Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = -2|x|
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 22
You invested \$30,000 in two accounts paying 2.19% and 2.45% annual interest. If the total interest earned for the year was \$705.88, how much was invested at each rate?
Verified step by step guidance1
Define variables for the amounts invested: let \(x\) be the amount invested at 2.19%, and \(y\) be the amount invested at 2.45%.
Write an equation representing the total amount invested: \(x + y = 30000\).
Write an equation representing the total interest earned: \(0.0219x + 0.0245y = 705.88\).
Use the first equation to express one variable in terms of the other, for example, \(y = 30000 - x\).
Substitute \(y = 30000 - x\) into the interest equation and solve for \(x\), then use that value to find \(y\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Linear Equations
This concept involves solving two or more equations with multiple variables simultaneously. In this problem, the total investment and total interest create two equations that must be solved together to find the amounts invested at each interest rate.
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Simple Interest Calculation
Simple interest is calculated using the formula I = P × r × t, where I is interest, P is principal, r is the annual interest rate, and t is time in years. Understanding this helps translate the interest earned from each account into algebraic expressions.
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Variable Assignment and Equation Setup
Assigning variables to unknown quantities (e.g., amounts invested) and setting up equations based on the problem's conditions is crucial. This step transforms the word problem into a solvable mathematical model.
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Related Practice
Textbook Question
In Exercises 15–26, use graphs to find each set. (- ∞, 5) ⋃ [1, 8)
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Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7x + 13 = 2(2x-5) + 3x + 23
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Textbook Question
In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x
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Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (x + 2)2 = 25
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Textbook Question
You invested \$20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was \$307.50, how much was invested at each rate?
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