Friday, June 29, 2012

Consider the following problem:

The instructions on a can of paint read that a half gallon of paint will cover approximately 175 square feet. How many half gallon cans of paint must be purchased to apply 2 coats of paint to cover 600 square feet per coat?


We can think of this problems in terms of direct variation. The amount of paint needed is directly proportional to the area that needs to be painted.

Let y = amount of paint in gallons

x = area to be painted in square foot.

Therefore, we use the equation for direction variation, y = kx.

Substitute ½ for y and 175 for x and solve for k.

½ = k(175) (Divide both sides by 175)

1/350 = k

To apply 2 coats over 600 square feet means we need enough paint to cover 1,200 square feet, therefore

y = (1/350)(1200)

y = 3.42 gallons.

We need to purchase 7 cans of paint because 7(1/2) = 3.5.

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