5 ：\(\text{Since we can't buy partial bags, we'll need to buy} \boxed{6} \text{ bags to cover the entire tabletop.}\)
Step 6 ：\(\text{Total cost} = 6 \text{ bags} \times $2.63/\text{bag} = $15.78\)
Step 7 ：\(\text{So, Jessica will need to spend} \boxed{$15.78} \text{ on tiles.}\)
