Question

carpeting
suppose you want to figure the cost of carpeting a room. room sizes are usually given in square feet. carpet prices are usually given in square yards. you need to apply three formulas.

the formula ( a = ell w ) is used to compute the area, ( a ), of a rectangle in square feet.
( a ) (area in square feet) ( = ell ) (length in feet) ( cdot w ) (width in feet)

the formula for the area in square yards is given below.
( a ) (area in square yards) ( = \frac{a \text{ (area in square feet)}}{9} )

the following formula can be used to compute the cost of carpeting.
( c ) (cost) ( = a ) (number of square yards) ( cdot p ) (price per square yard)

example
find the cost of carpeting a room 21 feet long and 15 feet wide if the carpeting costs $7.70 per square yard.
( a = ell cdot w )
( = 21 cdot 15 )
( = 315 ) square feet
( a = \frac{a}{9} )
( = \frac{315}{9} )
( = 35 ) square yards
( c = a cdot p )
( = 35 cdot $7.70 )
( = $269.50 )

the cost of carpeting the room is $269.50.

find the cost of carpeting each room listed in the chart below.

room	length	width	price per square yard	cost per room
2. dining room	15	15	$22.50
3. den	12	9	$15.00
4. bedroom a	12	18	$18.50
5. bedroom b	9	15	$21.00
6. bathroom	6	6	$8.95

1. find the total carpeting bill.

Explanation:

Room 1: Living Room

Step1: Calculate area in square feet

$a = l \cdot w = 18 \cdot 24 = 432$ square feet

Step2: Convert to square yards

$A = \frac{a}{9} = \frac{432}{9} = 48$ square yards

Step3: Calculate cost

$c = A \cdot p = 48 \cdot 17.00 = 816.00$ dollars

Step1: Calculate area in square feet

$a = l \cdot w = 15 \cdot 15 = 225$ square feet

Step2: Convert to square yards

$A = \frac{a}{9} = \frac{225}{9} = 25$ square yards

Step3: Calculate cost

$c = A \cdot p = 25 \cdot 22.50 = 562.50$ dollars

Step1: Calculate area in square feet

$a = l \cdot w = 12 \cdot 9 = 108$ square feet

Step2: Convert to square yards

$A = \frac{a}{9} = \frac{108}{9} = 12$ square yards

Step3: Calculate cost

$c = A \cdot p = 12 \cdot 15.00 = 180.00$ dollars

Answer:

$816.00$

Room 2: Dining Room