Problem 6 In each of Exercises 1–10, mat... [FREE SOLUTION] (2024)

Get started for free

Log In Start studying!

Get started for free Log out

Chapter 2: Problem 6

In each of Exercises 1–10, match the question with the most appropriatetranslation from the column on the right. Some choices are used more thanonce. _____23 is what percent of \(57 ?\) $$ a) a=(0.57) 23\quad b) 57=0.23 y \quad c) n 23=57\quad d) n 57=23\quad e) 23=0.57 y\quad f) a=(0.23) 57\quad $$

Short Answer

Expert verified

e) 23=0.57 y

Step by step solution


Set up the equation

To find out what percent 23 is of 57, we use the formula: \[ \text{Percentage} = \frac{\text{part}}{\text{whole}} \times 100 \times 100 \tag{1} \]


Substitute the values

Here, the part is 23 and the whole is 57. Substitute these values into equation (1): \[ \text{Percentage} = \frac{23}{57} \times 100 \ \text{Percentage} = \frac{23}{57} \times 100 \]


Compare with the given choices

We need to match this with the given options. The corresponding choice should be in the form: \[23=0.23 \times y\]


Identify the correct choice

Among the given options, e) 23 = 0.57 y is the correct basic format. Therefore, the translation should match e).

Key Concepts

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


Percentages are a way to express a number as a fraction of 100. They are denoted using the percent symbol \(%\). For example, 50% is the same as saying 50 out of 100 or 0.50. When trying to find out what percent one number is of another, we use a simple formula:
\[ \text{Percentage} = \frac{\text{part}}{\text{whole}} \times 100 \]
Here, the 'part' is the smaller value or the value we are focused on, and the 'whole' is the larger value or the total amount. This formula helps simplify percentage problems, whether in a classroom setting or everyday life.
For instance, if you need to find what percent 23 is of 57, identify 23 as the part and 57 as the whole. Then apply the formula to get the percentage. This straightforward method makes understanding percentages much simpler.

Equation Setup

Setting up the correct equation is crucial for solving algebra word problems. In percentage problems, you often translate a word problem into a math equation. This involves identifying the variables and constants involved and structuring them correctly.
For the problem '23 is what percent of 57?', we start by setting up an equation using the percentage formula. Knowing that:
\[ \text{Percentage} = \frac{23}{57} \times 100 \]
This equation allows us to identify the variables and isolate what we need to solve for. In this case, we substitute 23 as the 'part' and 57 as the 'whole'. This setup forms the basis for solving the equation. It ensures accuracy and helps lay a solid foundation for finding the solution.
Correctly setting up equations is essential in algebra as it directly leads to finding the right answers efficiently and accurately.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. In percentage word problems, these expressions are used to represent the parts of our problem numerically and symbolically.
Take the exercise '23 is what percent of 57?' After setting up the equation, our algebraic expression is:
\[ 23 = 0.57 \times y \]
In general, for any percentage word problem, you may re-write it as:
\[ \text{part} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100 \]
Using this algebraic expression, you can easily manipulate and solve for the variable you're interested in, such as the percentage (\(y\)) in this case. Understanding and being able to craft algebraic expressions is key in translating word problems into solvable equations, which is a fundamental skill in algebra.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Problem 6 In each of Exercises 1–10, mat... [FREE SOLUTION] (3)

Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. All Seasons Well Drilling offers two plans. Under the "pay-as-you-go" plan,they charge \(\$ 500\) plus \(\$ 8\) per foot for a well of any depth. Under their"guaranteed-water" plan, they charge a flat fee of \(\$ 4000\) for a well thatis guaranteed to provide adequate water for a household. For what depths wouldit save a customer money to use the pay-as-you-go plan?Use an inequality and the five-step process to solve each problem. The formula \(R=-0.0065 t+4.3259\) can be used to predict the world record, inminutes, for the 1 -mi run \(t\) years after \(1900 .\) Determine (in terms of aninequality) those years for which the world record will be less than \(3.6\mathrm{min}\)After 9 quizzes, Blythe's average is 84. Is it possible for Blythe to improveher average by two points with the next quiz? Why or why not?Translate to an inequality. The time of the test was between 45 min and 55 min.Solve $$ x
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation


Read Explanation


Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.


Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.


Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

Problem 6 In each of Exercises 1–10, mat... [FREE SOLUTION] (2024)


Top Articles
Latest Posts
Article information

Author: Maia Crooks Jr

Last Updated:

Views: 5991

Rating: 4.2 / 5 (63 voted)

Reviews: 94% of readers found this page helpful

Author information

Name: Maia Crooks Jr

Birthday: 1997-09-21

Address: 93119 Joseph Street, Peggyfurt, NC 11582

Phone: +2983088926881

Job: Principal Design Liaison

Hobby: Web surfing, Skiing, role-playing games, Sketching, Polo, Sewing, Genealogy

Introduction: My name is Maia Crooks Jr, I am a homely, joyous, shiny, successful, hilarious, thoughtful, joyous person who loves writing and wants to share my knowledge and understanding with you.