The sum of three consecutive integers is 417. Let n be the first one. Write and solve an equation that will determine the three integers.

they are n, n+1 and n+2

n+n+1+n+2 = 417
or
3 n +3 = 417

3 n = 414

n = 138

138
139
140

Let's set up the equation as follows:

n + (n+1) + (n+2) = 417.

Now let's solve the equation step by step:

1. Combine like terms:
3n + 3 = 417.
3n = 417 - 3.
3n = 414.

2. Divide both sides by 3:
n = 414 / 3.
n = 138.

Therefore, the three consecutive integers are 138, 139, and 140.

To solve this problem, we need to write an equation based on the given information and then solve it.

Let's assume that n is the first integer. Since we are dealing with consecutive integers, the second integer would be n + 1, and the third integer would be n + 2.

The sum of these three consecutive integers is 417, so we can write the equation as:

n + (n + 1) + (n + 2) = 417.

Now we can solve this equation to find the value of n.

Combining like terms, we have:

3n + 3 = 417.

To isolate the variable term, we subtract 3 from both sides:

3n = 414.

Finally, to find the value of n, we divide both sides by 3:

n = 138.

Therefore, the first integer is 138, the second integer is 138 + 1 = 139, and the third integer is 138 + 2 = 140.