/*! 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 1 Translate to a proportion. Do no... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 1

Translate to a proportion. Do not solve. $$ \text { What is } 37 \% \text { of } 74 ? $$

Short Answer

Expert verified
\( \frac{37}{100} = \frac{x}{74} \)

Step by step solution

01

Identify the problem

The problem is asking to translate 'What is 37% of 74?' into a proportion.
02

Set up the proportion

The problem involves finding 37% of 74. Start by recognizing that 'percent' means 'per hundred.' Therefore, 37% can be written as the fraction \( \frac{37}{100} \).
03

Express the proportion

Set up a proportion where \( x \) (the unknown quantity) is 37% of 74. This can be written as \( \frac{37}{100} = \frac{x}{74} \).

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.

fractions
To understand how to translate percentages into proportions, it's crucial to know about fractions. A fraction has two parts: the numerator (top number) and the denominator (bottom number).
For example, in the fraction \(\frac{37}{100}\), 37 is the numerator, and 100 is the denominator. The numerator represents a part of the whole, while the denominator represents the total number of equal parts.
In our problem, 37% can be converted into the fraction \(\frac{37}{100}\). As we progress, this fraction helps us set up the proportion needed to solve for the unknown variable.
percentages
Percentages are another critical concept here. A percentage represents a number out of 100. For example, 37% means 37 out of 100.
You can always convert a percentage to a fraction by putting the percentage number over 100. So, 37% becomes \(\frac{37}{100}\).
Understanding this conversion is key in setting up proportion problems, as it directly ties into the fractions we discussed earlier.
proportion problems
Proportion problems deal with establishing relationships between different ratios or fractions. In our problem, we need to set up a proportion to represent the relationship between 37% and 74.
The term 'proportion' refers to an equation that states two ratios are equal. For instance, in the context of our problem, we set up the proportion as \(\frac{37}{100} = \frac{x}{74}\). This implies that 37% (or 37 out of 100) is equivalent to some unknown value \(x\) out of 74.
Solving the proportion will then allow us to find the value of \(x\). But for now, we are only asked to translate, not solve.
unknown variable
Finally, we need to understand the concept of an unknown variable, often represented as \(x\). In the context of our problem, \(x\) stands for the unknown value that is 37% of 74.
Setting up a proportion allows us to solve for this unknown variable by making the two ratios equal. In our proportion \(\frac{37}{100} = \frac{x}{74}\), \(x\) is the number we want to find.
By understanding how to set up the fraction and percentages correctly, you can easily solve for any unknown variable in similar proportion problems in the future.

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

Convert to standard notation. $$ 4.03 \text { trillion } $$

Solve. A family invests \(\$ 4000\) in an account paying \(6 \%\), compounded monthly. How much is in the account after 5 months?

On a test, Maj Ling got \(86 \%,\) or \(81.7,\) of the items correct. (There was partial credit on some items.) How many items were on the test?

Solve. Luke has a balance of \(\$ 5328.88\) on a credit card with an annual percentage rate (APR) of \(18.7 \%\) a) Many credit cards require a minimum monthly payment of \(2 \%\) of the balance. What is Luke's minimum payment on a balance of \(\$ 5328.88 ?\) Round the answer to the nearest dollar. b) Find the amount of interest and the amount applied to reduce the principal in the minimum payment found in part (a). c) If Luke had transferred his balance to a card with an APR of \(13.2 \%\), how much of his payment would be interest and how much would be applied to reduce the principal? d) Compare the amounts for \(13.2 \%\) from part (c) with the amounts for \(18.7 \%\) from part (b).

Convert to standard notation. $$ \text { 5.8 million } $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.