The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?

Options

A. 4.5
B. 4.6
C. 4.7
D. 4.8

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total sum of the six numbers
The average of six numbers is given as 3.95. To find the total sum of these six numbers, we can use the formula:

\[ \text{Total Sum} = \text{Average} \times \text{Number of Items} \]

So, we calculate:

\[ \text{Total Sum} = 3.95 \times 6 = 23.7 \]

### Step 2: Calculate the sum of the first two numbers
The average of the first two numbers is given as 3.4. We can find their total sum using the same formula:

\[ \text{Sum of First Two Numbers} = 3.4 \times 2 = 6.8 \]

### Step 3: Calculate the sum of the second two numbers
The average of the second two numbers is given as 3.85. We can find their total sum as follows:

\[ \text{Sum of Second Two Numbers} = 3.85 \times 2 = 7.7 \]

### Step 4: Find the sum of the remaining two numbers
Now, we can find the sum of the remaining two numbers (let's call them E and F) by subtracting the sums of the first four numbers from the total sum of all six numbers:

\[ \text{Sum of Remaining Two Numbers} = \text{Total Sum} - (\text{Sum of First Two Numbers} + \text{Sum of Second Two Numbers}) \]

Substituting the values we have:

\[ \text{Sum of Remaining Two Numbers} = 23.7 - (6.8 + 7.7) = 23.7 - 14.5 = 9.2 \]

### Step 5: Calculate the average of the remaining two numbers
Finally, we can find the average of the remaining two numbers by dividing their total sum by 2:

\[ \text{Average of Remaining Two Numbers} = \frac{\text{Sum of Remaining Two Numbers}}{2} = \frac{9.2}{2} = 4.6 \]

### Final Answer:
The average of the remaining two numbers is **4.6**.

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