Question

1. at a certain summer camp there are ten 9-year-olds, six 12-year-olds, and three 11-year-olds. what is the average age of the campers?

Explanation:

Step1: Calculate total age

To find the total age, we multiply the number of campers by their respective ages and sum them up.
For 9 - year - olds: There are 10 campers, so the total age contribution is \(10\times9 = 90\).
For 12 - year - olds: There are 6 campers, so the total age contribution is \(6\times12=72\).
For 11 - year - olds: There are 3 campers, so the total age contribution is \(3\times11 = 33\).
The total age of all campers is \(90 + 72+33=195\).

Step2: Calculate total number of campers

The total number of campers is the sum of the number of 9 - year - olds, 12 - year - olds, and 11 - year - olds.
So, total number of campers \(=10 + 6+3=19\).

Step3: Calculate the average age

The formula for the average (mean) is \(\text{Average}=\frac{\text{Total Age}}{\text{Total Number of Campers}}\).
Substituting the values we found: \(\text{Average}=\frac{195}{19}\approx10.26\) (rounded to two decimal places) or as a fraction \(\frac{195}{19}\). If we want a mixed number, \(\frac{195}{19}=10\frac{5}{19}\).

Answer:

The average age of the campers is \(\frac{195}{19}\) (or approximately \(10.26\) years old)