Find three consecutive odd numbers where the sum of the last two is 85 more than the first.

To solve the problem of finding three consecutive odd numbers where the sum of the last two is 85 more than the first, we can define these numbers algebraically and set up an equation.

### Step-by-Step Solution:

1. **Define the three consecutive odd numbers:**

   Let the first odd number be \( x \).  
   Since they are consecutive odd numbers, the second number will be \( x + 2 \), and the third number will be \( x + 4 \).

2. **Formulate the equation:**

   According to the problem, the sum of the last two numbers (i.e., \( x + 2 \) and \( x + 4 \)) is 85 more than the first number \( x \). We can write this as:

   \[
   (x + 2) + (x + 4) = x + 85
   \]

3. **Simplify the equation:**

   Combine like terms:

   \[
   2x + 6 = x + 85
   \]

   Subtract \( x \) from both sides:

   \[
   x + 6 = 85
   \]

   Subtract 6 from both sides:

   \[
   x = 79
   \]

4. **Find the three consecutive odd numbers:**

   The first number is \( x = 79 \).  
   The second number is \( x + 2 = 81 \).  
   The third number is \( x + 4 = 83 \).

5. **Verify the solution:**

   Check if the sum of the last two numbers is 85 more than the first:

   \[
   (81 + 83) = 164, \quad \text{and} \quad 79 + 85 = 164.
   \]

   Since both sides are equal, the solution is correct.

### Conclusion:

The three consecutive odd numbers are **79, 81, and 83**.

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Would you like more details or have any questions?

### Related Questions:

1. What if the three consecutive numbers were even instead of odd?
2. How would the solution change if the numbers were consecutive multiples of 3?
3. Can you solve for three consecutive numbers where the sum of the first two is 50 more than the third?
4. What if the sum of all three numbers is given instead?
5. How do you find four consecutive odd numbers with a similar property?

### Tip:
When dealing with consecutive numbers, always define a single variable and express the others in terms of it to simplify your equations.

Solve the problem of finding three consecutive odd numbers where the sum of the last two numbers is 85 more than the first. This problem involves key algebraic concepts and linear equations, suitable for students in Grades 6-8.

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