Average age of 6 boys is 14 years. Average age of 11 girls is 12 years. What is the average age (in years) of all boys and girls?

Options

A. 12.7
B. 14.6
C. 19.3
D. 8.5

Answer

To find the average age of all boys and girls, we can follow these steps:

### Step 1: Calculate the total age of the boys.
Given that the average age of 6 boys is 14 years, we can find the total age of the boys by multiplying the average age by the number of boys.

\[ \text{Total age of boys} = \text{Average age of boys} \times \text{Number of boys} = 14 \times 6 = 84 \text{ years} \]

### Step 2: Calculate the total age of the girls.
Similarly, for the girls, the average age is 12 years for 11 girls. We can find the total age of the girls in the same way.

\[ \text{Total age of girls} = \text{Average age of girls} \times \text{Number of girls} = 12 \times 11 = 132 \text{ years} \]

### Step 3: Calculate the total age of all boys and girls.
Now, we can find the total age of all boys and girls by adding the total ages we calculated in the previous steps.

\[ \text{Total age of all boys and girls} = \text{Total age of boys} + \text{Total age of girls} = 84 + 132 = 216 \text{ years} \]

### Step 4: Calculate the total number of boys and girls.
Next, we need to find the total number of boys and girls.

\[ \text{Total number of boys and girls} = \text{Number of boys} + \text{Number of girls} = 6 + 11 = 17 \]

### Step 5: Calculate the average age of all boys and girls.
Finally, we can find the average age of all boys and girls by dividing the total age by the total number of boys and girls.

\[ \text{Average age of all boys and girls} = \frac{\text{Total age of all boys and girls}}{\text{Total number of boys and girls}} = \frac{216}{17} \approx 12.71 \text{ years} \]

### Final Answer:
The average age of all boys and girls is approximately **12.71 years**.

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