Problem 8 For each problem, familiarize yo... [FREE SOLUTION] (2024)

Get started for free

Log In Start studying!

Get started for free Log out

Chapter 1: Problem 8

For each problem, familiarize yourself with the situation. Then translate tomathematical language. You need not actually solve the problem; just carry outthe first two steps of the five-step strategy. You will be asked to completesome of the solutions as Exercises 35–42. The sum of two numbers is \(88 .\) One of the numbers is 6 more than the other.What are the numbers?

Short Answer

Expert verified

Let the numbers be \(x\) and \(x + 6\); the equation is \(x + (x + 6) = 88\).

Step by step solution

01

- Define Variables

Let the two numbers be represented by variables. Define the first number as \(x\). Since the second number is 6 more than the first number, define the second number as \(x + 6\).

02

- Translate into Equations

According to the problem, the sum of the two numbers is 88. Therefore, create the equation \(x + (x + 6) = 88\).

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

variable definition

In the context of solving mathematical problems, defining variables is the first crucial step. Variables are symbols that represent unknown values. In our exercise, we need to find two numbers that add up to 88, with one number being 6 more than the other. To simplify our work, we assign a variable to the first unknown number. Let’s use the variable \(x\) to represent the first number.
Now, since the second number needs to be 6 more than the first, we define it as \(x + 6\). By using variables, we turn the word problem into a mathematical one, setting ourselves up for translating it into an equation later.

translation to equations

Once variables are defined, the next step is translating the word problem into mathematical equations. In this exercise, the problem states the sum of two numbers is 88. From our variable definitions, we know:
- The first number is \(x\)
- The second number is \(x + 6\)
To find their sum, we add these two expressions together. Therefore, the equation representing their sum is:
\(x + (x + 6) = 88\)
By setting up this equation, we’ve successfully translated the word problem into a mathematical relationship. This equation can now be simplified and solved in the problem-solving strategy.

problem-solving strategy

Building a strategy for solving the problem involves a series of logical steps. First, we start with our equation:
\(x + (x + 6) = 88\).
Combine like terms to simplify the equation:
\(2x + 6 = 88\).
Next, isolate the term with the variable by subtracting 6 from both sides:
\(2x = 82\).
Finally, solve for \(x\) by dividing both sides by 2:
\(x = 41\).
With these steps completed, we’ve found the first number, which is 41. To find the second number, recall our variable definition: the second number is \(x + 6\). Therefore,
\(41 + 6 = 47\).
In conclusion, the two numbers are 41 and 47. Each step ensures a clear path from defining variables to solving the equation, making linear equations approachable and easy to understand.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Problem 8 For each problem, familiarize yo... [FREE SOLUTION] (3)

Most popular questions from this chapter

Use roster notation to write each set. The set of all days of the weekWrite an equivalent expression using the distributive law. $$ 5 x(y-z+w) $$Tico's scores on four tests are \(83,91\) \(78,\) and \(81 .\) How many points abovehis current average must Tico score on the next test in order to raise hisaverage 2 points?Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers;\(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers;\(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of realnumbers. $$ \mathrm{H} \subseteq R $$Divide. $$ \left(-\frac{2}{11}\right) \div(-6) $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.

Sign-up for free

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.

Necessary

Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

Problem 8 For each problem, familiarize yo... [FREE SOLUTION] (2024)
Top Articles
Latest Posts
Article information

Author: Msgr. Benton Quitzon

Last Updated:

Views: 5551

Rating: 4.2 / 5 (43 voted)

Reviews: 82% of readers found this page helpful

Author information

Name: Msgr. Benton Quitzon

Birthday: 2001-08-13

Address: 96487 Kris Cliff, Teresiafurt, WI 95201

Phone: +9418513585781

Job: Senior Designer

Hobby: Calligraphy, Rowing, Vacation, Geocaching, Web surfing, Electronics, Electronics

Introduction: My name is Msgr. Benton Quitzon, I am a comfortable, charming, thankful, happy, adventurous, handsome, precious person who loves writing and wants to share my knowledge and understanding with you.