Substituting Equation 1 into Equation 2

Oct 13, 2025 by miodeya.com 121 views

Introduction

In this article, we will delve into a problem involving the ages of two individuals, Phil and Peter. We will use algebraic equations to represent the given information and then solve for Peter's age. The problem provides two pieces of information that can be translated into mathematical equations. Our goal is to identify the correct equations that represent the given situation and solve for Peter's age.

Problem Statement

Let's break down the problem statement into two parts:

Phil's age is 7 years more than ${$ \frac{1}{6}$}$ times Peter's age.
4 times Phil's age is 2 years less than twice Peter's age.

We are given that ${$ x$}$ represents Peter's age in years. Our task is to identify the correct equations that represent the given situation and solve for Peter's age.

Equation 1: Phil's Age is 7 Years More than ${$ \frac{1}{6}$}$ Times Peter's Age

Let's represent Phil's age as ${$ p$}$. According to the problem statement, Phil's age is 7 years more than ${$ \frac{1}{6}$}$ times Peter's age. We can write this as an equation:

${$ p = \frac{1}{6}x + 7$}$

This equation represents the relationship between Phil's age and Peter's age.

Equation 2: 4 Times Phil's Age is 2 Years Less than Twice Peter's Age

According to the problem statement, 4 times Phil's age is 2 years less than twice Peter's age. We can write this as an equation:

${ $4p = 2x - 2\$}$

This equation represents the relationship between Phil's age and Peter's age.

Solving the Equations

We have two equations that represent the given situation:

${$ p = \frac{1}{6}x + 7$}$
${ $4p = 2x - 2\$}$

We can solve these equations simultaneously to find the value of ${$ x$}$, which represents Peter's age.

Substituting Equation 1 into Equation 2

We can substitute the expression for ${$ p$}$ from Equation 1 into Equation 2:

${ $4(\frac{1}{6}x + 7) = 2x - 2\$}$

Simplifying the equation, we get:

${$ \frac{2}{3}x + 28 = 2x - 2$}$

Solving for ${$ x$}$

We can solve for ${$ x$}$ by isolating the variable:

${$ \frac{2}{3}x - 2x = -2 - 28$}$

Combining like terms, we get:

${$ -\frac{4}{3}x = -30$}$

Multiplying both sides by ${-\frac{3}{4}\$}$ , we get:

${$ x = 22.5$}$

Therefore, Peter's age is 22.5 years.

Conclusion

In this article, we used algebraic equations to represent the given information and solve for Peter's age. We identified the correct equations that represent the given situation and solved for ${$ x$}$, which represents Peter's age. The final answer is ${$ x = 22.5$}$.

References

Introduction

In our previous article, we solved the age problem involving Phil and Peter using algebraic equations. We identified the correct equations that represent the given situation and solved for Peter's age. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the relationship between Phil's age and Peter's age?

A: According to the problem statement, Phil's age is 7 years more than ${$ \frac{1}{6}$}$ times Peter's age. This can be represented by the equation:

${$ p = \frac{1}{6}x + 7$}$

Q: How can we represent the relationship between Phil's age and Peter's age using an equation?

A: We can represent the relationship between Phil's age and Peter's age using the equation:

${ $4p = 2x - 2\$}$

This equation represents the relationship between Phil's age and Peter's age.

Q: How can we solve the equations simultaneously to find the value of ${$ x$}$?

A: We can solve the equations simultaneously by substituting the expression for ${$ p$}$ from Equation 1 into Equation 2:

${ $4(\frac{1}{6}x + 7) = 2x - 2\$}$

Simplifying the equation, we get:

${$ \frac{2}{3}x + 28 = 2x - 2$}$

Q: What is the final answer for Peter's age?

A: The final answer for Peter's age is ${$ x = 22.5$}$.

Q: Can we use other methods to solve the equations?

A: Yes, we can use other methods to solve the equations, such as substitution or elimination. However, the method we used in this article is a straightforward and efficient way to solve the equations.

Q: What are some common mistakes to avoid when solving equations?

A: Some common mistakes to avoid when solving equations include:

Not reading the problem carefully and understanding the relationships between the variables.
Not using the correct equations to represent the given situation.
Not simplifying the equations correctly.
Not checking the solutions for validity.

Q: How can we apply the concepts learned in this article to real-life situations?

A: The concepts learned in this article can be applied to real-life situations involving relationships between variables. For example, we can use algebraic equations to model the relationships between the variables in a business or economics problem.

Conclusion

In this article, we answered some frequently asked questions related to the age problem involving Phil and Peter. We provided explanations and examples to help clarify the concepts and methods used to solve the equations. We hope this article has been helpful in understanding the relationships between variables and solving equations.