The problem states that the sum of 5 consecutive odd integers is 75. We need to find the largest of these 5 integers.

1. Problem Description

The problem states that the sum of 5 consecutive odd integers is

7

5. We need to find the largest of these 5 integers.

2. Solution Steps

Let $n$ be the first odd integer. Since the integers are consecutive odd integers, the other four integers are $n+2$, $n+4$, $n+6$, and $n+8$. The sum of these five integers is given as

7

5. Therefore, we can write the equation:

$n + (n+2) + (n+4) + (n+6) + (n+8) = 75$

Combining like terms, we have:

$5n + 20 = 75$

Subtracting 20 from both sides:

$5n = 75 - 20$

$5n = 55$

Dividing both sides by 5:

$n = \frac{55}{5}$

$n = 11$

Now we find the five consecutive odd integers:

$n = 11$

$n+2 = 11+2 = 13$

$n+4 = 11+4 = 15$

$n+6 = 11+6 = 17$

$n+8 = 11+8 = 19$

The five consecutive odd integers are 11, 13, 15, 17, and

1

9. The largest of these is

1

9.

3. Final Answer

19