/*! 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 77 In the following exercises, tran... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 77

In the following exercises, translate and solve. 81 is 75% of what number?

Short Answer

Expert verified
108

Step by step solution

01

- Set up the equation

We are given that 81 is 75% of a certain number. Let the unknown number be represented by Let the unknown number be represented by \( x \). The statement 81 is 75% of what number can be written as an equation: \[ 81 = 0.75x \].
02

- Solve for x

To find the value of \( x \), divide both sides of the equation by 0.75:\[ x = \frac{81}{0.75} \].
03

- Perform the division

Now, perform the division:\[ x = \frac{81}{0.75} = 108 \].

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.

Translating Verbal Statements to Equations
Understanding how to translate verbal statements into equations is crucial for solving percentage problems. Let's break down the process. Typically, words like 'is,' 'of,' and 'what number' give clues on how to form the equation. For example, '81 is 75% of what number?' can be interpreted as:
  • '81' is the result or part of the equation.
  • 'is' translates to '=' in mathematical terms.
  • '75%' translates to '0.75' (since percentages are out of 100, you convert them to decimals by dividing by 100).
  • 'of what number?' indicates that we are trying to find a missing value, often represented by a variable like 'x'.
Combining all these clues, the verbal statement '81 is 75% of what number?' becomes the equation: \[81 = 0.75x\]. This step is important for setting up the equation correctly, so make sure to interpret each part of the statement accurately.
Solving Linear Equations
After translating the verbal problem into the equation \[81 = 0.75x\], the next step is solving for the unknown variable 'x'. This process typically involves isolating the variable on one side of the equation. Here's a step-by-step approach:
  • Recognize that you need to solve for the variable 'x.'
  • Identify that '0.75x' means '0.75' times 'x.'
  • To isolate 鈥榵,鈥� you need to perform the opposite operation. Since '0.75' is multiplying 'x,' you'll divide both sides of the equation by '0.75.'
  • This will leave 鈥榵鈥� alone on one side of the equation: \[x = \frac{81}{0.75}\]
Dividing both sides by `0.75` simplifies the equation, which then allows you to find the value of 'x'. Finally, perform the division step to solve for 'x'.
Basic Percentage Calculations
Basic percentage calculations are essential for addressing problems involving proportions and parts of a whole. Here are the key concepts:
  • A percentage represents a fraction out of 100. When you see '75%', think of it as \[\frac{75}{100} = 0.75\].
  • To convert a percentage to a decimal, divide by 100. For example, '75%' becomes '0.75.'
  • Percentage of a number can be found by multiplying the percentage (as a decimal) by that number. For instance, if you need to find 75% of 'x,' you calculate '0.75 * x.'
Applying these steps, you can handle any percentage problem easily. In our exercise, given '81 is 75% of what number?', recognizing how to convert and operate with percentages is crucial. You set up the equation \[81 = 0.75x\] and solve accordingly.

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

In the following exercises, solve. Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?

In the following exercises, solve. Saul drove his truck 3 hours from Dallas towards Kansas City and stopped at a truck stop to get dinner. At the truck stop he met Erwin, who had driven 4 hours from Kansas City towards Dallas. The distance between Dallas and Kansas City is 542 miles, and Erwin's speed was eight miles per hour slower than Saul's speed. Find the speed of the two truckers.

In the following exercises, solve using rectangle properties. The length of a rectangle is three meters less than twice the width. The perimeter of the rectangle is 36 meters. Find the dimensions of the rectangle.

In the following exercises, solve using rectangle properties. The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.

In the following exercises, solve. Five student government officers want to go to the state convention. It will cost them \(\$ 110\) for registration, \(\quad \$ 375\) for transportation and food, and \(\$ 42\) per person for the hotel. There is \(\$ 450\) budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge \(\$ 5\) per car, how many cars must they wash in order to have enough money to pay for the trip?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

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.