Question

The number of gallons of a waterproof sealant needed to cover a wood deck varies directly as the area of the deck. If one gallon of sealant will cover 150 square feet, how many gallons must you purchase to cover a deck that is 570 square feet? ________ gal

Answer 1

Given:

a.) The number of gallons of a waterproof sealant needed to cover a wood deck varies directly as the area of the deck.

b.) One gallon of sealant will cover 150 square feet.

Let,

y = the number of gallons of a waterproof sealant needed

x = the area of the deck

It says that the number of gallons of a waterproof sealant needed to cover a wood deck varies directly as the area of the deck.

Putting this in the equation will be,

$\text{ y = kx}$

Step 1: Let's first determine the constant of proportionality (k).

y = 1 gallon

x = 150 square feet

$\text{ y = kx }\rightarrow\text{ 1 = k(150)}$$\text{ k = }\frac{1\text{ gallons}}{\text{ 150 square feet}}\text{ =}\frac{1}{150}\text{ gallons per square foot}$

Step 2: Let's now determine how many gallons must you purchase to cover a deck that is 570 square feet.

y = unknown

x = 570 square feet

We get,

$\text{ y = kx = }\frac{1}{150}\text{x}$$\text{ y = (}\frac{1}{\text{150}})(\text{570) = }\frac{\text{ 570}}{\text{ 150}}$$\text{ y = }\frac{\text{ 19}}{\text{ 5}}\text{ or 3.8 gallons}$

Therefore, the answer is 19/5 or 3.8 gallons.