/*! 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 17 Solve the formula for the given ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 17

Solve the formula for the given variable. $$A=P+P r ; P \quad \text { (Business) }$$

Short Answer

Expert verified
The solution to the equation is \(P = \frac{A}{1+r}\)

Step by step solution

01

Set Up the Equation

We start by writing down the equation: \(A = P + Pr\)
02

Group Terms with P

In this step, take \(P\) as a common factor for the terms on the right-hand side of the equation. The equation becomes \(A = P(1+r)\)
03

Isolate P

The last step is to isolate the variable \(P\) by dividing both sides of the equation by \(1 + r\). The final equation becomes \(P = \frac{A}{1+r}\)

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.

Equation Solving
Equation solving is a crucial mathematical skill that allows us to find unknown values by manipulating equations. In the context of the exercise, we are given the equation \( A = P + Pr \) and asked to solve for \( P \).

To tackle problems like this, we follow a systematic approach:
  • Identify the variable you need to solve for, ensuring clarity on what you are trying to find.
  • Carefully rearrange and simplify terms to make the solving process smoother.
  • Use operations such as addition, subtraction, multiplication, division, or even taking common factors to eliminate terms or isolate the desired variable.
In our specific example, we first rewrite the equation to make the term \( P \) easy to isolate. Understanding such processes is essential in both academic exercises and practical applications.
Isolate Variable
Isolating a variable involves rearranging an equation so that the variable stands alone on one side. This is a pivotal step in finding the solution to an equation.

In our exercise, the goal is to solve for \( P \) from the equation \( A = P + Pr \). We approach this by:
  • Taking \( P \) as a common factor from the terms on the right-hand side, we have \( A = P(1 + r) \).
  • Next, we need to get \( P \) alone. We do this by dividing both sides of the equation by \( 1 + r \), leading to \( P = \frac{A}{1+r} \).
This step is all about clarity and precision in making sure the equation balances while achieving our goal to isolate \( P \). Mastery of isolating variables is essential for solving many types of mathematical equations.
Business Mathematics
Business mathematics involves using mathematical methods to solve financial and business-related problems. The formula \( A = P(1 + r) \) appears frequently in business scenarios, particularly when dealing with interest and investment calculations.

Here鈥檚 how this formula is often applied in a business context:
  • \( A \) represents the total amount after interest.
  • \( P \) is the principal, or the initial amount of money or investment.
  • \( r \) stands for the interest rate applied to the principal.
Understanding how to manipulate and solve such equations is vital for tasks like calculating loan repayments, determining investment growth, or predicting future profits. By mastering these concepts, students can enhance their ability to make informed decisions in the business world.

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

Given the expression \(\frac{1}{y-3},\) choose some values of \(y\) and evaluate the expression for those values. Is it possible to choose a value of \(y\) for which the value of the expression is greater than \(10,000,000 ?\) If so, give such a value. If not, explain why it is not possible.

Uniform Motion Because of bad weather, a bus driver reduced the usual speed along a 150 -mile bus route by \(10 \mathrm{mph}\). The bus arrived only \(30 \mathrm{min}\) later than its usual arrival time. How fast does the bus usually travel?

Simplify. $$\frac{4 x}{6-x}+\frac{5}{x-6}$$

Simplify. $$\frac{x+4}{x^{2}-x-42}+\frac{3}{7-x}$$

After sailing \(15 \mathrm{mi}\), a sailor changed direction and increased the boat's speed by 2 mph. An additional 19 mi was sailed at the increased speed. The total sailing time was \(4 \mathrm{h}\). Find the rate of the boat for the first \(15 \mathrm{mi}\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Pure 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.