Solving the Equation: 'Twenty more than four times a number is equal to the difference between -71 and three times the number'

As an excellent high school mathematics teacher, I'm excited to share with you a detailed approach to solving a challenging word problem involving equations. This problem requires a deep understanding of algebraic concepts and the ability to translate the given information into a mathematical equation.

The Problem

The problem statement is as follows:

"Twenty more than four times a number is equal to the difference between -71 and three times the number. Find the number."

To solve this problem, we need to set up an equation and then solve for the unknown number.

Step 1: Translate the Problem into an Equation

Let's start by assigning a variable to represent the unknown number. Let's call this variable 'x'.

The problem statement can be translated into the following equation:

4x + 20 = -71 - 3x

Step 2: Simplify the Equation

Now, let's simplify the equation by combining the terms on the right-hand side:

4x + 20 = -71 - 3x 4x + 20 = -71 + (-3x) 4x + 20 = -71 - 3x 7x + 20 = -71 7x = -91 x = -13

Step 3: Check the Solution

To verify that the solution is correct, we can substitute the value of x back into the original equation:

4x + 20 = -71 - 3x 4(-13) + 20 = -71 - 3(-13) -52 + 20 = -71 + 39 -32 = -32 (the equation is true)

Therefore, the number that satisfies the given equation is -13.

Conclusion

In this article, we have walked through the step-by-step process of solving a challenging high school mathematics word problem involving equations. By translating the problem statement into an equation, simplifying the equation, and verifying the solution, we were able to find the unknown number. This type of problem-solving skill is essential for success in high school mathematics and beyond.