Phil (P) Has 7 More Chickens Than Cole (C). The Sum Of Their Chickens Is 19. Find The Number Of Chickens Each Person Has.${ P = [?] }$ { C = [?] \}

by ADMIN 150 views

Introduction

In this article, we will delve into a simple yet intriguing mathematical problem involving two individuals, Phil and Cole, and their respective number of chickens. The problem states that Phil has 7 more chickens than Cole, and the sum of their chickens is 19. Our goal is to find the number of chickens each person has.

Problem Statement

Let's denote the number of chickens Phil has as P and the number of chickens Cole has as C. We are given two pieces of information:

  1. Phil has 7 more chickens than Cole: P = C + 7
  2. The sum of their chickens is 19: P + C = 19

Step 1: Setting Up the Equations

We have two equations:

  1. P = C + 7
  2. P + C = 19

We can substitute the first equation into the second equation to eliminate P.

Step 2: Substituting and Simplifying

Substituting P = C + 7 into the second equation, we get:

(C + 7) + C = 19

Combine like terms:

2C + 7 = 19

Subtract 7 from both sides:

2C = 12

Divide both sides by 2:

C = 6

Step 3: Finding the Number of Chickens Phil Has

Now that we have found the number of chickens Cole has, we can find the number of chickens Phil has by substituting C = 6 into the first equation:

P = C + 7 P = 6 + 7 P = 13

Conclusion

In conclusion, Phil has 13 chickens, and Cole has 6 chickens. This problem demonstrates a simple yet effective approach to solving linear equations, which is a fundamental concept in mathematics.

Mathematical Concepts

This problem involves the following mathematical concepts:

  • Linear Equations: A linear equation is an equation in which the highest power of the variable(s) is 1. In this problem, we have two linear equations: P = C + 7 and P + C = 19.
  • Substitution Method: The substitution method is a technique used to solve systems of linear equations by substituting one equation into another.
  • Simplifying Equations: Simplifying equations involves combining like terms and performing arithmetic operations to isolate the variable(s).

Real-World Applications

This problem may seem trivial, but it demonstrates the importance of mathematical problem-solving skills in real-world applications. For example, in agriculture, farmers need to manage their chicken flocks, and understanding mathematical concepts like linear equations can help them make informed decisions.

Tips and Variations

  • Graphical Approach: This problem can also be solved graphically by plotting the two equations on a coordinate plane and finding the point of intersection.
  • System of Equations: This problem is a simple example of a system of linear equations. In real-world applications, systems of equations can be more complex and involve multiple variables.
  • Word Problems: This problem is a classic example of a word problem, which involves translating a real-world scenario into a mathematical equation.

Conclusion

Introduction

In our previous article, we solved the problem of Phil and Cole's chickens using linear equations. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the difference between Phil and Cole's chickens?

A: Phil has 7 more chickens than Cole.

Q: How many chickens do Phil and Cole have in total?

A: The sum of their chickens is 19.

Q: Can you show me the steps to solve the problem?

A: Here are the steps to solve the problem:

  1. Set up the equations: P = C + 7 and P + C = 19
  2. Substitute the first equation into the second equation: (C + 7) + C = 19
  3. Combine like terms: 2C + 7 = 19
  4. Subtract 7 from both sides: 2C = 12
  5. Divide both sides by 2: C = 6
  6. Find the number of chickens Phil has by substituting C = 6 into the first equation: P = C + 7 = 6 + 7 = 13

Q: What if I have more chickens than Phil and Cole combined?

A: If you have more chickens than Phil and Cole combined, you can still use the same method to solve the problem. Just set up the equations and follow the steps.

Q: Can I use a graphical approach to solve the problem?

A: Yes, you can use a graphical approach to solve the problem. Plot the two equations on a coordinate plane and find the point of intersection.

Q: What if I have a system of linear equations with multiple variables?

A: If you have a system of linear equations with multiple variables, you can use the same method to solve the problem. Just set up the equations and follow the steps.

Q: Can I use this method to solve other types of problems?

A: Yes, you can use this method to solve other types of problems that involve linear equations. Just set up the equations and follow the steps.

Q: What if I get stuck on a problem?

A: If you get stuck on a problem, try breaking it down into smaller steps or asking for help from a teacher or tutor.

Conclusion

In conclusion, this Q&A article provides answers to frequently asked questions related to Phil and Cole's chickens problem. By following the steps and using the graphical approach, you can solve this problem and many others that involve linear equations.

Mathematical Concepts

This problem involves the following mathematical concepts:

  • Linear Equations: A linear equation is an equation in which the highest power of the variable(s) is 1.
  • Substitution Method: The substitution method is a technique used to solve systems of linear equations by substituting one equation into another.
  • Simplifying Equations: Simplifying equations involves combining like terms and performing arithmetic operations to isolate the variable(s).
  • Graphical Approach: The graphical approach involves plotting the two equations on a coordinate plane and finding the point of intersection.

Real-World Applications

This problem may seem trivial, but it demonstrates the importance of mathematical problem-solving skills in real-world applications. For example, in agriculture, farmers need to manage their chicken flocks, and understanding mathematical concepts like linear equations can help them make informed decisions.

Tips and Variations

  • Word Problems: This problem is a classic example of a word problem, which involves translating a real-world scenario into a mathematical equation.
  • System of Equations: This problem is a simple example of a system of linear equations. In real-world applications, systems of equations can be more complex and involve multiple variables.
  • Graphical Approach: This problem can also be solved graphically by plotting the two equations on a coordinate plane and finding the point of intersection.