The Sum Of Two Numbers Is 28. The First Number Is 7 More Than Twice The Second Number. Let { A $}$ Represent The First Number. Let { B $}$ Represent The Second Number. What Is The Second Number?Use The Table To Guess And
Introduction
In this article, we will delve into a mathematical puzzle that involves two unknown numbers. The sum of these two numbers is given as 28, and we are provided with a relationship between the two numbers. Our goal is to find the value of the second number. We will use algebraic techniques to solve this problem and provide a step-by-step solution.
Problem Statement
Let { a $}$ represent the first number and { b $}$ represent the second number. The sum of the two numbers is 28, which can be expressed as:
Additionally, we are given that the first number is 7 more than twice the second number, which can be expressed as:
Using Algebra to Solve the Problem
We can use algebraic techniques to solve this problem. Let's start by substituting the expression for { a $}$ into the equation { a + b = 28 $}$. This will give us an equation in terms of { b $}$ only.
Combine like terms:
Subtract 7 from both sides:
Divide both sides by 3:
Discussion
The solution to this problem is { b = 7 $}$. This means that the second number is 7. We can verify this solution by substituting { b = 7 $}$ into the equation { a = 2b + 7 $}$. This gives us:
Substituting { a = 21 $}$ and { b = 7 $}$ into the equation { a + b = 28 $}$ also verifies the solution:
Conclusion
In this article, we used algebraic techniques to solve a mathematical puzzle involving two unknown numbers. We were given the sum of the two numbers and a relationship between the two numbers. By substituting the expression for the first number into the equation for the sum, we were able to solve for the second number. The solution to this problem is { b = 7 $}$, which means that the second number is 7.
Table of Contents
Mathematical Formulas
Variables
- : the first number
- : the second number
The Sum of Two Numbers: A Mathematical Puzzle - Q&A =====================================================
Introduction
In our previous article, we solved a mathematical puzzle involving two unknown numbers. The sum of the two numbers was given as 28, and we were provided with a relationship between the two numbers. We used algebraic techniques to solve for the second number, which was found to be 7. In this article, we will answer some frequently asked questions (FAQs) related to this problem.
Q&A
Q: What is the first number in the problem?
A: The first number is represented by the variable { a $}$. We found that { a = 21 $}$ in our previous solution.
Q: How did you find the value of the second number?
A: We used algebraic techniques to solve for the second number. We started by substituting the expression for the first number into the equation for the sum. This gave us an equation in terms of the second number only, which we could then solve.
Q: What is the relationship between the two numbers?
A: The first number is 7 more than twice the second number. This can be expressed as:
Q: Can you explain the steps to solve the problem?
A: Here are the steps to solve the problem:
- Write down the equation for the sum of the two numbers:
- Substitute the expression for the first number into the equation:
- Combine like terms:
- Subtract 7 from both sides:
- Divide both sides by 3:
Q: What if I get stuck on a problem like this?
A: Don't worry! If you get stuck on a problem like this, try breaking it down into smaller steps. Write down the equation and try to identify the variables and constants. Then, try to substitute the expression for one variable into the equation and see if you can solve for the other variable.
Q: Can I use this method to solve other problems?
A: Yes, you can use this method to solve other problems that involve algebraic equations. Just remember to identify the variables and constants, and try to substitute the expression for one variable into the equation to solve for the other variable.
Conclusion
In this article, we answered some frequently asked questions related to the mathematical puzzle involving two unknown numbers. We provided step-by-step solutions to the problem and explained the relationship between the two numbers. We also offered tips and advice for solving similar problems.
Table of Contents
Mathematical Formulas
Variables
- : the first number
- : the second number
Tips and Advice
- Break down complex problems into smaller steps
- Identify the variables and constants in an equation
- Substitute the expression for one variable into the equation to solve for the other variable
- Use algebraic techniques to solve equations