Question

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?

Answer 1

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

It will cost $ 24.

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,

`20 + 0.80x = 21 + 0.60x`

`0.80x - 0.60x = 21 - 20`

`0.20x = 1`

`\implies x = (1)/(0.20)=5`

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

Answer 2

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:

`y = 0.80x + 20`
For Debs online music club:

`y = 0.60x + 21`
Equaling both equations we have:

`0.80x + 20 = 0.60x + 21`
Clearing x we have:

`0.80x - 0.60x = 21 - 20 0.20x = 1 x = 1 / 0.20 x = 5 songs`
Substituting the value of x for any of the equations we have:

`y = 0.60 (5) + 21 y = 3 + 21 y = 24 $`
Answer:
The monthly charge will be the same for 5 songs in both clubs.
the cost will be $ 24