Let's denote the average marks of students in the first class as \( A \).

We know the total number of students in both classes is \( 55 + 48 = 103 \).

The average marks of all the students in both classes is given as 59.067961165048544.

Using the formula for the average, we can write the total marks for all students in both classes as:
\[ \text{Total marks} = \text{Average marks of all students} \times \text{Total number of students} \]
\[ \text{Total marks} = 59.067961165048544 \times 103 \]

Now, we can express the total marks for all students as the sum of the total marks from the first class and the second class:
\[ \text{Total marks} = (A \times 55) + (58 \times 48) \]

We can now solve for \( A \) using the following equation:
\[ 59.067961165048544 \times 103 = (A \times 55) + (58 \times 48) \]

First, let's calculate the total marks for all students:
\[ 59.067961165048544 \times 103 = 6084.000000000000 \]

Next, let's calculate the total marks for the second class:
\[ 58 \times 48 = 2784 \]

Now we can solve for \( A \):
\[ 6084.000000000000 = (A \times 55) + 2784 \]
\[ 6084.000000000000 - 2784 = A \times 55 \]
\[ 3300 = A \times 55 \]
\[ A = \frac{3300}{55} \]
\[ A = 60 \]

Therefore, the average marks of students in the first class is 60.
첫 번째 수업에 참여한 학생들의 평균 점수를 \( A \ )로 표시합니다.

두 반의 총 학생 수가 \( 55 + 48 = 103 \)이라는 것을 알고 있습니다.

두 반 학생 전체의 평균 점수는 59.067961165048544로 주어집니다.

평균 공식을 사용하여 두 반 학생 전체의 총점을 다음과 같이 쓸 수 있습니다:
\[ \text{총점} = \text{모든 학생의 평균 점수} \times \text{총 학생 수} \]
\[ \text{총점} = 59.067961165048544 \times 103 \]

이제 모든 학생의 총점을 첫 번째 수업과 두 번째 수업의 총점의 합으로 표현할 수 있습니다:
\[ \text{총점} = (A \times 55) + (58 \times 48) \]

이제 다음 방정식을 사용하여 \( A \)를 풀 수 있습니다:
\[ 59.067961165048544 \times 103 = (A \times 55) + (58 \times 48) \]

먼저 모든 학생의 총점을 계산해 보겠습니다:
\[ 59.067961165048544 \times 103 = 6084.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000