/*! 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 29 Translate to an equation and sol... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 29

Translate to an equation and solve. \(70 \%\) of what is \(14 ?\)

Short Answer

Expert verified
The number is 20.

Step by step solution

01

Understanding the problem

The problem states that 70% of a certain number is equal to 14. The goal is to find that number.
02

Convert percentage to decimal

To work with the percentage, convert 70% to a decimal by dividing by 100. So, 70% becomes 0.7.
03

Set up the equation

Let the unknown number be represented by the variable x. The equation will be: 0.7x = 14
04

Solve for x

To solve for x, divide both sides of the equation by 0.7: \[ x = \frac{14}{0.7} \]
05

Calculate the result

Perform the division: \[ x = 20 \]
06

Verification

Verify the result by multiplying 20 by 0.7: \[ 20 \times 0.7 = 14 \]. This confirms that the solution is correct.

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 conversion
In this exercise, percentage conversion is a key step. Percentages represent a part of a whole number out of 100. For example, 70% means 70 out of 100.
To make calculations easier, it's helpful to convert percentages to decimals. This is done by dividing the percentage by 100. In our case, we have 70%.
Dividing 70 by 100, we get 0.7.
This decimal form makes it simpler to set up and solve equations.
basic algebra
Basic algebra helps us solve for unknown variables. In this problem, we need to find what number 70% of 14 represents.
Let's use a variable, like x, to represent this unknown number. Using our converted percentage (0.7), we set up an equation: 0.7x = 14.
To isolate x (our unknown number), we divide both sides of the equation by 0.7: \[ x = \frac{14}{0.7} \].
With basic algebra operations, such as multiplication and division, we find that x equals 20.
problem-solving steps
Problem-solving involves breaking down the exercise into manageable steps.
Here's a quick way to handle problems like these:
  • Understand the Problem: Identify what's given and what you need to find. Here, 70% of a number equals 14, and we need to find that number.
  • Convert Percentages: Change percentages to decimals for easier calculations. So, 70% becomes 0.7.
  • Set Up the Equation: Use a variable (like x) to represent the unknown number and create an equation. In this case, it's 0.7x = 14.
  • Solve the Equation: Use basic algebra to solve for x. Divide both sides by 0.7 to get x = 20.
  • Verify Your Answer: Multiply your result by the percentage in decimal form to ensure it's correct. 20 times 0.7 does indeed equal 14, confirming our solution.
Following these steps ensures you understand and solve these types of problems accurately and efficiently.

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

As world population increases and the number of acres of farmland decreases, improvements in food production and packaging must be implemented. Also, wealthy countries need to waste less food. In the United States, 17 pounds of every 90 pounds of fruits and vegetables purchased go uneaten and are discarded in the home. What percent of the total supply of fruits and vegetables is wasted in the home?

Solve. Alyssa earns \(\$ 408\) for selling \(\$ 3400\) worth of shoes. What is the commission rate?

Find the \(\mathrm{LCM}\) of 18 and 60 .

On a test of 80 items, Pedro got \(93 \%\) correct. (There was partial credit on some items.) How many items did he get correct? incorrect?

Michael has disposable monthly income of $$\$ 3400 .$$ Each month, he pays $$\$ 470$$ toward his credit-card debt. What percent of his disposable income is allotted to paying off credit-card debt?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied 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.