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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?

Respuesta :

Approximately 1 gallon of 4 buckets will be needed to paint 90ft²of fences.

Formula used: N = kA / p

Given information:

  • N = 3 (buckets)
  • k = constant
  • A = area that is72
  • p = components of a bucket (1 gallon in this case)

So,

Determine k.

This is something you must work out with the units when solving for k.

  • 3 buckets = k × 72 ft^2/1 gallon
  • 3 buckets × 1 gallon = k × 72 ft²
  • 3 bucket gallons / 72 ft² = k
  • k = 1/24 bucket gallons / ft² = k

Then, we get:

  • k = 0.04166666666 × bucket gallons / ft²  = k

Now, solve for 90 ft² as follows:

  • n = k × Area / p
  • p = 1
  • k = 0.04166666
  • Area = 90

So,

  • n = 0.041666666 × 90 / 1
  • n = 3.75 buckets

After rounding off, the answer will be 4 buckets of 1-gallon.

Therefore, approximately 1 gallon of 4 buckets will be needed to paint 90ft²of fences.

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