Use the following information. Suppose a gallon of paint...

use the following information. Suppose a gallon of paint costs $\$ 16$ and covers 400 square feet. Two coats of paint are recommended for even coverage. The room to be painted is 10 feet high, 15 feet long, and 15 feet wide. The homeowner has $1 \frac{1}{2}$ gallons of paint left from another project. Is this enough paint for the walls of the room? Explain.

use the following information. Suppose a gallon of paint costs $\$ 16$ and covers 400 square feet. Two coats of paint are recommended for even coverage. The room to be painted is 10 feet high, 15 feet long, and 15 feet wide.
The homeowner has $1 \frac{1}{2}$ gallons of paint left from another project. Is this enough paint for the walls of the room? Explain.

Key Concepts

Resource Sufficiency Analysis

This concept is about comparing the available amount of paint with the calculated amount required to complete the painting task. It includes evaluating whether the current resources are sufficient or if additional materials need to be procured.

Paint Coverage Estimation

This concept involves using the provided coverage rate (for instance, square feet per gallon) to determine how much surface area can be covered with a given amount of paint. It is essential for estimating the quantity of paint needed for a project.

Multiple Coating Application

This concept refers to the practice of applying more than one coat of paint to ensure proper coverage and durability. It involves multiplying the area to be painted by the number of coats, thereby increasing the total amount of paint required.

Surface Area Calculation

This concept involves determining the area of the surfaces that need to be painted using the dimensions of the room or object. It requires understanding how to calculate the area of rectangles and summing the relevant areas to get the total surface area where paint will be applied.

Transcript

00:01 All right.

00:02 So for this problem, we want to paint just the walls of a room and you know that the height of the room is 10 feet.

00:10 The width is 15 and that the length of the room is also 15 feet.

00:17 Some other information that you know is that one gallon of paint will cover 400 square feet and a gallon cost $16.

00:28 Dollars, i want to know that if i'm going to paint just the walls of my room and i own a gallon, right, so i have a gallon and a half, will i be able to cover my room? and it's also really important to know that they're assuming you're going to do two coats of this.

00:57 That way the paint actually goes on even and it would look a little nicer.

01:02 All right, so first thing i need to do is i need to figure out, well, how much square footage am i actually painting? and then based off of that, i can tell you if i have enough paint or not.

01:13 So we're going to go through and pretty much we are going to find the lateral area.

01:18 All right, we are painting the walls.

01:21 So we are going to have a pair of walls that are the height, 10 by the width 15.

01:29 So we are going to have two times 10 by 15.

01:33 15 because there are two walls by the dimensions 10 by 15 right and we are also going to paint two walls that are the height 10 by the length which is also 15 so again we got two more that are going 10 by 15 yes this is also the same as just multiplying four to 10 by 15 all right 10 by 15 is 150 and you're doubling that so that is 300 square feet all right and then uh doing the same thing two times 10 by 15 is going to be another 300 so we are using a total of 600 or we're painting a surface area of 600 square feet all right and essentially you want to be able to do two coats of this so if you want to get two coats of paint on this, you're actually covering 1 ,200 feet squared...

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