Math Problem Statement

Fred is 4 times as old as Nathan and is also 27 years older than Nathan. Let f be Fred's age and let n be Nathan's age. Which system of equations represents this situation?

Solution

Let me analyze the image for the math problem. One moment, please. PIL import Image import pytesseract

Open the uploaded image

image_path = "/mnt/data/1738178986379u5askxmh.jpg" image = Image.open(image_path)

Use OCR to extract the text from the image

extracted_text = pytesseract.image_to_string(image) extracted_textThe OCR extraction didn't capture the mathematical text clearly. Let me refine my approach to focus on the specific mathematical content in the problem. One moment. Refining OCR with configuration for mathematical text custom_config = r'--psm 6' # Set OCR to treat the image as a single block of text refined_text = pytesseract.image_to_string(image, config=custom_config) refined_textThe refined OCR attempt still contains inaccuracies and noise, making it difficult to extract the math problem directly. However, from your provided context and partial text visible in the image, the problem is asking which system of equations best represents the relationship between Fred's and Nathan's ages.

The conditions are:

  1. Fred (ff) is 4 times as old as Nathan (nn): f=4nf = 4n.
  2. Fred (ff) is 27 years older than Nathan (nn): f=n+27f = n + 27.

Correct System of Equations:

f = 4n \\ f = n + 27 \end{cases}$$ This matches **option D**. Would you like a detailed explanation of why this is correct? --- ### Related Questions: 1. How can you solve this system of equations to find $$f$$ and $$n$$? 2. Why can't $$f = 4n$$ and $$n = f + 27$$ represent the situation correctly? 3. How would you graphically represent these equations to confirm the solution? 4. What happens if the age relationship changes (e.g., Fred is 3 times Nathan's age)? 5. How do you check if a solution satisfies both equations? --- ### Tip: When solving a system of equations, ensure the equations align with the problem's conditions—recheck verbal descriptions for clarity!

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations

Formulas

f = 4n
f = n + 27

Theorems

Solving Systems of Equations by Substitution

Suitable Grade Level

Grades 7-9