The Sum Of Two Numbers Is -16. One Number Is 20 Less Than The Other. Find The Two Numbers.A) -2 And 8 B) -18 And 2 C) -36 And 20 D) -12 And 4
Introduction
Mathematics is a fascinating subject that involves solving problems and puzzles using logical reasoning and mathematical concepts. In this article, we will explore a classic mathematical puzzle that involves finding two numbers whose sum is -16, with one number being 20 less than the other. This puzzle requires the application of algebraic equations and logical thinking to arrive at the correct solution.
The Problem Statement
The problem statement is as follows:
"The sum of two numbers is -16. One number is 20 less than the other."
Let's denote the two numbers as x and y, where x is the larger number and y is the smaller number. We can write the given information as two equations:
- x + y = -16 (The sum of the two numbers is -16)
- x = y - 20 (One number is 20 less than the other)
Solving the Equations
To solve the equations, we can use the substitution method. We can substitute the expression for x from equation (2) into equation (1):
y - 20 + y = -16
Combine like terms:
2y - 20 = -16
Add 20 to both sides:
2y = 4
Divide both sides by 2:
y = 2
Now that we have found the value of y, we can substitute it into equation (2) to find the value of x:
x = y - 20 x = 2 - 20 x = -18
Checking the Solution
Let's check our solution by plugging the values of x and y back into the original equations:
-
x + y = -16 -18 + 2 = -16 (True)
-
x = y - 20 -18 = 2 - 20 (True)
Our solution satisfies both equations, so we can conclude that the two numbers are indeed -18 and 2.
Conclusion
In this article, we have solved a classic mathematical puzzle involving two numbers whose sum is -16, with one number being 20 less than the other. We used algebraic equations and logical thinking to arrive at the correct solution, which is -18 and 2. This puzzle requires a deep understanding of algebraic equations and logical reasoning, making it an excellent example of a mathematical problem that requires critical thinking.
Frequently Asked Questions
Q: What is the sum of the two numbers?
A: The sum of the two numbers is -16.
Q: What is the relationship between the two numbers?
A: One number is 20 less than the other.
Q: How do we solve the equations?
A: We use the substitution method to solve the equations.
Q: What is the value of x?
A: The value of x is -18.
Q: What is the value of y?
A: The value of y is 2.
Step-by-Step Solution
Step 1: Write the given information as two equations
x + y = -16 x = y - 20
Step 2: Substitute the expression for x from equation (2) into equation (1)
y - 20 + y = -16
Step 3: Combine like terms
2y - 20 = -16
Step 4: Add 20 to both sides
2y = 4
Step 5: Divide both sides by 2
y = 2
Step 6: Substitute the value of y into equation (2) to find the value of x
x = y - 20 x = 2 - 20 x = -18
Final Answer
The final answer is -18 and 2.
Introduction
In our previous article, we solved a classic mathematical puzzle involving two numbers whose sum is -16, with one number being 20 less than the other. We used algebraic equations and logical thinking to arrive at the correct solution, which is -18 and 2. In this article, we will provide a Q&A section to help readers understand the solution and answer any questions they may have.
Q&A
Q: What is the sum of the two numbers?
A: The sum of the two numbers is -16.
Q: What is the relationship between the two numbers?
A: One number is 20 less than the other.
Q: How do we solve the equations?
A: We use the substitution method to solve the equations.
Q: What is the value of x?
A: The value of x is -18.
Q: What is the value of y?
A: The value of y is 2.
Q: Can you explain the substitution method?
A: The substitution method is a technique used to solve equations by substituting one expression for another. In this case, we substituted the expression for x from equation (2) into equation (1).
Q: Why do we need to add 20 to both sides of the equation?
A: We need to add 20 to both sides of the equation to isolate the variable y.
Q: Can you explain the concept of variables?
A: Variables are letters or symbols that represent unknown values. In this case, x and y are variables that represent the two numbers.
Q: How do we know which number is larger?
A: We know which number is larger by looking at the equation x = y - 20. This equation tells us that x is 20 less than y, so x is the smaller number.
Q: Can you explain the concept of algebraic equations?
A: Algebraic equations are equations that involve variables and constants. In this case, the equation x + y = -16 is an algebraic equation.
Q: How do we check the solution?
A: We check the solution by plugging the values of x and y back into the original equations.
Q: Can you explain the concept of logical thinking?
A: Logical thinking is the ability to reason and think critically. In this case, we used logical thinking to arrive at the correct solution.
Common Mistakes
Mistake 1: Not using the substitution method
A: Not using the substitution method can lead to incorrect solutions.
Mistake 2: Not adding 20 to both sides of the equation
A: Not adding 20 to both sides of the equation can lead to incorrect solutions.
Mistake 3: Not checking the solution
A: Not checking the solution can lead to incorrect solutions.
Tips and Tricks
Tip 1: Use the substitution method to solve equations
A: The substitution method is a powerful technique for solving equations.
Tip 2: Check the solution by plugging the values back into the original equations
A: Checking the solution is an important step in ensuring that the solution is correct.
Tip 3: Use logical thinking to arrive at the correct solution
A: Logical thinking is an essential skill for solving mathematical problems.
Conclusion
In this article, we provided a Q&A section to help readers understand the solution to the mathematical puzzle involving two numbers whose sum is -16, with one number being 20 less than the other. We also provided tips and tricks for solving equations and checking the solution. We hope that this article has been helpful in understanding the solution to this puzzle.
Frequently Asked Questions
Q: What is the sum of the two numbers?
A: The sum of the two numbers is -16.
Q: What is the relationship between the two numbers?
A: One number is 20 less than the other.
Q: How do we solve the equations?
A: We use the substitution method to solve the equations.
Q: What is the value of x?
A: The value of x is -18.
Q: What is the value of y?
A: The value of y is 2.
Step-by-Step Solution
Step 1: Write the given information as two equations
x + y = -16 x = y - 20
Step 2: Substitute the expression for x from equation (2) into equation (1)
y - 20 + y = -16
Step 3: Combine like terms
2y - 20 = -16
Step 4: Add 20 to both sides
2y = 4
Step 5: Divide both sides by 2
y = 2
Step 6: Substitute the value of y into equation (2) to find the value of x
x = y - 20 x = 2 - 20 x = -18
Final Answer
The final answer is -18 and 2.