/*! 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 27 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 27

In the following exercises, solve each number word problem. The sum of two numbers is 20 . One number is four less than the other. Find the numbers.

Short Answer

Expert verified
The numbers are 8 and 12.

Step by step solution

01

Define the Variables

Let the two numbers be x and y. We need to form equations based on the problem statement.
02

Set Up the Equations

From the problem, we know that the sum of the two numbers is 20. Thus, we can write the equation: x + y = 20
03

Express One Variable in Terms of the Other

We also know that one number is four less than the other. Assuming that x is the number that is four less, we can write: x = y - 4
04

Substitute and Solve

Substitute the expression for x from the second equation into the first equation: (y - 4) + y = 20 Simplify and solve for y: 2y - 4 = 20 2y = 24 y = 12
05

Find the Other Number

Substitute the value of y back into the equation x = y - 4 to find x: x = 12 - 4 x = 8
06

Verify the Solution

Check the solution by verifying that the sum of the two numbers is 20 and that one number is four less than the other. 8 + 12 = 20 8 is indeed four less than 12.

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.

solving equations
Solving equations is a fundamental aspect of algebra. When faced with an equation, the goal is to find the unknown values, known as variables, that make the equation true. In word problems, you often have to first translate the described relationships into algebraic equations.
In the given problem, we had to set up two equations based on the information provided:
  • the sum of the two numbers is 20
  • one number is four less than the other
Once we have the equations, we use algebraic methods such as substitution or elimination to solve for the variables.
number problems
Number problems in algebra often involve finding numbers that satisfy given conditions. These problems require setting up algebraic expressions based on the relationships described in the problem.
For the given problem, we were given two relationships: the sum of the two numbers being 20, and one number being four less than the other. These conditions translate into two equations.
Number problems frequently appear in algebra courses because they provide practical applications of the concepts of variables and equations.
substitution method
The substitution method is a technique for solving systems of equations. In this method, we solve one equation for one variable and then substitute that expression into another equation.
For example, in our problem, we expressed one variable in terms of the other:
  • x = y - 4
We then substituted this expression into the equation x + y = 20:
  • (y - 4) + y = 20
This allowed us to solve for y. Substitution is helpful because it reduces the number of variables, making the equations easier to solve.
variable definition
Defining variables is the first step in solving word problems algebraically. By assigning letters to represent unknown quantities, we create a framework to write equations.
In this problem, we defined the variables as:
  • x for one number
  • y for the other number
This step is crucial because it translates the written problem into a mathematical form.
Clear variable definitions help in setting up correct equations and avoiding confusion. It is essential to consistently follow the definitions throughout the problem-solving process.

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

Maximum Weight on a Boat In \(2004,\) a water taxi sank in Baltimore harbor and five people drowned. The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?

In the following exercises, solve using rectangle properties. A rectangular room is 15 feet wide by 14 feet long. What is its perimeter?

In the following exercises, solve. Marlon's TV plan costs \(\$ 49.99\) per month plus \(\$ 5.49\) per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of \(\$ 100 ?\)

Sarah wants to arrive at her friend's wedding at 3:00. The distance from Sarah's house to the wedding is 95 miles. Based on usual traffic patterns, Sarah predicts she can drive the first 15 miles at 60 miles per hour, the next 10 miles at 30 miles per hour, and the remainder of the drive at 70 miles per hour. (a) How long will it take Sarah to drive the first 15 miles? (b) How long will it take Sarah to drive the next 10 miles? (c) How long will it take Sarah to drive the rest of the trip? (d) What time should Sarah leave her house?

Shower Budget Penny is planning a baby shower for her daughter-in-law. The restaurant charges \(\$ 950\) for up to 25 guests, plus \(\$ 31.95\) for each additional guest. How many guests can attend if Penny wants the total cost to be no more than \(\$ 1,500 ?\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.