The problem asks for four consecutive odd integers that add up to 312.

Let's define the integers as follows:

• Let the first odd integer be $x$.
• The next consecutive odd integers are $x + 2$, $x + 4$, and $x + 6$.

The sum of these four integers is given by: $x + (x + 2) + (x + 4) + (x + 6) = 312$

Simplifying the equation: $4x + 12 = 312$

Now, subtract 12 from both sides: $4x = 300$

Finally, divide by 4: $x = 75$

Thus, the four consecutive odd integers are: $75, 77, 79, 81$

Would you like further details or have any questions?

Here are 5 relative questions for practice:

1. What is the sum of four consecutive even integers that add up to 400?
2. How would the approach change if the integers were consecutive even integers instead of odd?
3. Can you derive a general formula for the sum of four consecutive odd numbers?
4. What happens if we are asked for three consecutive odd numbers instead of four?
5. How do we handle cases where the sum isn't a multiple of four? Can there still be consecutive odd numbers that satisfy the equation?

Tip: For consecutive integers, using variables like $x, x+2, x+4$, etc., simplifies solving such problems.