Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?

For this case, the first thing we must do is define variables.
We have then:
x: number of songs.
y: total charge
For Treys online music club:
[tex]y = 0.80x + 20 [/tex]
For Debs online music club:
[tex]y = 0.60x + 21 [/tex]
Equaling both equations we have:
[tex]0.80x + 20 = 0.60x + 21 [/tex]
Clearing x we have:
[tex]0.80x - 0.60x = 21 - 20 0.20x = 1 x = 1 / 0.20 x = 5 songs[/tex]
Substituting the value of x for any of the equations we have:
[tex]y = 0.60 (5) + 21 y = 3 + 21 y = 24 $[/tex]
Answer:
The monthly charge will be the same for 5 songs in both clubs.
the cost will be $ 24

parmesanchilliwack parmesanchilliwack · Answer 2 · 2025-04-03T16:31:13-04:00

Answer:

For 5 songs the monthly charge be the same for both clubs.

It will cost $ 24.

Step-by-step explanation:

Let, for x songs, the monthly charges are same for both clubs,

Given,

For Treys online music club,

Monthly rate = $ 20,

Additional Charges for a song = $ 0.80,

⇒ Additional Charges for x song = $ 0.80x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 20 + 0.80x

Now, for Debs online music club,

Monthly rate = $ 21,

Additional Charges for a song = $ 0.60,

⇒ Additional Charges for x song = $ 0.60x,

Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song

= 21 + 0.60x

Hence, we can write,

[tex]20 + 0.80x = 21 + 0.60x[/tex]

[tex]0.80x - 0.60x = 21 - 20[/tex]

[tex]0.20x = 1[/tex]

[tex]\implies x = \frac{1}{0.20}=5[/tex]

Hence, for 5 songs the monthly charge be the same for both clubs.

Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24