Calculate Class Size: Finding Total Students with Scores 85 and 92 Using Mean of 88.5

To solve this problem, we'll first set up an equation representing the given situation:

• Let $n$ represent the total number of students.
• The number of students scoring 85 is $\frac{n}{2}$, and the number scoring 92 is also $\frac{n}{2}$.
• The total sum of all scores is $\frac{n}{2} \times 85 + \frac{n}{2} \times 92$.
• Given that the average score is 88.5, set up the equation:
$\frac{\frac{n}{2} \times 85 + \frac{n}{2} \times 92}{n} = 88.5$

Simplify and solve the equation:

First, calculate the total score:

$\frac{n}{2} \times 85 + \frac{n}{2} \times 92 = \frac{n}{2} (85 + 92)$

$= \frac{n}{2} \times 177 = 88.5 \times n$

Now, set up the equation:

$\frac{n \times 177}{2} = 88.5 \times n$

Cancel $n$ from both sides (assuming $n \neq 0$):

$\frac{177}{2} = 88.5$

The equation is inherently true, and $n$ cancels out, showing that $n$ could be any even and positive integer to satisfy the given conditions.

Therefore, the number of students in the class could be any even and positive integers.