Final answer:
To determine how many awards Frankie can paint, we calculate the area of one award and then divide the total area that can be painted using the pint of paint by the area of a single award. Frankie can paint the front of approximately 952 awards with one pint of paint.
Step-by-step explanation:
The student's question revolves around finding the number of circular awards Frankie can paint with a given amount of paint, considering the diameter of the awards and the coverage area of the paint.
To find the answer, we first need to calculate the area of a single circular award using the formula for the area of a circle A = πr^2, where r is the radius. Since the diameter is 3.8 inches, the radius would be half of that, which is 1.9 inches.
Next, we calculate the area: A = π(1.9 inches)^2 ≈ 11.34 square inches. With the given information that one ounce of paint covers 675 square inches, we can determine how much area the entire pint (16 ounces) can cover by multiplying 675 square inches per ounce by 16 ounces, which gives us 10,800 square inches.
Finally, to determine the number of awards Frankie can paint, we divide the total coverage area by the area of one award: 10,800 square inches ÷ 11.34 square inches per award ≈ 952.55. Therefore, Frankie can paint the front of approximately 952 awards with a pint of paint.