The Sum Of Two Intergers Is _105. If One Of Them Is 95 Then Find The -other
Introduction
Mathematics is a fascinating subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various aspects of life, from science and engineering to finance and economics. In this article, we will discuss a simple yet effective math problem that involves the sum of two integers.
The Problem
The problem states that the sum of two integers is 105. One of the integers is 95. We need to find the other integer.
Step 1: Understand the Problem
To solve this problem, we need to understand the concept of integers and their operations. Integers are whole numbers, either positive, negative, or zero, without a fractional part. The sum of two integers is the result of adding them together.
Step 2: Identify the Given Information
We are given two pieces of information:
- The sum of the two integers is 105.
- One of the integers is 95.
Step 3: Use Algebraic Manipulation
To find the other integer, we can use algebraic manipulation. Let's represent the unknown integer as x. We can write an equation based on the given information:
95 + x = 105
Step 4: Solve for x
To solve for x, we need to isolate the variable x on one side of the equation. We can do this by subtracting 95 from both sides of the equation:
x = 105 - 95
Step 5: Calculate the Value of x
Now, we can calculate the value of x by evaluating the expression:
x = 10
Conclusion
In this article, we discussed a simple yet effective math problem that involves the sum of two integers. We used algebraic manipulation to solve for the unknown integer, and we found that the other integer is 10.
Why is this Problem Important?
This problem is important because it demonstrates the concept of integers and their operations. It also shows how algebraic manipulation can be used to solve equations and find unknown values.
Real-World Applications
This problem has real-world applications in various fields, such as:
- Accounting: When calculating the total cost of an item, you need to add the cost of the item and the tax.
- Finance: When calculating the total amount of money in a bank account, you need to add the principal amount and the interest.
- Science: When calculating the total distance traveled by an object, you need to add the initial distance and the distance traveled.
Tips and Tricks
Here are some tips and tricks to help you solve this problem:
- Make sure to read the problem carefully and understand what is being asked.
- Use algebraic manipulation to solve equations and find unknown values.
- Check your work by plugging in the values and making sure they are correct.
Common Mistakes
Here are some common mistakes to avoid when solving this problem:
- Not reading the problem carefully and understanding what is being asked.
- Not using algebraic manipulation to solve equations and find unknown values.
- Not checking your work by plugging in the values and making sure they are correct.
Conclusion
Introduction
In our previous article, we discussed a simple yet effective math problem that involves the sum of two integers. We used algebraic manipulation to solve for the unknown integer, and we found that the other integer is 10. In this article, we will provide a Q&A section to help you better understand the problem and its solution.
Q&A
Q: What is the sum of two integers?
A: The sum of two integers is the result of adding them together.
Q: What is the problem asking for?
A: The problem is asking for the other integer when the sum of two integers is 105 and one of the integers is 95.
Q: How do I solve this problem?
A: To solve this problem, you can use algebraic manipulation. Let's represent the unknown integer as x. We can write an equation based on the given information:
95 + x = 105
Q: How do I isolate the variable x?
A: To isolate the variable x, you can subtract 95 from both sides of the equation:
x = 105 - 95
Q: What is the value of x?
A: The value of x is 10.
Q: Why is this problem important?
A: This problem is important because it demonstrates the concept of integers and their operations. It also shows how algebraic manipulation can be used to solve equations and find unknown values.
Q: What are some real-world applications of this problem?
A: This problem has real-world applications in various fields, such as:
- Accounting: When calculating the total cost of an item, you need to add the cost of the item and the tax.
- Finance: When calculating the total amount of money in a bank account, you need to add the principal amount and the interest.
- Science: When calculating the total distance traveled by an object, you need to add the initial distance and the distance traveled.
Q: What are some common mistakes to avoid when solving this problem?
A: Some common mistakes to avoid when solving this problem include:
- Not reading the problem carefully and understanding what is being asked.
- Not using algebraic manipulation to solve equations and find unknown values.
- Not checking your work by plugging in the values and making sure they are correct.
Q: How can I practice solving this type of problem?
A: You can practice solving this type of problem by:
- Working on similar problems and exercises.
- Using online resources and math tools to help you solve the problem.
- Asking a teacher or tutor for help and guidance.
Conclusion
In conclusion, this Q&A article provides a comprehensive guide to help you better understand the problem and its solution. We hope that this article has been helpful in answering your questions and providing you with a deeper understanding of the concept of integers and their operations.
Additional Resources
- Khan Academy: Algebra
- Mathway: Algebra Solver
- Wolfram Alpha: Algebra Calculator
Final Thoughts
We hope that this article has been helpful in providing you with a better understanding of the problem and its solution. Remember to practice solving this type of problem and to use algebraic manipulation to solve equations and find unknown values. Good luck!