Final answer:
The smallest possible number of girls in Miss Quaffley's class, where they make up more than 45% but less than 50%, is 11 as long as the total number of students in the class is at least 23.
Step-by-step explanation:
To find the smallest possible number of girls in Miss Quaffley's class, where they make up more than 45% but less than 50%, we need to consider how percentages work with whole numbers. Since we cannot have a fraction of a student, we look for the smallest class size where at least 45.01% (since it must be more than 45%) and up to 49.99% (since it must be less than 50%) of students are girls.
Let's denote the total number of students in the class as N and the number of girls as G. The range for the percentage of girls can be written as 0.4501 <= G/N < 0.5. Since the percentage must be between these two values, we need the smallest whole number N for which 0.4501*N is also a whole number. The smallest such N is 23 because 0.4501 * 23 = 10.3523; therefore, we need to round up to the nearest whole number for the count of girls, which is 11.
This means the smallest possible number of girls must be 11, with the class having at least 23 students to ensure the girls make up more than 45% but less than 50% of the class.