SOLUTION: A chemical company needs to paint twenty chemical tanks including the top and the bottom of the tanks. Each tank has a height of 10 ft and a diameter of 5 ft. Paint can be purchase

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Question 732124: A chemical company needs to paint twenty chemical tanks including the top and the bottom of the tanks. Each tank has a height of 10 ft and a diameter of 5 ft. Paint can be purchased in 1-gallon cans or in 5-gallon cans that cost the same as 4 1-gallon cans. Each gallon of paint will cover 350 square feet. How many of each should be purchased to keep the cost of painting the tanks as low as possible?
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
One of the basic ideas is, the company will purchase whole numbers of any sizes of cans and must use the highest quantity of the 5 gallon size cans with remainder being purchased as the smaller 1 gallon size cans. Note from the description that the 5 gallon cans are less expensive than the 1 gallon cans.

Let's say, the unit of money is "cash". The 1-gal cans are 1 cash per gallon and the 5-gallon size is 4 cash per 5 gallons.

How many gallons of paint needed?
Radius is 2.5 feet.
feet^2 of surface to paint.

Using now the ratio of 1 gallon covering 350 ft^2,
gallons of paint needed.

NOW you can figure what is the largest number of 5-gallon cans that will give that amount of paint and have less than 5 gallons as a remainder. The remainder will be taken from the 1-gallon sized cans. You are then ready to figure the cost.