The number of buckets of paint n, needed to paint a fence varies directly with the total area a, of the fence and inversely with the amount of paint p, in a bucket. it takes three 1-gallon buckets of paint to paint 72 square feet of fence. how many 1-gallon buckets will be needed to paint 90 square feet of fence? i need with the amount of buckets it will take, as i feel like i've got this wrong.

Formula
N = k A / p

Givens
N = 3 (buckets)
k = a constant that we have to solve for
A = area (which is 72)
p = the contents of a bucket (1 gallon in this case)

Solution
Solve for k
This is something that you have to work out with the units when you solve for k.
3 buckets = k * 72 ft^2/1 gallon
3 buckets * 1 gallon = k * 72 ft^2
3 bucket gallons / 72 ft^2 = k 
k = 1/24 bucket gallons / ft^2 = k 

I like to use decimals. So
k = 0.04166666666 * bucket gallons / ft^2 = k

Solution
Solve for 90 ft^2

n = k * Area / p
p = 1
k = 0.04166666
Area = 90

n = 0.041666666 * 90 / 1
n = 3.75 buckets

Rounding
The question does not say you can buy quarts or liters so the best thing to do is round the number of buckets up 1, because you can't get 3/4 of a bucket of 1 gallon paint.

4 <<<<<< answer.