what is the cost to install new carpet in an 15' by 21' room if the price of the carpet including installation is $14.50 a square yard?

Just figure the area of the room:

area = 15'*21' = 315 ft^2
one yd^2 = (3ft)^2 = 9 ft^2
so, area = 315/9 yd^2 = 35 yd^2

now you can take the last step:

cost = 35 yd^2 * $14.50/yd^2 = $507.50

To calculate the cost of installing new carpet in a 15' by 21' room, you need to first convert the room dimensions to square yards.

To do this, you divide the length and width of the room by 3, since there are 3 feet in a yard:

Length in yards = 15' / 3 = 5 yards
Width in yards = 21' / 3 = 7 yards

Next, you calculate the total area of the room in square yards by multiplying the length and width:

Area in square yards = Length in yards * Width in yards = 5 yards * 7 yards = 35 square yards

Now that you have the room's area in square yards, you can calculate the cost of the carpet installation.

Given that the price of the carpet, including installation, is $14.50 per square yard, you multiply the area by the cost per square yard:

Total cost = Area in square yards * Price per square yard
Total cost = 35 square yards * $14.50/square yard

Therefore, the cost to install new carpet in a 15' by 21' room is:

Total cost = 35 square yards * $14.50/square yard = $507.50