Calculating Marbles in Bags: Determining the 9 Count from an Average of 9.64

Each bag of marbles contains an average of $9.64$ marbles.

The first bag has 18 marbles, another two have 12 marbles, and the last three have 7 marbles.

How many bags contain 9 marbles?

To solve this problem, we'll follow these steps:

• Step 1: Identify the number of bags and compute the total number of marbles.
• Step 2: Apply the formula for the average and solve for the unknown.
• Step 3: Solve the equation to determine the number of bags containing 9 marbles.

Let's work through these steps:

Step 1: The problem details that the average number of marbles per bag is 9.64. We need to find the total number of bags. Let $n$ be the number of bags that contain 9 marbles. Calculating the total number of bags is necessary as a starting point.

Given bags and their marbles:
- 1 bag containing 18 marbles
- 2 bags containing 12 marbles each: Total $= 2 \times 12 = 24$ marbles
- 3 bags containing 7 marbles each: Total $= 3 \times 7 = 21$ marbles

Total marbles in known bags = $18 + 24 + 21 = 63$ marbles

Step 2: Use the total average calculation to find the number of bags:

Total marbles = $63 + 9n$

The number of total bags is $1 + 2 + 3 + n = 6 + n$.

Thus, by the average formula:

Step 3: Solve for $n$.

Subtract $57.84$ from both sides:

Divide by 0.64 to solve for $n$:

This result implies rounding is needed, thus $n = 8$ bags.

Therefore, the solution to the problem is $8$ bags.