I don't know how to solve this

Question

A music website charges

x dollars for individual songs and y dollars for

entire albums. Person A pays $25.92

to download 6 individual songs and

2 albums. Person B pays $33.93

to download 4 individual songs

and 3 albums. How much does

the website charge to download

a song? an entire album?

Answer 1

For person A: 6x + 2y = 25.92

For person B: 4x +3y = 33.93

we solve this system of linear equations to find the values of x (cost per song) and y (cost per album)

We can use substitution or elimination methods to solve. Here we use the elimination method.

We now multiply equation 1 by 3 and equation 2 by 2

3(6x + 2y = 25.92) = 18x + 6y = 77.76

2 (4x + 3y = 33.93) = 8x + 6y = 67.86

by subtracting the second modified equation from the first modified equation, we can eliminate y

(18x + 6y ) - (8x + 6y) = 77.76 - 67.86

18x -8x + 6y - 6y = 9.9

10x = 9.9

x = 0.99

Now that we have x = 0.99, we substitute this value back into one of the original equations to solve for y. Using equation 1:

6(0.99) + 2y = 25.92

5.94 + 2y = 25.92

2y = 25.92 - 5.94

2y = 19.98

y = 9.99

Therefore, the website charges $0.99 to download a song and $9.99 to download an entire album.

Answer 2

We can set up the following equation for person A:

6x + 2y = $25.92

We can set up the following equation for person B:

4x + 3y = $33.93

Now we have two equations with two unknowns which we can solve by substitution.

Let's start by solving equation 1 for y.

6x + 2y = 25.92

we subtract 6x from both sides.

2y = 25.92 - 6x

then we divide both sides by 2

y = 12.96 - 3x

Now we can substitute this for y in the second equation which gets us:

4x + 3 (12.96 - 3x) = $33.93

Now we solve for x:

4x + 3 (12.96 - 3x) = 33.93

4x + 38.88 - 9x = 33.93

38.88 - 5x = 33.93

-5x = -4.95

x = 0.99

So, x = 0.99 meaning one individual song is 99 cents.

Now we plug that x value into either equation. I chose the first one:

6x +2y = $25.92

so,

6(0.99) + 2y = 25.92

then we solve for y:

5.94 + 2y = 25.92

2y = 19.98

y = 9.99

So, y = 9.99 meaning an entire album is $9.99