Question

Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions. Two music CDs and four music cassette tapes cost a total of 40 dollars. However, three music CDs and five cassette tapes cost 55 dollars. Find the price of each. a. $C D$= 12 dollars; cassette = 4 dollars b. $C D$= 15 dollars; cassette = 2 dollars c. $C D$= 10 dollars; cassette = 5 dollars

Name: Problem 4, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2020-03-12T06:23:11-08:00
Duration: 2 min
Channel: Surjit Tewari

   Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions.
Two music CDs and four music cassette tapes cost a total of 40 dollars. However, three music CDs and five cassette tapes cost
55 dollars. Find the price of each.
a. $C D$= 12 dollars; cassette = 4 dollars
b. $C D$= 15 dollars; cassette = 2 dollars
c. $C D$= 10 dollars; cassette = 5 dollars

Beginning and Intermediate Algebra

Elayn Martin-Gay 4th Edition

Chapter 4, Problem 4

Instant Answer

Solved by Expert Surjit Tewari

03/12/2020

Step 1

Let's denote the price of a CD as $x$ and the price of a cassette as $y$. From the problem, we have the following two equations: \begin{align*} 2x + 4y &= 40 \\ 3x + 5y &= 55 \end{align*} Show more…

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Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions. Two music CDs and four music cassette tapes cost a total of 40 dollars. However, three music CDs and five cassette tapes cost 55 dollars. Find the price of each. a. $C D$= 12 dollars; cassette = 4 dollars b. $C D$= 15 dollars; cassette = 2 dollars c. $C D$= 10 dollars; cassette = 5 dollars

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Key Concepts

System of Linear Equations

This concept involves setting up and solving two or more equations that contain the same unknown variables. In the context of word problems, especially those related to costs or quantities, information is translated into equations whose solution yields the values of the unknowns.

Formulating Equations from Word Problems

This key idea involves interpreting the language of a problem to construct mathematical equations that accurately reflect the relationships described. It is essential for translating real-world situations into a form that can be analyzed with algebraic methods.

Verification of Candidate Solutions

In multiple-choice contexts, it is efficient to check whether the given answer options satisfy the conditions of the problem. This concept emphasizes testing each proposed solution in the original equations to identify the one that correctly meets all constraints.

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