Which real-world problem situation can be represented by the equation below?
 

14 = 4*x* - 10

A.Valerie's brother is 4 years less than 10 times her age. Her brother is 14 years old. How old is Valerie?

B.While playing a video game, Bradley received a bonus that quadrupled his score, then he received a 10-point penalty. He ended the game with a score of 14 points. What was Bradley’s original score?

C.Valerie‘s brother is 4 years less than 14 times her age. Her brother is 10 years old. How old is Valerie?

D.While playing a video game, Bradley received a bonus that quadrupled his score, then he received a 14-point bonus. He ended the game with a score of 10 points. What was Bradley’s original score?


Let's analyze the equation \( 14 = 4x - 10 \) in the context of the given options.

The equation can be interpreted as starting with a value \( x \), multiplying it by 4, and then subtracting 10 to get a final result of 14.

- **Option A**: "Valerie's brother is 4 years less than 10 times her age. Her brother is 14 years old. How old is Valerie?"  
  This option is incorrect because it involves multiplying Valerie's age by 10, not 4, and then subtracting 4, not 10.

- **Option B**: "While playing a video game, Bradley received a bonus that quadrupled his score, then he received a 10-point penalty. He ended the game with a score of 14 points. What was Bradley’s original score?"  
  This option correctly matches the equation. Bradley's original score is multiplied by 4, then 10 points are subtracted, leaving him with 14 points.

- **Option C**: "Valerie‘s brother is 4 years less than 14 times her age. Her brother is 10 years old. How old is Valerie?"  
  This option is incorrect because it incorrectly assigns the coefficients and constants in the equation.

- **Option D**: "While playing a video game, Bradley received a bonus that quadrupled his score, then he received a 14-point bonus. He ended the game with a score of 10 points. What was Bradley’s original score?"  
  This option is incorrect because it involves adding 14 points instead of subtracting 10.

**Correct Answer: Option B**  
The equation \( 14 = 4x - 10 \) corresponds to the situation described in Option B.

Do you have any questions or would you like further details? 

Here are 5 related questions for practice:
1. Which equation represents the situation: "A number is tripled and then decreased by 5 to get 16"?
2. If the equation \(2x + 8 = 18\) represents a real-world situation, what could that situation be?
3. What is the real-world situation for the equation \(5x + 3 = 28\)?
4. If a person's age is doubled and then increased by 7 to get 25, what is their age?
5. Which equation represents the situation where "5 less than twice a number equals 9"?

**Tip:** When translating real-world problems into equations, focus on the operations (addition, subtraction, multiplication, division) and the order in which they are applied to the unknown variable.

Explore how linear equations are used to solve real-world problems. This example focuses on interpreting and solving equations involving operations with algebraic expressions. Suitable for Grades 7-9 students.

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