Question 1137671: Hello,
I have a math problem and I wanted to check to see if I have the correct answers.
The average college dorm room measures 10 feet by 18 feet.
a. Convert the measurements to inches by inches.
b. Find the area of the room in square yards
c. How much would it cost to carpet a room if the carpet cost $17.90 per meter squared?
a. 10 feet=120 inches, 18 feet=216 inches
b. (10)x(18)= 180/9=20 square feet
c. (20)x(17.90)= $358
Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the room measures 10 feet by 18 feet.
a. Convert the measurements to inches by inches.
10 feet * 12 = 120 inches.
18 feet * 12 = 216 inches.
the room measures 120 inches by 216 inches.
b. Find the area of the room in square yards
number of feet are equal to number of yards * 3.
number of inches are equal to number of feet * 12.
conversely, .....
number of yards are equal to number of feet / 3.
number of feet are equal to number of inches / 12.
if you are looking for square yards and square feet and square inches, you would do the following conversions.
square feet are equal to number of square yards * 3^2 which is equal to number of square yards * 9.
square inches are equal to number of square feet * 12^2 which is equal to number of square feet * 144.
number of square yards are equal to number of square feet / 9.
number of square feet are equal to number of square inches / 144.
you were given the dimensions of the room in feet.
that was 10 feet by 18 feet.
the number of square feet would be 10 * 18 = 180 square feet.
the number of square yards would be 1800 / 9 = 20 square yards.
you can confirm that's true by converting the feet to yards and then finding the area.
10 feet / 3 = 10/3 yards.
18 feet / 3 = 6 yards.
10/3 * 6 = 60/3 = 20 square yards.
i think in your answer to b, you meant 20 square yards and not 20 square feet.
so far, you're doing good.
c. How much would it cost to carpet a room if the carpet cost $17.90 per meter squared?
here they tossed you a curve.
they asked the price per square meter, not per square yard.
if it was 17.90 per square yard, your answer would have been correct at 17.90 * 20 = 358.
if they really wanted per square meter, then you need to convert square yards to square meters.
yards are equal to meters / 1.09361.
meters areequal to yards * 1.09361.
square yards are equal to square meters / 1.19599
square meters are equal to square yards * 1.19599.
not that 1.19599 is equal to 1.09361 squared and then rounded to 5 decimal places.
therefore, 20 square yards / 1.19599 is equal to 16.72254785 square meters and the cost will be 17.90 * 16.72254785 = 299.3336065 = 299.33 rounded to 2 decimal places.
if they meant cost per square yard, then you were right.
\if they meant cost per square meter, than what i gave you should be the answer.
note that you could have converted the yard measurements to meter measurements and got the same answer.
10/3 yards / 1.09361 = 3.048009193 meters.
6 yards / 1.09361 = 5.486416547 meters.
square meters are 3.04..... * 5.48..... = 16.72264807 square meters * 17.9 = 299.33 rounded to 2 decimal places.
bottom line is you did ok but there are some wrinkles that either shouldn't be there or that you didn't account for in part c.
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