Question

This grade is really important, i would love it if someone could please help!!!!

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 buckets of paint to paint 72 square feet of fence. how many one gallon buckets will be needed to paint 90 square feet of fence?

Answer 1

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

translates to

n = k*a/p

Answer 2

it takes three buckets of paint to paint 72 square feet of fence

so we know that

n = 3 and a = 72

Answer 3

plug this in and solve for k


n = k*a/p

3 = k*72/p

3p = 72k

72k = 3p

k = 3p/72

k = p/24

Answer 4

it further asks

how many one gallon buckets will be needed to paint 90 square feet of fence?

so we now can say that

n = unknown, a = 90, p = 1

-----------------------

n = k*a/p

n = (p/24)*(a/p)

n = (1/24)*(90/1)

n = 90/24

n = 15/4

n = 3.75

You'll need to round up because you can't use 0.75 of a bucket. So you round up to get 4

Answer 5

Thank you so much!!!!

Answer 6

yw