A designer enlarged both the length and the width of a rectangular carpet by 60 percent. The new carpet was too large so the designer was asked to reduce its length and width by 25 percent. By what percent was the area of the final design greater than the area of the original design?

(5/3)^2 * (3/4)^2 = (5/4)^2 = 1.5625

To solve this problem, we can break it down step by step:

1. Let's assume that the original dimensions of the rectangular carpet are L (length) and W (width).
2. When the designer increases the length and width by 60 percent, the new dimensions become 1.6L and 1.6W.
3. The area of the new carpet is calculated by multiplying the length and width, so the new area is (1.6L) * (1.6W) = 2.56LW.
4. The new carpet is too large, so the designer is asked to reduce its length and width by 25 percent. This means the final dimensions will be 0.75 times the previous dimensions.
5. Hence, the length of the final design will be 0.75 * 1.6L = 1.2L, and the width will be 0.75 * 1.6W = 1.2W.
6. The area of the final design is then calculated by multiplying the length and width, so it is (1.2L) * (1.2W) = 1.44LW.

Now that we have both the area of the original design (LW) and the area of the final design (1.44LW), we can calculate the percent increase:

Percent increase = ((Final area - Original area) / Original area) * 100

Plugging in the values, we get:

Percent increase = ((1.44LW - LW) / LW) * 100

Simplifying further:

Percent increase = (0.44LW / LW) * 100

LW cancels out, and we are left with:

Percent increase = 44%

Therefore, the area of the final design is 44 percent greater than the area of the original design.