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?



Solution:



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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