Question

Moe is deciding which music streaming service to join. Apple Music charges an initial fee of $95 for the first month, and $12 for each additional month. Spotify charges an initial fee of $47 for the first month, and $18 for each additional month. How many months, m, will it take for Apple Music and Spotify to be the same?

A) 3 months
B) 4 months
C) 5 months
D) 6 months

Answer 1

After setting up an equation to represent the total cost of Apple Music and Spotify over m months, and solving for m, we find that it will take 9 months for the costs of the two music streaming services to be the same.

Step-by-step explanation:

To determine how many months it will take for the cost of Apple Music and Spotify to be the same, we can set up an equation where the total cost of each service is equal. The total cost for Apple Music after m months is the initial fee of $95 plus $12 for each additional month, which can be represented as 95 + 12(m-1). The total cost for Spotify after m months is the initial fee of $47 plus $18 for each additional month, represented as 47 + 18(m-1).

We set the two expressions equal to each other to find the value of m:
95 + 12(m-1) = 47 + 18(m-1).

Distributing and simplifying the equation gives us:
95 + 12m - 12 = 47 + 18m - 18.

Then, we simplify further to:
83 + 12m = 29 + 18m.

Subtracting 12m from both sides gives us:
83 = 29 + 6m.

Subtracting 29 from both sides, we get:
54 = 6m.

Dividing both sides by 6, we find m:

Therefore, it will take 9 months for the costs of Apple Music and Spotify to be the same.