Math / Geometry

QuestionQuestion 8
Jean's bedroom is 14 feet by 11 feet. She has chosen a carpet which costs $\$ 30.95$ per squa yard. This includes installation.
Determine her cost to carpet her room. $\square$ Calculator
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Studdy Solution

STEP 1

1. Jean's bedroom is rectangular with dimensions $14$ feet by $11$ feet.
2. The cost of the carpet is $\$30.95$ per square yard.
3. The cost includes installation.

STEP 2

1. Calculate the area of the room in square feet.
2. Convert the area from square feet to square yards.
3. Calculate the total cost to carpet the room.

STEP 3

Calculate the area of the room in square feet:
$\text{Area in square feet} = \text{Length} \times \text{Width}$ $= 14 \text{ ft} \times 11 \text{ ft}$

STEP 4

Convert the area from square feet to square yards. Note that $1$ square yard equals $9$ square feet:
$\text{Area in square yards} = \frac{\text{Area in square feet}}{9}$

STEP 5

Calculate the total cost to carpet the room:
$\text{Total Cost} = \text{Area in square yards} \times \text{Cost per square yard}$
STEP_1: Calculate the area of the room in square feet:
$\text{Area in square feet} = 14 \text{ ft} \times 11 \text{ ft} = 154 \text{ ft}^2$
STEP_2: Convert the area from square feet to square yards:
$\text{Area in square yards} = \frac{154 \text{ ft}^2}{9} \approx 17.11 \text{ yd}^2$
STEP_3: Calculate the total cost to carpet the room:
$\text{Total Cost} = 17.11 \text{ yd}^2 \times \$30.95/\text{yd}^2 \approx \$529.74$
The total cost to carpet Jean's room is:
$\boxed{\$529.74}$

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