/*! 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 314 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 314

In the following exercises, solve the equation. $$ 0.18 n=5.4 $$

Short Answer

Expert verified
n = 30

Step by step solution

01

Identify the equation

The given equation is 0.18n = 5.4. This equation states that 0.18 times an unknown number n equals 5.4.
02

Isolate the variable

To solve for n, isolate the variable on one side of the equation. This can be done by dividing both sides of the equation by 0.18.
03

Perform the division

Divide both sides of the equation by 0.18: \[ n = \frac{5.4}{0.18} \]Performing the division gives\[ n = 30 \]
04

Verify the solution

To verify the solution, substitute n = 30 back into the original equation and check if both sides are equal: \[ 0.18 \times 30 = 5.4 \]Since both sides are equal, the solution n = 30 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.

Isolate the Variable
Isolating the variable means getting the unknown variable by itself on one side of the equation. This makes it easier for us to solve the equation. In the example given, we start with the equation: \(0.18n = 5.4\).
To isolate the variable \(n\), we need to get rid of the coefficient (the number in front of the variable).
Here, the coefficient is 0.18. We can do this by performing the opposite operation. Since 0.18 is multiplying \(n\), we will divide both sides of the equation by 0.18.

When we divide 0.18n by 0.18, we simply get \(n\). So, we make sure \(n\) stands alone on one side.
This gives us a new simplified equation: \[n = \frac{5.4}{0.18}\]
Perform Division
To solve the equation completely, we need to perform the division we set up in the previous step. This means dividing the number on the right-hand side by the coefficient we used to isolate the variable. In our example:
\[n = \frac{5.4}{0.18}\]
To make this calculation easier, you can use a calculator or perform the division manually. Dividing 5.4 by 0.18 gives us 30. So it turns out that: \[n = 30\]
This is the solution to our equation. Once this is clear, we can feel confident about the next step: checking our work.
Verify the Solution
Verification is a crucial step in solving equations. It helps in confirming that our solution is correct. To verify our solution, we substitute the value of \(n\) back into the original equation and check if both sides remain equal. For our case:
Our solution is \(n = 30\). To check, we substitute 30 for \(n\) in the original equation \(0.18n = 5.4\):
\(0.18 \times 30 = 5.4\)
Calculating this gives us:
\(5.4 = 5.4\)
Since both sides of the equation are the same, our solution is verified and correct. This step ensures that we have solved the equation accurately and there are no mistakes in our calculations.

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, convert each decimal to a fraction or mixed number. $$2.482$$

In the following exercises, find the unit rate. Round to two decimal places, if necessary. 576 miles on 18 gallons of gas

In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. $$1.638$$

Kathryn ate a 4 -ounce cup of frozen yogurt and then went for a swim. The frozen yogurt had 115 calories. Swimming burns 422 calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning.

In the following exercises, round each number to the nearest hundredth. $$0.697$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

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.