/*! 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 46 Solve for the indicated variable... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 46

Solve for the indicated variable. Investment at Simple Interest Solve for \(r: A=P+P r t\)

Short Answer

Expert verified
The rate of interest \(r\) is given by \(r = \frac{A - P}{P t}\).

Step by step solution

01

Isolate terms containing \(r\)

Subtract \(P\) from both sides of the equation to isolate terms that contain \(r\). The equation becomes: \(A - P = P r t\).
02

Isolate \(r\)

Divide both sides of the equation by \(P t\) to isolate \(r\). This will give: \(r = \frac{A - P}{P t}\).

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.

Investment Problems
Investment problems often involve dealing with various financial calculations to determine interest, time, or rate of return. When dealing with investments, especially those related to simple interest, it's crucial to understand the basic formula:
  • Simple Interest Formula: The formula to calculate simple interest is given by: \[ A = P + Prt \]where:
    • \( A \) = the total amount after interest,
    • \( P \) = the principal amount or initial investment,
    • \( r \) = the rate of interest,
    • \( t \) = the time period for which the interest is calculated.
To solve investment problems, you are usually asked to find one of the variables in that formula given the others. The key is to properly rearrange the formula to solve for the unknown, depending on what information you have.
Solving Equations
Solving equations involves finding the value of the variable that makes the equation true. In this context, we're solving for the variable \( r \), the rate of interest in an equation derived from the simple interest formula. The goal is to isolate \( r \) on one side of the equation so you can determine its value straightforwardly. To tackle such a problem, you need to:
  • Identify the expressions or terms involving \( r \) and aim to have them on one side.
  • Reorganize the equation to simplify and solve it.
  • Never forget to perform the same operation on both sides of the equation to maintain equality.
In our specific example, we moved all terms containing \( r \) to one side to make solving feasible.
Algebraic Manipulation
Algebraic manipulation is the process of rearranging and simplifying equations to find solutions for unknown variables. This involves strategic operations such as adding, subtracting, multiplying, or dividing both sides of an equation. For our exercise, we did:
  • Step 1: Subtract \( P \) from both sides. This helps in isolating parts of the equation that contain \( r \): \[ A - P = Prt \]
  • Step 2: Divide both sides by \( Pt \). This isolates \( r \) and solves the equation: \[ r = \frac{A - P}{Pt} \]
Working systematically through each step ensures clarity and precision, minimizing errors. By mastering algebraic manipulation, you can solve various kinds of equations with confidence.

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

Operations with Rational Expressions Simplify the expression. $$\frac{2}{z+2}-\left(3-\frac{2}{z}\right)$$

Find \(a\) and \(b\) in the equation \(x+\sqrt{x-a}=b\) when the solution is \(x=20 .\) (There are many correct answers.)

(p. 200) An airline offers daily flights between Chicago and Denver. The total monthly cost \(C\) (in millions of dollars) of these flights is modeled by \(c=\sqrt{0.2 x+1}\) where \(x\) is the number of passengers (in thousands). The total cost of the flights for June is 2.5 million dollars. How many passengers flew in June?

Solve the inequality and graph the solution on the real number line. Use a graphing utility to verify your solution graphically. $$2 x^{3}+13 x^{2}-8 x-46 \geq 6$$

Solving an Equation Involving an Absolute Value Find all solutions of the equation algebraically. Check your solutions. $$|x+1|=x^{2}-5$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.