Question

Tara and Veronica are making a parallelogram-shaped banner for a football game. They will paint the entire banner except for a rectangular section where a photo of the school's mascot will be placed. The photo of the mascot has an area of 6 square feet. If a 16-ounce bottle of primer covers 24 square feet, how many bottles of paint will they need?

Answer 1

To determine the number of bottles of paint needed, we first find the total area of the banner. Then, using the given information about the coverage of the paint, we set up a proportion to find the amount of paint required. The final expression for the number of bottles of paint needed is (2/3)(b * h - 6) ounces.

Step-by-step explanation:

To find the number of bottles of paint needed, we first need to find the total area of the banner. Since it is a parallelogram, we can use the formula for the area of a parallelogram, which is base times height. We know that the area of the photo is 6 square feet, so the area of the banner without the photo is the total area minus the area of the photo. Let's denote the base as b and the height as h.

Area of photo = 6 square feet

Area of banner without photo = b · h - 6 square feet

Next, we need to determine how many bottles of paint we will need. Since 16 ounces of primer covers 24 square feet, we can set up a proportion:

16 ounces / 24 square feet = x ounces / (b · h - 6 square feet)

Solving for x, we find that x = (16 · (b · h - 6)) / 24, which simplifies to x = 2/3(b · h - 6) ounces.