A.Write and solve an equation to find three consecutive integers with a sum of 126. Let n= the first integer.

B. In part A, could you solve the problem by letting n= the middle integer,n-1= the smallest integer, and n+1= the largest integer?

A. To find three consecutive integers with a sum of 126, we can assign the first integer as 'n'. The next two consecutive integers would be 'n + 1' and 'n + 2'.

So, the equation representing the sum of these three consecutive integers is:
n + (n + 1) + (n + 2) = 126

Now, let's solve the equation:
Combine like terms:
3n + 3 = 126

Subtract 3 from both sides:
3n = 123

Divide by 3:
n = 41

Therefore, the three consecutive integers are 41, 42, and 43.

B. Yes, we can also solve the problem by letting 'n' represent the middle integer, 'n - 1' represent the smallest integer, and 'n + 1' represent the largest integer.

In this case, the equation representing the sum of these three consecutive integers is still:
(n - 1) + n + (n + 1) = 126

Now, let's solve the equation:
Combine like terms:
3n = 126

Divide by 3:
n = 42

Therefore, the three consecutive integers are 41, 42, and 43, which are the same integers as in the previous solution.