https://file.aiquickdraw.com/mathbot/file/1726972580963cnt9wmki.jpg

The problem provided involves two consecutive positive integers, where the square of the second integer added to six times the first integer equals 85. We are tasked with setting up the correct equation for this word problem.

Let’s define the two consecutive integers:

- First integer: \( x \)
- Second integer: \( x + 1 \)

According to the problem, the equation should be:

\[
6x + (x + 1)^2 = 85
\]

This equation states that 6 times the first integer (\( x \)) plus the square of the second integer (\( (x + 1)^2 \)) is equal to 85.

The correct answer is:

\[
6x + (x + 1)^2 = 85
\]

This matches the option you have selected in the image.

---

Would you like further explanation on how to solve this equation? Here are some related questions to consider:

1. What steps would you take to solve the equation \( 6x + (x + 1)^2 = 85 \)?
2. How do we expand the term \( (x + 1)^2 \)?
3. What are consecutive integers, and why does the second integer equal \( x + 1 \)?
4. How can we verify the solution to this equation once found?
5. What other types of problems involve consecutive integers?

**Tip:** When solving equations involving squares, always check for extraneous solutions by plugging the result back into the original equation.

Consider two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 85. Set up an equation to solve the given word problem.

Learn how to set up and solve an equation involving two consecutive integers where the square of the second integer added to six times the first equals 85. This problem covers key algebraic concepts and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation