Question

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

Answer 1

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.