A hotel is building a fitness center measuring 261 ft × 42 ft.

The flooring to cover the space is made of a special 3-layered cushioned tile and costs 10.00 per square foot.
How much will it cost for the new flooring?

The area of the fitness center is 261 ft × 42 ft = <<261*42=10962>>10,962 square feet.

The cost for the new flooring will be 10.00 x 10,962 = $<<10*10962=109,620>>109,620. Answer: \boxed{109,620}.

To find out how much it will cost for the new flooring, we need to calculate the area of the fitness center and then multiply it by the cost per square foot.

The area of the fitness center can be calculated by multiplying its length by its width:
Area = Length × Width
Area = 261 ft × 42 ft

Now, we can determine the cost by multiplying the area by the cost per square foot:
Cost = Area × Cost per square foot
Cost = (261 ft × 42 ft) × $10.00/ft²

To calculate this, we need to convert the units to square feet:
Area = (261 ft × 42 ft) ÷ 1 ft²/ft²
Area = 10962 ft²

Now, we can calculate the cost:
Cost = 10962 ft² × $10.00/ft²
Cost = $109,620.00

Therefore, it will cost $109,620.00 for the new flooring.