Gustavo will have new carpet put on the rectangular floors of two rooms in his house. One floor is
15 3/4 feet long, and the other floor is
12 1/2 feet long. Each floor has a width of 10 feet. What is the total area in square feet of the new carpet?
The area of a rectangle is found by multiplying the length by the width.
For the first room, the length is 15 3/4 feet and the width is 10 feet. We need to convert 15 3/4 to an improper fraction:
15 3/4 = (15 * 4 + 3) / 4 = 63/4
So the area of the first room is (63/4) * 10 = 630/4 = 315/2 = 157.5 square feet.
For the second room, the length is 12 1/2 feet and the width is 10 feet. We need to convert 12 1/2 to an improper fraction:
12 1/2 = (12 * 2 + 1) / 2 = 25/2
So the area of the second room is (25/2) * 10 = 250/2 = 125 square feet.
The total area of the new carpet is 157.5 + 125 = 282.5 square feet. Answer: \boxed{282.5}.