Half Of A Number Is Added To 4 Times The Number Is Equal To 35
Introduction
Mathematics is a fascinating subject that has been a part of human life for centuries. It is a language that helps us describe the world around us, from the simplest arithmetic operations to the most complex mathematical theories. In this article, we will delve into a simple yet intriguing mathematical problem that will test our problem-solving skills. The problem states that half of a number is added to 4 times the number is equal to 35. Let's break it down and find the solution.
Understanding the Problem
The problem can be written as an equation:
(1/2)x + 4x = 35
where x is the unknown number. Our goal is to find the value of x that satisfies this equation.
Breaking Down the Equation
To solve this equation, we need to isolate the variable x. We can start by combining the two terms on the left-hand side of the equation:
(1/2)x + 4x = (1/2)x + (8/2)x
Simplifying the equation, we get:
(1/2)x + (8/2)x = (9/2)x
Now, the equation becomes:
(9/2)x = 35
Solving for x
To solve for x, we need to isolate x by dividing both sides of the equation by (9/2):
x = 35 / (9/2)
To simplify the division, we can multiply the numerator by the reciprocal of the denominator:
x = 35 * (2/9)
x = 70/9
x = 7.78
Therefore, the value of x that satisfies the equation is approximately 7.78.
Conclusion
In this article, we solved a simple yet intriguing mathematical problem that involved a linear equation. We broke down the equation, combined like terms, and isolated the variable x to find its value. The solution to the problem is x = 7.78, which satisfies the equation. This problem is a great example of how mathematics can be used to solve real-world problems and how problem-solving skills can be developed through practice and experience.
Real-World Applications
The problem we solved in this article may seem simple, but it has real-world applications in various fields such as finance, economics, and engineering. For example, in finance, the problem can be used to calculate the interest on a loan or the return on investment. In economics, the problem can be used to model the behavior of economic systems and make predictions about future trends. In engineering, the problem can be used to design and optimize systems, such as electrical circuits or mechanical systems.
Tips and Tricks
When solving linear equations, it's essential to follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
By following these steps, you can ensure that you solve linear equations correctly and efficiently.
Common Mistakes
When solving linear equations, it's easy to make mistakes. Here are some common mistakes to avoid:
- Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
- Not combining like terms: Failing to combine like terms can make the equation more complicated than it needs to be.
- Not isolating the variable: Failing to isolate the variable can make it difficult to solve the equation.
By avoiding these common mistakes, you can ensure that you solve linear equations correctly and efficiently.
Conclusion
In conclusion, solving the equation (1/2)x + 4x = 35 is a simple yet intriguing mathematical problem that requires problem-solving skills and attention to detail. By breaking down the equation, combining like terms, and isolating the variable, we can find the value of x that satisfies the equation. The solution to the problem is x = 7.78, which has real-world applications in various fields such as finance, economics, and engineering. By following the order of operations and avoiding common mistakes, you can ensure that you solve linear equations correctly and efficiently.