Question

6 (a) trouve 3 nombres entiers consécutifs dont la somme est 75.

Explanation:

Part (a)

Step 1: Define the integers

Let the first integer be \( n \). Then the next consecutive integers are \( n + 1 \) and \( n + 2 \).

Step 2: Set up the equation

The sum of these three integers is 75, so we have the equation:

$$ n+(n + 1)+(n + 2)=75 $$

Step 3: Simplify and solve the equation

Simplify the left - hand side:

$$ n+n + 1+n + 2=75\\ 3n+3 = 75 $$

Subtract 3 from both sides:

$$ 3n=75 - 3\\ 3n=72 $$

Divide both sides by 3:

$$ n=\frac{72}{3}\\ n = 24 $$

Step 4: Find the other two integers

If \( n = 24 \), then \( n + 1=24 + 1 = 25 \) and \( n + 2=24+2 = 26 \)

Answer:

The three consecutive integers are 24, 25, and 26.