Final answer:
The correct answer is option D. The fraction of doughnuts with sprinkles is 11/12, not matched by any given option. There are 22 out of 24 doughnuts with sprinkles after accounting for 12 with vanilla frosting and 10 with chocolate frosting.
Step-by-step explanation:
Isaiah brought a total of two dozen doughnuts to a class party. Since one dozen equals 12 doughnuts, two dozen would be 24 doughnuts. According to the problem, half of the doughnuts had vanilla frosting with sprinkles, 2 had strawberry frosting with cream filling, and the rest had chocolate frosting with sprinkles. Half of 24 is 12, so there were 12 vanilla frosted with sprinkles. There were 2 with strawberry frosting and thus without sprinkles, leaving us with 10 chocolate frosted with sprinkles. To find the fraction of doughnuts with sprinkles, we add the vanilla and chocolate frosted doughnuts (12 + 10 = 22) and divide by the total amount of doughnuts (22/24). When simplified, 22/24 reduces to 11/12, which is not one of the options provided. Since none of the initial options (A. 1/2, B. 1/3, C. 2/3, D. 3/4) are correct, we must note there may have been a mistake in the provided options. It's important to communicate this discrepancy with the student and clarify the problem or the provided options.
To find the fraction of doughnuts that had sprinkles, we need to know how many doughnuts had sprinkles out of the total number of doughnuts brought by Isaiah.
Isaiah brought two dozen doughnuts, which is equal to 2 x 12 = 24 doughnuts.
Half of the doughnuts had vanilla frosting with sprinkles, which is 1/2 x 24 = 12 doughnuts.
2 doughnuts had strawberry frosting with cream filling, which are not mentioned to have sprinkles.
The rest of the doughnuts (12 - 2 = 10) had chocolate frosting with sprinkles.
Therefore, out of the 24 doughnuts, 22 had sprinkles, which is 22/24 or 11/12.
Since the question asks for the fraction, we simplify 11/12 to the lowest terms, which is 2/3.