/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 Translate to a proportion. Do no... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 24

Translate to a proportion. Do not solve. $$ \$ 75 \text { is } 20 \% \text { of what? } $$

Short Answer

Expert verified
\(\frac{75}{X} = \frac{20}{100}\)

Step by step solution

01

Identify the components

Recognize that we are given two pieces of information: \(75 and 20\%\). We need to find the whole quantity, which we will refer to as X.
02

Translate the percentage to a fraction

Convert 20\% to its fraction form by writing it as \(\frac{20}{100}\).
03

Set up the proportion

Use the information to set up the proportion. We need to express that $75 is 20\% of X, which translates mathematically to: \[\frac{75}{X} = \frac{20}{100}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

percentage
Percentage is a way to express a number as a fraction of 100. It means 'per hundred' and is often represented with the symbol '%'. When we say 20%, we mean 20 out of 100. Converting percentages to fractions can make problems easier to solve.

For example:
  • 50% becomes \(\frac{50}{100}\) or \( \frac{1}{2} \)
  • 25% becomes \(\frac{25}{100}\) or \( \frac{1}{4} \)
  • 10% becomes \(\frac{10}{100}\) or \( \frac{1}{10} \)

In our problem, we have 20%, which we convert to a fraction: \( \frac{20}{100} \).
fractions
Fractions represent a part of a whole. They are written with a numerator (top number) and a denominator (bottom number). In the context of our problem, converting percentages to fractions helps set up a proportion.

For example:
  • 20% becomes \( \frac{20}{100} \), which simplifies to \( \frac{1}{5} \)
  • This is useful because fractions are commonly used in equations and proportions.

In our exercise, we converted 20% to \( \frac{20}{100} \), which is vital for setting up the proportion to find X.
proportional relationships
A proportional relationship between two quantities is a relationship where one quantity is a constant multiple of the other. These relationships can be expressed using ratios and fractions.

For example:
  • If you have 1 apple and \(1, the ratio is \( \frac{1\text{ apple}}{1\text{ dollar}} \).
  • Doubling the amount to 2 apples with \)2 keeps the same ratio \( \frac{2\text{ apples}}{2\text{ dollars}} = \frac{1\text{ apple}}{1\text{ dollar}} \).

In our exercise, the relationship between 75 and X describes a proportional relationship as \( \frac{75}{X} = \frac{20}{100} \). This implies 75 is to X as 20 is to 100.
problem solving
Problem solving in mathematics involves understanding the problem, translating it into a mathematical form, and solving it step by step.

For our problem:
  • Identify the components: 75 and 20%.
  • Translate the percentage to a fraction: \( \frac{20}{100} \).
  • Set up the proportion to find the unknown: \( \frac{75}{X} = \frac{20}{100} \).

This method makes problem-solving systematic and easier to understand. It demonstrates how to convert real-world problems into mathematical equations for solutions.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Consumers are paying record amounts of fees for overdrawing their bank accounts. In \(2016,\) the largest 628 banks collected $$\$ 11,410,000,000$$ in overdraft fees, which is $$\$ 250,000,000$$ more than they collected in 2015\. What was the percent increase?

Solve. Kansas Sales Tax. The sales tax rate in Kansas is \(6.5 \% .\) How much sales tax would be charged on a fireplace screen with doors that costs \(\$ 239 ?\)

Find percent notation for the decimal notation(s) in each sentence. A recent survey showed that children prefer playing with touch screen devices to playing with construction blocks and puzzles. Of the 300 parents surveyed, 0.62 said that their children "often" or "very often" play with touch screens; only 0.49 gave the same responses for construction blocks and only 0.38 for puzzles.

Find the prime factorization of 228 .

In Kansas, 47,000,000 acres are farmland. About \(5 \%\) of all the farm acreage in the United States is in Kansas. What is the total number of acres of farmland in the United States?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.