The problem asks us to find the largest of three consecutive odd integers that sum to 45.

1. Problem Description

The problem asks us to find the largest of three consecutive odd integers that sum to

4

5.

2. Solution Steps

Let $x$ be the first odd integer. Then the next two consecutive odd integers are $x+2$ and $x+4$.

We are given that their sum is

4

5. Therefore, we can write the equation:

$x + (x+2) + (x+4) = 45$

Combine the terms:

$3x + 6 = 45$

Subtract 6 from both sides:

$3x = 45 - 6$

$3x = 39$

Divide by 3:

$x = \frac{39}{3}$

$x = 13$

So the three consecutive odd integers are 13, 15, and

1

7. The largest of these three integers is

1

7.

3. Final Answer

17