Let's denote the amount of mixed fruit juice opened as \( x \) litres.

The cost of the mixed fruit juice opened is \( 262.85x \) dollars.

The cost of the açaí berry juice added is \( 3104.35 \times 24.666666666666668 \) dollars.

The total cost of the superfruit juice cocktail is \( 1399.45 \times (x + 24.666666666666668) \) dollars.

According to the problem, the cost of the mixed fruit juice and the açaí berry juice should add up to the total cost of the cocktail. Therefore, we can set up the following equation:

\[ 262.85x + 3104.35 \times 24.666666666666668 = 1399.45 \times (x + 24.666666666666668) \]

Let's calculate the cost of the açaí berry juice added:

\[ 3104.35 \times 24.666666666666668 = 76599.99999999997 \] (approximately \( 76600 \) dollars)

Now, let's plug this value into the equation:

\[ 262.85x + 76600 = 1399.45x + 1399.45 \times 24.666666666666668 \]

Let's calculate \( 1399.45 \times 24.666666666666668 \):

\[ 1399.45 \times 24.666666666666668 = 34532.99999999999 \] (approximately \( 34533 \) dollars)

Now, the equation becomes:

\[ 262.85x + 76600 = 1399.45x + 34533 \]

Let's move the terms involving \( x \) to one side and the constants to the other side:

\[ 76600 - 34533 = 1399.45x - 262.85x \]

\[ 42067 = 1136.6x \]

Now, let's solve for \( x \):

\[ x = \frac{42067}{1136.6} \]

\[ x \approx 37.02 \]

Therefore, the manager has opened approximately 37.02 litres of the mixed fruit juice.
개봉한 혼합 과일 주스의 양을 \( x \) 리터로 표시해 보겠습니다.

개봉한 혼합 과일 주스의 비용은 262.85달러입니다.

아사이 베리 주스를 추가한 비용은 3104.35달러입니다.

슈퍼푸드 주스 칵테일의 총 비용은 1399.45달러입니다.

문제에 따르면 혼합 과일 주스와 아사이 베리 주스의 비용은 칵테일의 총 비용에 합산되어야 합니다. 따라서 다음 방정식을 설정할 수 있습니다:

\[ 262.85x + 3104.35 \times 24.666666666666668 = 1399.45 \times (x + 24.666666666666668) \]

아사이 베리 주스를 추가한 비용을 계산해 보겠습니다:

\[ 3104.35 \times 24.666666666666668 = 76599.99999999997 \] (약 76600달러)

이제 이 값을 방정식에 대입해 보겠습니다:

\[ 262.85x + 76600 = 1399.45x + 1399.45 \times 24.666666666666668 \]

1399.45 \times 24.66666666666668 \):

\[ 1399.45 \times 24.66666666666668 = 34532.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999