To solve the problem using Polya's four-step problem-solving method, we will proceed as follows:

Problem Statement:

The problem is to find three consecutive odd integers such that their sum is 27.

Step 1: Understand the Problem

We need to find three consecutive odd integers. Let's define these integers:

• Let the first odd integer be $x$.
• The next consecutive odd integer will be $x + 2$.
• The third consecutive odd integer will be $x + 4$.

The problem states that their sum is equal to 27: $x + (x + 2) + (x + 4) = 27$

Step 2: Devise a Plan

Our plan is to set up an equation based on the sum of these integers and then solve for $x$. Once we find $x$, we'll substitute it to find all three integers.

Step 3: Carry Out the Plan

Let's simplify the equation: $x + (x + 2) + (x + 4) = 27$ Combine like terms: $3x + 6 = 27$ Subtract 6 from both sides: $3x = 21$ Divide by 3: $x = 7$

Now, substitute $x = 7$ into the expressions for the three integers:

• First integer: $7$
• Second integer: $7 + 2 = 9$
• Third integer: $7 + 4 = 11$

Step 4: Look Back (Check the Solution)

To verify the solution, we check if the sum of these integers is indeed 27: $7 + 9 + 11 = 27$ The solution is correct.

Solution

The three consecutive odd integers are $7$, $9$, and $11$.

Would you like more details or have any questions about the solution process?

Related Questions

1. What are Polya's four steps for problem-solving in mathematics?
2. How do you solve problems involving consecutive even integers?
3. What other methods can be used to solve problems like this one?
4. How would the approach change if the sum was given as 30 instead of 27?
5. Can this problem be solved using a different algebraic approach?

Tip

When dealing with consecutive integers, always express them in terms of the first integer to simplify the algebraic setup.