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.