In a class, 18 students had an average midterm exam grade of 85 and the 12 remaining students had an average midterm exam grade of 90. What is the average midterm exam grade of the entire class?

Answer

To find the average midterm exam grade of the entire class, we can follow these steps:

### Step 1: Calculate the total number of students
We know there are 18 students with one average and 12 students with another average. Therefore, the total number of students is:
\[ \text{Total students} = 18 + 12 = 30 \]

### Step 2: Calculate the total sum of grades for the first group of students
The average grade for the first group of 18 students is 85. We can find the total sum of grades for these students using the formula:
\[ \text{Total sum for 18 students} = \text{Average} \times \text{Number of students} = 85 \times 18 \]
Calculating this gives:
\[ 85 \times 18 = 1530 \]

### Step 3: Calculate the total sum of grades for the second group of students
The average grade for the second group of 12 students is 90. We can find the total sum of grades for these students using the same formula:
\[ \text{Total sum for 12 students} = \text{Average} \times \text{Number of students} = 90 \times 12 \]
Calculating this gives:
\[ 90 \times 12 = 1080 \]

### Step 4: Calculate the total sum of grades for the entire class
Now, we can find the total sum of grades for all 30 students by adding the total sums from both groups:
\[ \text{Total sum for 30 students} = \text{Total sum for 18 students} + \text{Total sum for 12 students} = 1530 + 1080 \]
Calculating this gives:
\[ 1530 + 1080 = 2610 \]

### Step 5: Calculate the average grade for the entire class
Finally, we can find the average grade for the entire class by dividing the total sum of grades by the total number of students:
\[ \text{Average grade} = \frac{\text{Total sum for 30 students}}{\text{Total number of students}} = \frac{2610}{30} \]
Calculating this gives:
\[ \frac{2610}{30} = 87 \]

### Final Answer
The average midterm exam grade of the entire class is **87**.

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