The sum of four consecutive odd integers is 296 .What is the greatest of the four consecutive oddintegers?

Let's solve this step by step:

Step 1: Let's denote the four consecutive odd integers as x, x+2, x+4, and x+6. They are consecutive odd integers, so each number is 2 more than the previous one.

Step 2: According to the problem, the sum of these four integers is 296. So, we can set up the following equation:

x + (x+2) + (x+4) + (x+6) = 296

Step 3: Simplify the equation:

4x + 12 = 296

Step 4: Subtract 12 from both sides of the equation:

4x = 284

Step 5: Divide both sides of the equation by 4:

x = 71

So, the smallest of the four consecutive odd integers is 71.

Step 6: To find the greatest of the four consecutive odd integers, we add 6 to x:

71 + 6 = 77

So, the greatest of the four consecutive odd integers is 77.