from 1 to an integer greater than 2. Today he calculates the average of the other house numbers (every house except his own) and adds his age to this average. The result is the fractional number 20.16 (or 20 + 16/100 ) Today is Benoît's birthday. What is Benoît's age?

Let's define the following:

- \( n \) is the total number of houses.
- \( x_1, x_2, \dots, x_n \) represent the house numbers.
- \( x_b \) is Benoît's house number.
- Benoît's age is \( a \).

Benoît calculates the average of all house numbers except his own, adds his age to this average, and gets \( 20.16 \), which is \( 20 + \frac{16}{100} = \frac{2016}{100} = \frac{504}{25} \).

The sum of all house numbers except Benoît's is:

\[
S - x_b
\]
where \( S \) is the sum of all house numbers \( x_1 + x_2 + \dots + x_n \), and the average of the other house numbers is:

\[
\frac{S - x_b}{n - 1}
\]

Benoît adds his age to this average:

\[
a + \frac{S - x_b}{n - 1} = \frac{504}{25}
\]

Thus, the equation becomes:

\[
a + \frac{S - x_b}{n - 1} = \frac{504}{25}
\]

This is the main equation we'll use to find \( a \), Benoît's age.

Since \( S \) and \( x_b \) depend on the house numbers, which are not directly given, we'll approach this by making assumptions about \( n \) (the number of houses) and using integer house numbers.

Would you like to explore different values of \( n \) to solve this equation, or is there a specific direction you'd like to take?

From 1 to an integer greater than 2. Today he calculates the average of the other house numbers (every house except his own) and adds his age to this average. The result is the fractional number 20.16 (or 20 + 16/100). Today is Benoît's birthday. What is Benoît's age?

Discover how to solve for Benoît's age using a real-world problem involving averages and linear equations. Learn how to apply the average formula and solve for unknowns in this engaging algebra problem, perfect for students in Grades 8-10.

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