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26. At the carpet store where you work, a customer wants to buy carpet for a room that is [tex]16 \frac{1}{2}[/tex] feet by [tex]18 \frac{1}{2}[/tex] feet in size. The carpet, pad, and installation will cost [tex]\[tex]$ 17.50[/tex] per square yard. To the nearest dollar, how much will it cost this customer to carpet the room?

A. [tex]\$[/tex] 68[/tex]
B. [tex]\[tex]$ 136[/tex]
C. [tex]\$[/tex] 305[/tex]
D. [tex]\[tex]$ 594[/tex]
E. [tex]\$[/tex] 1,781[/tex]

Sagot :

GinnyAnswer
To solve this problem, we need to determine the cost of carpeting a room with the given dimensions and cost per unit area. Let's break this down step-by-step:

1. Convert the room dimensions from fractions to decimal feet:
- Length: [tex]\(16 \frac{1}{2}\)[/tex] feet can be written as [tex]\(16.5\)[/tex] feet.
- Width: [tex]\(18 \frac{1}{2}\)[/tex] feet can be written as [tex]\(18.5\)[/tex] feet.

2. Convert the dimensions from feet to yards:
- Since [tex]\(1\)[/tex] yard equals [tex]\(3\)[/tex] feet, we need to divide the dimensions in feet by [tex]\(3\)[/tex].
- Length in yards: [tex]\( \frac{16.5 \text{ feet}}{3} = 5.5 \text{ yards} \)[/tex]
- Width in yards: [tex]\( \frac{18.5 \text{ feet}}{3} = 6.16666666667 \text{ yards} \approx 6.17 \text{ yards} \)[/tex]

3. Calculate the area of the room in square yards:
- Area = Length [tex]\(\times\)[/tex] Width
- Area = [tex]\( 5.5 \text{ yards} \times 6.16666666667 \text{ yards} = 33.91666666667 \text{ square yards} \approx 33.92 \text{ square yards} \)[/tex]

4. Calculate the total cost of carpeting the room:
- The cost per square yard is [tex]\( \$17.50 \)[/tex].
- Total cost = Area [tex]\(\times\)[/tex] Cost per square yard
- Total cost = [tex]\( 33.91666666667 \text{ square yards} \times \$17.50 \text{ per square yard} = \$593.54166666667 \approx \$593.54 \)[/tex]

5. Round the total cost to the nearest dollar:
- Rounded total cost = [tex]\( \$594 \)[/tex]

Thus, the total cost to carpet the room is to the nearest dollar:

J. \$594
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