/*! 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 307 In the following exercises, tran... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 307

In the following exercises, translate to a proportion. 77 is 110\(\%\) of what number?

Short Answer

Expert verified
The number is 70.

Step by step solution

01

Identify the Variables

Let the unknown number be represented by the variable, say it is denoted by 'x'.
02

Write the Proportion

The statement '77 is 110% of what number?' can be translated into the proportion: \(\frac{77}{x} = \frac{110}{100}\)
03

Simplify the Right Side of the Proportion

Simplify the right side of the proportion: \(\frac{110}{100} = 1.1\)
04

Set Up the Equation

Thus, the proportion becomes: \(\frac{77}{x} = 1.1\)
05

Solve for x

To find 'x', multiply both sides of the equation by 'x' and then divide both sides by 1.1: \(77 = 1.1x \) \( x = \frac{77}{1.1} \) \( x = 70 \)

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.

percentages
Percentages are a way of expressing a number as a fraction of 100. It's like splitting a pie into 100 pieces and saying how many pieces make up a particular part. For instance, 50% means 50 out of 100, which is also half of the whole pie.
When dealing with percentages:
  • You can convert percentages to decimals by dividing by 100. For example, 110% becomes 1.1.
  • To increase a number by a certain percentage, multiply the number by 1 plus the decimal form of the percentage.
  • To find what percentage one number is of another, divide the first number by the second and then multiply by 100.
In our exercise, 77 is 110% of some number 'x'. We convert 110% to a decimal by dividing by 100, which gives us 1.1. Now the problem is easier to solve.
solving equations
Solving equations means finding the value of the variable that makes the equation true. In our exercise, the equation is \[ \frac{77}{x} = 1.1 \]. This is a proportion, meaning two ratios are equal.
To solve it, we first rewrite it to get rid of the fraction:
  • Multiply both sides by 'x': \ (77 = 1.1x) \.
  • Then, solve for 'x' by dividing both sides by 1.1: \ (x = \frac{77}{1.1})\.
  • This gives us:
    \[ x = 70 \]Always check your solution by substituting the value back into the original equation:
    • In our case, 110% of 70 is indeed 77 \ ([ \frac{77}{70} = 1.1 ]) which confirms our solution is correct.
.
prealgebra
Prealgebra lays the foundation for all higher-level math subjects. It includes basic arithmetic operations like addition, subtraction, multiplication, and division, as well as introductory algebra concepts.
In this exercise, we use several key prealgebra skills:
  • Understanding of percentages and how to convert them to decimals.
  • Writing proportions correctly to represent a situation.
  • Solving a simple linear equation for an unknown variable.
These basic skills are essential as they pave the way for more complex algebra and other higher-level math topics. By mastering prealgebra, you're setting yourself up for success in future math studies. And remember, practice makes perfect. Keep working on these foundational skills, and soon they'll become second nature!

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

Sales of video games and consoles fell from \(\$ 1,150\) million to \(\$ 1,030\) million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)

In the following exercises, solve. Last year Bernard bought a new car for \(\$ 30,000\) . This year the car is worth \(\$ 24,000\) . Find the percent decrease.

In the following exercises, translate and solve. 7.9\(\%\) of what number is \(\$ 4.74 ?\)

Dimple gets paid \(\$ 3,200\) per month. She pays \(\$ 960\) a month for rent. What percent of her monthly pay goes to rent?

In the following exercises, write each sentence as a proportion. 95 miles to 3 gallons is the same as 475 miles to 15 gallons.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.