A hotel director is purchasing custom carpet for a rectangular conference room that measur… — Armed Services Vocational Aptitude Battery (ASVAB)

A hotel director is purchasing custom carpet for a rectangular conference room that measures $45\text{ feet}$ in length and $36\text{ feet}$ in width. The carpet is priced at $\$15$ per square yard. What is the total cost of the carpet needed to completely cover the room?

A
$\$810$
$\$2,700$ Answer
C
$\$8,100$
D
$\$24,300$

Answer

\$2,700

First, the area of the rectangular room is found by multiplying the length and width:

45\text{ feet} \times 36\text{ feet} = 1,620\text{ square feet}

. Next, because the carpet is priced per square yard, the area must be converted. Since

1\text{ square yard}

equals

9\text{ square feet}

, divide the area by 9:

1,620 \div 9 = 180\text{ square yards}

. Finally, multiply the

180\text{ square yards}

by the unit price of

\$15

to get the total cost of

\$2,700

Step-by-Step Solution

Calculate the total area of the room in square feet.

45\text{ feet} \times 36\text{ feet} = 1,620\text{ square feet}

The area formula for a rectangle (length multiplied by width) determines the total floor space to be covered.

Convert the area from square feet to square yards.

1,620 \div 9 = 180\text{ square yards}

The carpet is priced per square yard. Because

1\text{ yard} = 3\text{ feet}

1\text{ square yard} = 3\text{ feet} \times 3\text{ feet} = 9\text{ square feet}

. You must divide by 9.

Calculate the total cost by multiplying the area in square yards by the price per square yard.

180\text{ square yards} \times \$15\text{/square yard} = \$2,700

Multiplying the total required material by the unit price gives the final cost.

Key Concept

Calculating rectangular area and converting between two-dimensional units (square feet to square yards) before applying rates.

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