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Chapter 2: Problem 46

Solve. What percent of 300 is \(57 ?\)

Short Answer

Expert verified
19%

Step by step solution

01

- Define the problem

We need to find what percent of 300 is equal to 57. This means we are looking for a percentage where an unknown percentage of 300 equals 57.
02

- Set up the equation

Let the unknown percent be represented by \(x\). In terms of an equation, this looks like \( \frac{x}{100} \times 300 = 57 \)
03

- Solve for the unknown percentage

Rearrange the equation to isolate \(x\). \[ x = \frac{57 \times 100}{300} \]
04

- Simplify the equation

Calculate the value by performing the division and multiplication. \[ x = \frac{5700}{300} = 19 \]
05

- Interpret the answer

The unknown percentage \(x\) is 19%. Therefore, 19% of 300 is 57.

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Key Concepts

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

algebra
In this exercise, algebra plays a crucial role. By defining an equation, we can solve for an unknown value. Here, we let the unknown percentage be represented by a variable, which is a foundational algebraic concept. The problem translates words into an algebraic expression. This process is vital because it provides a structured way to solve real-world problems mathematically.
percentages
Understanding percentages is essential for this problem. Percentages are a way of expressing numbers as parts of 100. Here, we aim to find out what percent of 300 makes up 57. By calculating the appropriate percentage, we convert our verbal question into a mathematical form. This helps in comparing quantities and understanding proportional relationships.
equation solving
Equation solving is a key step in finding the answer. Once we set up our equation, we need to isolate the variable, which in this case is the percentage represented by \( x \). We achieve this by performing operations that simplify the equation step by step. Solving equations is crucial for determining unknown values in many types of math problems.
mathematical simplification
Mathematical simplification involves making calculations more straightforward. After forming our equation, we simplify it to find the unknown value. In this problem, we simplify the fraction \( \frac{5700}{300} \) to find that \( x = 19 \). Simplifying makes it easier to handle complicated expressions and find accurate answers quickly.

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Most popular questions from this chapter

To prepare for Section \(2.6,\) review inequalities. Write a second inequality with the same meaning. $$5>y$$

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The sum of two consecutive odd integers is less than \(100 .\) What is the largest pair of such integers?
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