Consecutive Integer Problems Lesson Plans & Worksheets - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Word Problems: Consecutive Integer Problems" with 15 problems related to consecutive integers. However, since I can't view or access images directly, I cannot see the actual content of the image.

But based on your description and the visible text in your message, here's what I can infer:

The worksheet asks students to solve various word problems involving consecutive integers, such as:
- Consecutive integers (e.g., x, x+1, x+2)
- Consecutive even integers (e.g., x, x+2, x+4)
- Consecutive odd integers (e.g., x, x+2, x+4)

Each problem likely gives a condition (like sum, product, or difference) and asks for the integers that satisfy it.

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Example Problem & Solution Format

Let me demonstrate how to solve one typical type of problem from this list so you understand the method.

#### Example Problem:
> Find three consecutive integers whose sum is 30.

Step-by-step solution:

1. Let the first integer be \( x \).
2. Then the next two consecutive integers are \( x+1 \) and \( x+2 \).
3. Their sum is:
\[
x + (x+1) + (x+2) = 30
\]
4. Simplify:
\[
3x + 3 = 30
\]
5. Subtract 3:
\[
3x = 27
\]
6. Divide by 3:
\[
x = 9
\]
7. So the integers are: 9, 10, 11

✔ Check: 9 + 10 + 11 = 30 → Correct!

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Now, let’s go through a few more types of problems based on common patterns:

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Type 1: Consecutive Integers (odd/even/regular)

Problem: Find two consecutive integers whose sum is 15.

Solution:
- Let the integers be \( x \) and \( x+1 \)
- \( x + (x+1) = 15 \)
- \( 2x + 1 = 15 \)
- \( 2x = 14 \)
- \( x = 7 \)
- Answer: 7 and 8

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Type 2: Consecutive Even Integers

Problem: Find two consecutive even integers whose sum is 26.

Solution:
- Let the integers be \( x \) and \( x+2 \)
- \( x + (x+2) = 26 \)
- \( 2x + 2 = 26 \)
- \( 2x = 24 \)
- \( x = 12 \)
- Answer: 12 and 14

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Type 3: Consecutive Odd Integers

Problem: Find two consecutive odd integers whose sum is 32.

Solution:
- Let the integers be \( x \) and \( x+2 \)
- \( x + (x+2) = 32 \)
- \( 2x + 2 = 32 \)
- \( 2x = 30 \)
- \( x = 15 \)
- Answer: 15 and 17

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Type 4: Product of Two Consecutive Integers

Problem: Find two consecutive integers whose product is 56.

Solution:
- Let integers be \( x \) and \( x+1 \)
- \( x(x+1) = 56 \)
- \( x^2 + x - 56 = 0 \)
- Factor: \( (x+8)(x-7) = 0 \)
- So \( x = -8 \) or \( x = 7 \)
- Two possible pairs: -8, -7 or 7, 8
- Check: (-8)(-7) = 56 ✔, (7)(8) = 56 ✔

So both are valid unless restricted to positive numbers.

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If you provide the text version of the problems (or describe them), I can help solve each one step-by-step.

Alternatively, if you want me to explain how to approach all 15 problems, I can give you a general strategy for each type.

Would you like me to:
1. Solve all 15 problems assuming standard wording?
2. Explain how to solve any specific problem?
3. Help you set up equations for a particular problem?

Please reply with either:
- The full text of the problems,
- Or tell me which ones you'd like solved.

I'm ready to help!