Question

Two music CDs and four DVDs cost a total of $\$ 40$. However, three music CDs and five DVDs cost $\$ 55 .$ Find the price of each. a. $C D=\$ 12 ; D V D=\$ 4$ b. $C D=\$ 15 ; D V D=\$ 2$ c. $\mathrm{CD}=\$ 10 ; \mathrm{DVD}=\$ 5$

Name: Problem 4, Chapter 4: Algebra A Combined Function
Uploaded: 2022-03-16T17:15:47-08:00
Duration: 2 min 54 s
Channel: Amanda Zielke
Description: Two music CDs and four DVDs cost a total of 40. However, three music CDs and five DVDs cost 55 . Find the price of each. a. C D= 12 ; D V D= 4 b. C D= 15 ; D V D= 2 c. CD= 10 ; DVD= 5

   Two music CDs and four DVDs cost a total of $\$ 40$. However, three music CDs and five DVDs cost $\$ 55 .$ Find the price of each.
a. $C D=\$ 12 ; D V D=\$ 4$
b. $C D=\$ 15 ; D V D=\$ 2$
c. $\mathrm{CD}=\$ 10 ; \mathrm{DVD}=\$ 5$

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 4, Problem 4

Instant Answer

Solved by Expert Amanda Zielke

03/16/2022

Step 1

Let's denote the price of a CD as C and the price of a DVD as D. From the problem, we know that: \begin{align*} 2C + 4D &= 40 \quad (1) \\ 3C + 5D &= 55 \quad (2) \end{align*} Show more…

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Two music CDs and four DVDs cost a total of $\$ 40$. However, three music CDs and five DVDs cost $\$ 55 .$ Find the price of each. a. $C D=\$ 12 ; D V D=\$ 4$ b. $C D=\$ 15 ; D V D=\$ 2$ c. $\mathrm{CD}=\$ 10 ; \mathrm{DVD}=\$ 5$

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Key Concepts

Elimination Method

The elimination method is a technique used to solve systems of equations by adding or subtracting the equations to cancel out one variable, thereby reducing the system to a single equation with one unknown. This method is efficient for solving systems where the coefficients of one of the variables are easily manipulated to cancel one another.

System of Linear Equations

A system of linear equations involves two or more linear equations with the same set of unknown variables. Solving these systems means finding the values for the variables that make all the equations valid simultaneously, a fundamental concept in algebra with wide applications in various fields.

Substitution Method

The substitution method involves solving one of the equations for one variable and then substituting this expression into the other equation(s). This technique reduces the system to fewer equations, making it simpler to isolate and solve for the remaining variable(s).

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