you have a subscription to a music website that allows you to download 25 songs from the site each month. You are charged an additional fee after the first 25 songs are downloaded. After downloading 28 songs, you paid a total of $34.80. After downloading 30 songs, you paid a total of $40.70.
a: what is the cost per song after the first downloaded?
b: what is the cost of the website subscription?
charge for first 25 songs --- x dollars per song
charge for songs over 25 ---- y dollars per song
25x + 3y = 34.8
25x + 5y = 40.7
subtract the 1st from the 2nd
2y = 5.9
y = $2.95
sub into the 1st
25x + 3(2.95) = 34.8
25x = 25.95
x = $1.04
To find the cost per song after the first downloaded (a), we need to subtract the cost of the subscription fee from the total charged and then divide that by the number of additional songs beyond the 25 that are included in the subscription.
To calculate the cost per song after the first downloaded:
1. Let's subtract the cost of the subscription fee from the total charged for both cases:
- In the first scenario, after downloading 28 songs, the total charge was $34.80. Since we can download 25 songs within the subscription fee, the cost of the remaining 3 songs is 34.80 - subscription fee.
- In the second scenario, after downloading 30 songs, the total charge was $40.70. Here, we can download 25 songs within the subscription fee, so the cost of the additional 5 songs is 40.70 - subscription fee.
2. Next, we need to find out how many additional songs were downloaded in each scenario:
- In the first scenario, we downloaded a total of 28 songs, with 25 of them covered by the subscription fee. So, we downloaded 28 - 25 = 3 additional songs.
- In the second scenario, we downloaded a total of 30 songs, with 25 of them covered by the subscription fee. Thus, we downloaded 30 - 25 = 5 additional songs.
3. Now, we can calculate the cost per song after the first downloaded:
- In the first scenario: (34.80 - subscription fee) / 3 = cost per song after the first downloaded.
- In the second scenario: (40.70 - subscription fee) / 5 = cost per song after the first downloaded.
To find the cost of the website subscription (b), we can use one of the scenarios where the total charge includes the subscription fee, and the additional song cost is eliminated.
Let's solve these equations to find the values of (a) and (b).