Let's solve this step by step.

We are given that the average of 5 consecutive odd numbers is 35. To find the largest number, we can set up the problem as follows:

1. Let the 5 consecutive odd numbers be:

$x, x+2, x+4, x+6, x+8$

Where $x$ is the first number, and each subsequent number increases by 2 (since they are odd numbers).

2. Calculate the average of these 5 numbers:

The average is the sum of the numbers divided by the number of numbers. Since the average is 35, we set up the equation:

$\frac{x + (x+2) + (x+4) + (x+6) + (x+8)}{5} = 35$

3. Simplify the equation:

$\frac{5x + 20}{5} = 35$

$5x + 20 = 175$

4. Solve for $x$:

$5x = 175 - 20$

$5x = 155$

$x = \frac{155}{5} = 31$

So, the first number is $x = 31$.

5. Find the largest number:

The largest of the 5 consecutive odd numbers is $x + 8$. Since $x = 31$, the largest number is:

$31 + 8 = 39$

So, the largest number is 39.

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Would you like more details, or do you have any other questions?

Here are five related questions to consider:

1. How can we check if the average of 5 numbers really equals 35?
2. What if the numbers were consecutive even numbers instead of odd ones?
3. How would the solution change if the average was a different number, say 40?
4. What is the sum of these 5 consecutive odd numbers?
5. How would you solve the same problem if there were 7 consecutive odd numbers?

Tip: When dealing with averages, it's useful to write the numbers in terms of a variable (like $x$) to simplify solving equations.