Answer:
According to the 2010 ADA standard, the number of wheelchair spaces required in a classroom depends on the total number of seats in the classroom. Specifically, 1 wheelchair space is required for the first 25 seats, and an additional wheelchair space is required for each 25 seats thereafter.
For the 5 classrooms on the 1st floor, there are a total of 5 x 20 = 100 seats. Therefore, we need 1 wheelchair space for the first 25 seats, and 1 additional wheelchair space for the next 25 seats. So in total, we need 2 wheelchair spaces for the 1st floor classrooms.
For the 8 classrooms on the 2nd floor, there are a total of 8 x 35 = 280 seats. Therefore, we need 1 wheelchair space for the first 25 seats in each classroom, and an additional wheelchair space for the next 25 seats. This means that each classroom needs 2 wheelchair spaces. So in total, we need 8 x 2 = 16 wheelchair spaces for the 2nd floor classrooms.
Therefore, the total number of wheelchair spaces needed in all 13 classrooms is 2 + 16 = 18.
However, it's important to note that the question asks for the "fewest total number" of wheelchair spaces needed. Since we can't have a fraction of a wheelchair space, we need to round up to the nearest whole number. Therefore, the answer is 18 rounded up to the nearest whole number, which is 19.
So the correct answer is not one of the options given. The closest option is K. 21, but that is too high.