You need to put a carpet in a rectangular room that measures 13 feet by 22 feet as a cost of $19.50 per square yard. Assuming that you can buy precisely the amount of carpet you need, how much will the carpet for the room cost? Demonstrate step-by-step solution.
I got $1,858.9999. is that right?
19.5 $/y^2 * 1 y^2/9ft^2 = (19.5/9)$/ft^2
13 ft * 22 ft = 286 ft^2
286 ft^2 * (19.5/9) $/ft^2 = 619.67dollars
approximate in head to see if reasonable
15 * 20 = 300 ft^2
about 10 ft^2 / yard^2 (nine is about ten)
so about 30 y^2
* 20 = 600 dollars
Okay I was dividing by 3 instead of 9. Got it now, thanks.
1 yd^2(3 ft/1yd)(3 ft/1 yd) = 9 ft^2/yd^2
always multiply by things that are the same top and bottom so the units come out (you are really always multiplying by one)
for example
3600 seconds is the same as 1 hour
so
3600 s/1 hr
is the same top and bottom
and
1 hr/3600 s
is the same top and bottom
same deal with 1 ft/12 in
or 12 in / 1 ft
or 1 mi / 5280 ft
or 5280 ft/ 1 mi
( if using landlubber miles )
or 16 oz /lb or 1 lb/16 oz
etc
Just get that idea in your head and these are easy.
Maria earns d dollars and owes $850 in expenses. How much, in dollars, does she have left after paying for expenses?
d-850
To calculate the cost of the carpet for the room, you need to find the total area of the room and convert it to square yards. Then, you can multiply the area in square yards by the cost per square yard.
Here is the step-by-step solution:
Step 1: Determine the area of the room in square feet.
To find the area of a rectangle, you multiply its length by its width. In this case, the length is 13 feet, and the width is 22 feet.
Area = length * width
Area = 13 feet * 22 feet = 286 square feet
Step 2: Convert the area from square feet to square yards.
Since the cost is given per square yard, we need to convert the area from square feet to square yards. There are 9 square feet in 1 square yard.
Area in square yards = Area in square feet / 9
Area in square yards = 286 square feet / 9 = 31.77 square yards (rounded to two decimal places)
Step 3: Calculate the cost of the carpet.
Multiply the area in square yards by the cost per square yard.
Cost of the carpet = Area in square yards * Cost per square yard
Cost of the carpet = 31.77 square yards * $19.50 per square yard = $619.52 (rounded to two decimal places)
Therefore, the cost of the carpet for the room is $619.52, not $1,858.9999.