Question

The average (arithmetic mean) number of students in 3 economics classes at a certain college is 24. If the total number of students in 2 of the classes combined is 38, how many students are in the remaining class?

• A. 14
• B. 19
• C. 24
• D. 31
• E. 34

Hint:

Whenever a problem gives you the average of a set of numbers, your first step should often be to calculate the total sum. Working with sums is usually easier and more direct than trying to manipulate averages.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This problem involves the concept of the arithmetic mean (average). The key is to use the average to find the total sum, and then use the partial sum to find the remaining value.
Step 2: Key Formula or Approach:
The relationship between average, sum, and count is:
\[ \text{Total Sum} = \text{Average} \times \text{Number of Items} \] Step 3: Detailed Explanation:
1. Find the total number of students in all 3 classes.
We are given that the average number of students in 3 classes is 24.
\[ \text{Total students} = 24 \text{ (students/class)} \times 3 \text{ (classes)} = 72 \text{ students} \] So, the three classes together have a total of 72 students.
2. Find the number of students in the remaining class.
We are given that the total number of students in 2 of the classes is 38.
To find the number of students in the third (remaining) class, we subtract the sum of the first two from the total sum.
\[ \text{Students in remaining class} = (\text{Total students in 3 classes}) - (\text{Total students in 2 classes}) \] \[ \text{Students in remaining class} = 72 - 38 = 34 \] Step 4: Final Answer:
There are 34 students in the remaining class.