Problem 4

Explanation

Let $n_A$ be the number of students in class A and $n_B$ be the number of students in class B.

Given the ratio of the average scores of class A and class B is:

And the ratio of the combined average to the average of class $A$ is:

The ratio of the number of students in class A to class B can be found using the combined average formula:

Substitute the values of $\bar{X}$ and $\bar{X}_B$ in terms of $\bar{X}_A$:

Divide both sides by $\bar{X}_A$ (since $\bar{X}_A \neq 0$):

Cross-multiply:

Group like terms:

Simplify the equation to find the ratio $n_A : n_B$:

Therefore, the ratio of the number of students in class A to class B is 2 : 1.