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A homeowner is planning to paint an 8 foot by 22 foot wall and wants to determine the cost of the project. She tests a 14 inch by 18 inch section of the wall and finds that 1 ounce of paint is needed for good coverage. If she uses paint that costs $28 per gallon, what will be the cost of the paint needed to give the entire wall a good coverage of paint?

Answer :

The cost of the paint needed to give the entire wall a good coverage of paint is $22

Firstly, we need to calculate the equivalent areas

Mathematically, we know that 1 ft is 12 inches

So to calculate the area of the wall in square inches, we have;

[tex]8\times22\times12\times\text{ 12 = 25,344 sq. inches}[/tex]

Now let us calculate the area of the test;

We have this as;

[tex]14\times\text{ 18 = 252 sq.inches}[/tex]

Now, we know that1 ounce is okay for the test, the number of ounces okay for the main wall would be;

[tex]\frac{25,344}{252}\text{ }\times\text{ 1 ounce =100.60 ounces}[/tex]

So, 100.60 ounces of paint would be enough to cover the wall

Finally, we proceed to get the cost of this as follows;

Mathematically, 1 ounce is 0.0078125 gallons

So, the number of ounces would be;

[tex]100.60\times0.0078125\text{ = 0.786 gallons}[/tex]

From the question, the cost per gallon is $28

So, the cost in 0.786 gallons would be;

[tex]0.786\times28\text{ = \$22}[/tex]

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