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One way to keep moisture out of your basement is to paint the walls with waterproof paint. The number g(of gallons)of paint you need varies directly with the area A of the basement. One gallon of paint covers 100 square feet.a)write a direct variation equation that relates g and A (solve for k first)b)how many gallons (g) do you need to cover 530 square feet?c)how many square feet (A) does 8.5 gallons of paint cover?

Respuesta :

[tex]\begin{gathered} a)\text{ g = kA} \\ k\text{ = }\frac{1}{100}\text{ gallon per square ft} \\ b)\text{ 5.3 gallons} \\ c)\text{ 850 square ft} \end{gathered}[/tex]

Here, we want to work with a direct variation

The variables are the number of gallons of paint g and the area A of the basement

From the question, we are told that the number of gallons vary directly as the area to be painted

Mathematically;

[tex]\begin{gathered} g\propto\text{ A} \\ \\ \text{Introduce constant k} \\ \\ g\text{ = kA} \end{gathered}[/tex]

a) we want to get the value of k, which is the variation constant given that one gallon of paint covers 100 square feet

Basically, we have to substitute 1 for g and 100 for A

We have this as;

[tex]\begin{gathered} 1\text{ = k }\times\text{ 100} \\ k\text{ = }\frac{1}{100}\text{ gallon per square ft} \end{gathered}[/tex]

b) We want to calculate the number of gallons that will cover 530 square feet

We simply can calculate this by substituting 530 for A in the equation

We have this as;

[tex]\begin{gathered} g\text{ = }\frac{1}{100}\times530 \\ g\text{ = 5.3 gallons} \end{gathered}[/tex]

c) Here, we want to calculate the area that could be painted by 8.5 gallons

Mathematically, we simply have to substitute 8.5 for g

We have this as;

[tex]\begin{gathered} 8.5\text{ = }\frac{1}{100}\times\text{ A} \\ A\text{ = 100}\times8.5 \\ \\ A\text{ = 850 square ft} \end{gathered}[/tex]