The Age Of A Father Is 2 Less Than 7 Times The Age Of His Son. In 3 Years, The Sum Of Their Ages Will Be 52. If The Son's Present Age Is S S S Years, Which Equation Models This Situation? A. ( S + 3 ) + [ ( 7 S − 2 ) + 3 ] = 52 (s+3)+[(7s-2)+3]=52 ( S + 3 ) + [( 7 S − 2 ) + 3 ] = 52 B.

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Introduction

In this article, we will explore a mathematical problem involving the ages of a father and son. The problem states that the age of the father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. We will use algebraic equations to model this situation and find the equation that represents the relationship between the son's present age and the sum of their ages in 3 years.

The Problem

Let's denote the son's present age as ss years. The problem states that the father's age is 2 less than 7 times the son's age. This can be represented as:

Father's age = 7s - 2

In 3 years, the son's age will be s+3s + 3 years, and the father's age will be (7s−2)+3(7s - 2) + 3 years. The sum of their ages in 3 years will be 52. This can be represented as:

(s+3)+[(7s−2)+3]=52(s + 3) + [(7s - 2) + 3] = 52

Modeling the Situation

To model this situation, we need to create an equation that represents the relationship between the son's present age and the sum of their ages in 3 years. Let's analyze the equation:

(s+3)+[(7s−2)+3]=52(s + 3) + [(7s - 2) + 3] = 52

This equation represents the sum of the son's age in 3 years and the father's age in 3 years, which is equal to 52.

Simplifying the Equation

To simplify the equation, we can combine like terms:

s+3+7s−2+3=52s + 3 + 7s - 2 + 3 = 52

Combine the ss terms:

8s+4=528s + 4 = 52

Subtract 4 from both sides:

8s=488s = 48

Divide both sides by 8:

s=6s = 6

Conclusion

The equation that models this situation is:

(s+3)+[(7s−2)+3]=52(s + 3) + [(7s - 2) + 3] = 52

This equation represents the relationship between the son's present age and the sum of their ages in 3 years. By simplifying the equation, we found that the son's present age is 6 years.

Discussion

This problem is a classic example of a linear equation in one variable. The equation is a simple linear equation that can be solved using basic algebraic techniques. The problem requires the student to analyze the situation, create an equation, and solve for the unknown variable.

Final Answer

The final answer is:

A. (s+3)+[(7s−2)+3]=52(s+3)+[(7s-2)+3]=52

This equation models the situation described in the problem.

Introduction

In our previous article, we explored a mathematical problem involving the ages of a father and son. The problem states that the age of the father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. We used algebraic equations to model this situation and found the equation that represents the relationship between the son's present age and the sum of their ages in 3 years.

Q&A

Q: What is the equation that models the situation?

A: The equation that models this situation is:

(s+3)+[(7s−2)+3]=52(s + 3) + [(7s - 2) + 3] = 52

This equation represents the relationship between the son's present age and the sum of their ages in 3 years.

Q: How do I simplify the equation?

A: To simplify the equation, you can combine like terms. First, combine the ss terms:

s+3+7s−2+3=52s + 3 + 7s - 2 + 3 = 52

Then, combine the constants:

8s+4=528s + 4 = 52

Subtract 4 from both sides:

8s=488s = 48

Divide both sides by 8:

s=6s = 6

Q: What is the son's present age?

A: The son's present age is 6 years.

Q: How do I know if the equation is correct?

A: To check if the equation is correct, you can plug in the value of ss into the equation and see if it is true. If the equation is true, then the equation is correct.

Q: What is the significance of the equation?

A: The equation represents the relationship between the son's present age and the sum of their ages in 3 years. This equation can be used to model similar situations where the ages of two people are related.

Q: Can I use this equation to solve other problems?

A: Yes, you can use this equation to solve other problems where the ages of two people are related. Simply substitute the values of the variables into the equation and solve for the unknown variable.

Conclusion

In this article, we answered some common questions about the equation that models the situation involving the ages of a father and son. We also provided a step-by-step guide on how to simplify the equation and find the son's present age. This equation can be used to model similar situations where the ages of two people are related.

Final Answer

The final answer is:

A. (s+3)+[(7s−2)+3]=52(s+3)+[(7s-2)+3]=52

This equation models the situation described in the problem.

Additional Resources

Discussion

This problem is a classic example of a linear equation in one variable. The equation is a simple linear equation that can be solved using basic algebraic techniques. The problem requires the student to analyze the situation, create an equation, and solve for the unknown variable.

Final Thoughts

In conclusion, the equation that models the situation involving the ages of a father and son is a simple equation that can be solved using basic algebraic techniques. This equation can be used to model similar situations where the ages of two people are related.