El promedio de las edades de 15 varones es 17 yla edad promedio de 14 mujeres es 16. Determi-na el promedio aritmético de las edades de to-das las personas.

1. Break Down the Problem

We need to find the average age of a group consisting of 15 men and 14 women. We will:

1. Calculate the total age of the men.
2. Calculate the total age of the women.
3. Sum the total ages of both groups.
4. Divide the total age by the total number of individuals.

2. Relevant Concepts

• The average (mean) is calculated by the formula:

$\text{Average} = \frac{\text{Total Sum of Values}}{\text{Number of Values}}$

3. Analysis and Detail

1. Calculate the total age of the men:

   • Average age of men = 17
   • Number of men = 15
   • Total age of men = $17 \times 15 = 255$

2. Calculate the total age of the women:

   • Average age of women = 16
   • Number of women = 14
   • Total age of women = $16 \times 14 = 224$

3. Calculate the total age of all individuals:

   • Total age of all individuals = Total age of men + Total age of women
   • Total age = $255 + 224 = 479$

4. Calculate the total number of individuals:

   • Total number of individuals = Number of men + Number of women
   • Total individuals = $15 + 14 = 29$

4. Verify and Summarize

Now, we can summarize the findings:

1. Total age of all individuals = 479
2. Total number of individuals = 29

Final Answer

The average age of all persons is:

$\text{Average} = \frac{479}{29} \approx 16.52$

Thus, the average age of all individuals is approximately 16.52 years.