Solve the problem by setting up and solving a system of two linear equations in two variables. Chip downloaded 21 songs for his MP3 player for a total cost of $22.20. The songs from Muchmore Music cost $1.00 each, and the songs from iTunes cost $1.20 each. How many songs did Chip download from each service?
A) 17 songs from Muchmore 4 songs from iTunes
B) 16 songs from Muchmore 5 songs from iTunes
C) 18 songs from Muchmore 3 songs from iTunes
D) 15 songs from Muchmore 6 songs from iTunes
E) 19 songs from Muchmore 2 songs from iTunes

Question

Quizplus · Accepted Answer

Let x be the number of songs downloaded from Muchmore Music and y be the number of songs downloaded from iTunes. We can set up the following system of equations:

x + y = 21 (total number of songs downloaded)
1.00x + 1.20y = 22.20 (total cost of songs downloaded)

To solve for x and y, we can use the elimination method. Multiplying the first equation by -1 and adding it to the second equation, we get:

-1x - 1y = -21
1.00x + 1.20y = 22.20
---------------------
0.20y = 1.20

y = 6

Substituting y=6 into the first equation, we get:

x + 6 = 21

x = 15

Therefore, Chip downloaded 15 songs from Muchmore Music and 6 songs from iTunes, making D the correct answer.

Solve the Problem by Setting Up and Solving a System