Solving Mathematical Puzzles: Finding the Original Number through Sequential Operations
Mathematical puzzles are not only entertaining but also a great way to improve problem-solving skills. This article will guide you through solving a specific puzzle where a series of arithmetic operations are applied to an original number, leading to a known result. Understanding the sequence and reversing these operations can help you find the initial number. Let's dive into how we can solve this problem using algebra and step-by-step reasoning.
Problem Description
The problem is: If you multiply a number by 10, then divide by 5, add 10, and then subtract by 20, the result is 10. We need to find the original number. Let's denote the original number as (X).
Solving the Problem Using Algebra
First, we will follow the operations described in the problem and form an equation to solve for (X).
Step 1: Multiply by 10
Let the original number be (X). When we multiply by 10, we get:
(X times 10)
Step 2: Divide by 5
Next, we divide the result by 5:
(frac{X times 10}{5})
This can be simplified to:
(2X)
Step 3: Add 10
Now, we add 10 to the result:
(2X 10)
Step 4: Subtract 20
Finally, we subtract 20 from the result:
(2X 10 - 20)
Which simplifies to:
(2X - 10)
According to the problem, this final result equals 10:
(2X - 10 10)
Solving the Equation
Now, we need to solve the equation (2X - 10 10) to find the original number (X).
Step 1: Add 10 to both sides of the equation
(2X - 10 10 10 10)
(2X 20)
Step 2: Divide both sides by 2
(frac{2X}{2} frac{20}{2})
(X 10)
Therefore, the original number is 10.
Conclusion
In conclusion, by following the sequence of arithmetic operations and solving the resulting equation, we were able to determine that the original number is 10. This problem is a great example of using algebra to reverse a series of operations and find an initial value.