the number of buckets of paint n needed to paint a wall varies jointly with the total area a and the thickness t of the wall, and inversely with the amount of paint p. It takes five 2 gallon buckets of paint to paint 100 square feet of wall with thickness 3 inches.What is the area of the wall with thickness 6 inches can eight 2 gallon buckets paint

The number of buckets is directly proportional to the area and the thickness of the wall and inversely proportional to the amount of paint. Mathematically, we can write:

n = k · (a · t) / p

where k is the proportionality constant which we do not know.

We can calculate k with the given data: 5 2-gallon buckets, area of 100 square feet and thickness 3 inches:

k = (n · p) / (a · t)
   = (5 · 2) / (100 · 3) = 0.0333

Now that we know the constant, we can calculate the area that can be painted with 8 2-gallon buckets if the thickness is 6 inches:

a =  (n · p) / (k · t)
   = (8 · 2) / (0.0333 · 6)
   = 80 ft²

Please, note that we made sure to have the exact same units of measurements than the previous case.

Therefore, the correct answer is an area of 80 ft².