Final answer:
The question is about finding the ratio of the number of students in two classes based on their average grades. After setting up an equation using the weighted average formula and solving for the ratio, we find that the ratio of the number of students in Class A to Class B is 5:4, which is not among the provided options.
Step-by-step explanation:
The student is asking how to find the ratio of the number of students in Class A to the number of students in Class B, given the average grades of the students in each class and the combined average grade. To solve for the ratio, let's denote the number of students in Class A as A and the number of students in Class B as B. We can use the weighted average formula, which is (A * 68.4 + B * 72) / (A + B) = 70. After rearranging the terms and simplifying, we can find the relationship between A and B, which will give us the ratio of the number of students in Class A to the number of students in Class B.
We can write the following equation based on the given averages:
A * 68.4 + B * 72 = 70(A + B)
Expanding both sides we get:
A * 68.4 + B * 72 = 70A + 70B
Subtracting 70A and 68.4A from both sides, we get:
-1.6A = -2B
Dividing both sides by -1.6 we get:
A = 1.25B
This simplifies to A/B = 5/4, which is the same as 20/16, meaning the ratio of the number of students in Class A to the number of students in Class B is 5:4, which is not among the options provided, indicating a possible Error in the question or the options.