To determine the cost of carpeting Mr. Rose's living room, we need to calculate the total area of the room in square yards and then multiply it by the cost per square yard for the carpet, padding, and installation.
First, let's convert the dimensions of the room from feet to yards. Since 1 yard equals 3 feet, the room dimensions would be 13ft/3 = 4.33 yards.
Next, we calculate the area of the room by multiplying the length and width: 4.33 yards * 4.33 yards = 18.71 square yards.
Now, let's calculate the cost of carpeting.
The carpeting itself costs $15.50 per square yard, so the cost of the carpeting will be: 18.71 square yards * $15.50 = $289.25.
The padding costs $3.50 per square yard, so the cost of the padding will be: 18.71 square yards * $3.50 = $65.49.
The installation cost is $2.50 per square yard, so the cost of installation will be: 18.71 square yards * $2.50 = $46.78.
Finally, to find the total cost of carpeting, we add up the cost of the carpeting, padding, and installation:
$289.25 + $65.49 + $46.78 = $401.52.
Therefore, it will cost Mr. Rose a total of $401.52 to carpet his living room.