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Chapter 6: Problem 367

In the following exercises, translate and solve. What percent of 340 is 595\(?\)

Short Answer

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Step by step solution

01

Set up the equation

To solve the problem, start by translating the question into a mathematical equation. The phrase 'What percent of 340 is 595?' can be translated to \(\frac{p}{100} \times 340 = 595\), where \(p\) is the percent we need to find.
02

Isolate the variable

To find \(p\), isolate \(p\) by dividing both sides of the equation by 340: \( \frac{p}{100} = \frac{595}{340} \).
03

Solve for the percentage

Next, solve for \(p\) by multiplying both sides by 100: \( p = \frac{595}{340} \times 100 \).
04

Calculate the value

Finally, perform the calculation: \( p = \frac{595}{340} \times 100 = 175 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percent Calculation
Understanding how to calculate percentages is fundamental in both academic and real-world scenarios. A percent represents a part per hundred. For example, if we say 50%, it means 50 out of 100. This concept is crucial when solving problems involving percent, like finding out what percent one number is of another.
Algebra
Algebra provides the tools to translate words into mathematical expressions. In this exercise, we use algebra to set up an equation. For instance, 'What percent of 340 is 595?' becomes \(\frac{p}{100} \times 340 = 595\). Algebra allows us to manipulate this equation to isolate and solve for the unknown variable, \(p\). Mastering these skills can make even complex problems more manageable.
Equation Solving
Solving equations is a critical step in algebra. Once you've set up your equation correctly, the next task is to solve it. In our example, we start with \(\frac{p}{100} \times 340 = 595\). The goal is to isolate \(p\). We do this by dividing both sides of the equation by 340: \(\frac{p}{100} = \frac{595}{340}\). Finally, we multiply both sides by 100 to get \(p = 175\). This step-by-step approach ensures accuracy and clarity in solving algebraic equations.
Pre-Algebra
Pre-algebra lays the foundation for all future math studies. It helps students learn to translate real-world problems into mathematical equations. Understanding how to work with variables, constants, and arithmetic operations is key. In our example, we begin with a simple translation: 'What percent of 340 is 595?' translates to \(\frac{p}{100} \times 340 = 595\). From here, we apply basic arithmetic to isolate and solve for \(p\). Building a strong base in pre-algebra promotes confidence and competence in handling more complex algebraic problems later on.

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