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Chapter 6: Problem 4

Translate to an equation. Do not solve. What percent of 25 is \(8 ?\)

Short Answer

Expert verified
Translate to \( \frac{x}{100} \times 25 = 8 \).

Step by step solution

01

Understand the Problem

The problem asks what percent of 25 is equal to 8. We need to find the percentage that makes this statement true.
02

Identify the Variables

Let the unknown percent be represented by the variable \( x \).
03

Set Up the Equation

Translate the word problem into a mathematical equation: \( x \% \) of 25 is equal to 8. Mathematically, this can be written as: \( \frac{x}{100} \times 25 = 8 \).

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Key Concepts

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

Percentage Problems
Understanding percentage problems is crucial as many real-world problems involve percentages. A percentage shows how much out of 100 something is. In this exercise, the problem asks what percentage of 25 is 8. To solve these kinds of problems, you have to translate the word problem into a mathematical statement that can be solved.
Setting Up Equations
Setting up an equation from a word problem is about translating English into math. In the given exercise, you need to find 'what percent of 25 is 8.' The unknown percentage is represented by a variable. Here, let's denote it by \( x \). The phrase 'x% of 25' can be written mathematically as: \( \frac{x}{100} \times 25 \). This step transforms the word problem into an algebraic expression that we can solve.
Identifying Variables
Identifying variables is a key step in solving word problems. A variable represents the unknown value you need to find. In the step-by-step solution, we used \( x \) to represent 'what percent'. Understanding which quantity is unknown and naming it with a variable is essential for setting up the correct equation. Once you can identify your variables accurately, you can easily translate words into a mathematical model.

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Most popular questions from this chapter

Solve. The sales tax on the purchase of a used car is \(\$ 434\) and the sales tax rate is \(7 \%\). What is the purchase price?

A cross-section of a standard, or nominal, "two-by-four" actually measures \(1 \frac{1}{2}\) in. by \(3 \frac{1}{2}\) in. The rough board is 2 in. by 4 in. but is planed and dried to the finished size. What percent of the wood is removed in planing and drying?

Solve: \(x+\frac{2}{5}=\frac{9}{10}\).

Solve. Joshua earns \(\$ 120\) for selling \(\$ 2400\) worth of television sets. What is the commission rate?

Solve. $$ \frac{x}{12}=\frac{24}{16} $$
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