Problem 21 - Prealgebra

Question

Solve each of the following problems. 37 is \(4 \%\) of what number?

Step-by-Step Solution

Answer

The number is 925.

Step 1: Understand the Problem

You are asked to find a number for which 37 represents 4% of that number. We can set this up as an equation.

Step 2: Set Up the Equation

Let the unknown number be represented by \( x \). The problem is asking for \( x \) such that 37 is 4% of \( x \). This can be written as: \( 0.04 \times x = 37 \).

Step 3: Solve for x

To isolate \( x \), divide both sides of the equation by 0.04: \( x = \frac{37}{0.04} \).

Step 4: Calculate the Result

Perform the division to find \( x \): \( x = 925 \).

Step 5: Verify the Result

Check if 37 is indeed 4% of 925. Calculate 4% of 925: \( 0.04 \times 925 = 37 \), which confirms our solution is correct.

Key Concepts

Understanding Prealgebra

Prealgebra is the foundation of mathematics where you begin to interact with variables and equations, setting the stage for more complex algebraic concepts. It's like laying bricks before constructing a house. Everything about prealgebra revolves around familiarity with basic math operations—addition, subtraction, multiplication, and division.
When you tackle a problem like finding a number for which 37 is 4% of that number, you're navigating the world of percentages and expressions. This will prepare you for algebraic problem solving in future studies.
For a student just getting acquainted with prealgebra, it's essential to understand not just the mechanical steps of solving problems, but also why they work. You will often need to translate real-world situations into mathematical expressions, just as you did in this problem by determining that 37 is 4% of some unknown quantity.

Effective Problem Solving Techniques

In order to successfully solve mathematical problems, it's crucial to have a methodical approach. Start by reading the problem carefully and ensuring you understand what is being asked. This clarity is the first step towards creating a structured solution.

• Identify the goal: What is the problem asking you to find?
• Break down the problem: Simplify complicated statements into smaller, manageable parts.
• Translate words into math: Convert the problem statement into mathematical equations.
• Check your solution: After calculating, always verify if your solution fits the conditions given in the problem.

By methodically applying these steps, complex problems can become much easier to navigate. It's like peeling an onion—layer by layer you'll reach the core. In our example, we set up the equation from understanding that "37 is 4% of a number", broke it down to "0.04 times x equals 37", then solved for the unknown number.

Working with Equations

Equations form the heart of algebra and are fundamental to understanding math as a language. An equation is essentially a balance between two sides. When you solve an equation, you're finding the value that makes both sides equal.
The equation in the example was set up from understanding a percentage: "0.04 times x equals 37". Solving this requires isolating the variable by performing operations to both sides—like dividing by 0.04—to maintain the balance while simplifying the equation.

• Understand operations: Grasp why you're multiplying, dividing, adding, or subtracting.
• Balance both sides: Whatever you do to one side, do to the other to keep the equation valid.
• Isolate the variable: This allows you to solve for unknowns.
• Verify: Substituting back can confirm whether your solution satisfies the original condition.

Through these practices, you'll gain a strong foundation in maneuvering through equations fluently. Remember, like any skill, practice is key to mastering the art of equations.