Jason got a new mp3 player for his birthday. He is very excited to get started downloading songs. He looks online and finds two companies that offer different pricing options for song downloads. Company A charges $1.25 per song. Company B charges $0.65 per song plus a one-time $4 membership fee. What is the maximum number of songs that can be purchased in order for Company A to be a better buy? Responses A 3 songs3 songs B 4 songs4 songs C 5 songs5 songs D 6 songs6 songs E 7 songs
To determine the maximum number of songs that can be purchased in order for Company A to be a better buy, we need to compare the total cost of purchasing songs from both companies.
For Company A, the cost of purchasing a song is $1.25, regardless of the number of songs purchased.
For Company B, the cost of purchasing a song is $0.65 plus a one-time $4 membership fee. So, the total cost of purchasing x number of songs from Company B would be: 4 + (0.65 * x).
Now, we can set up an inequality to represent the condition when Company A is a better buy than Company B:
1.25x < 4 + 0.65x
Subtracting 0.65x from both sides, we get:
0.6x < 4
Now, dividing both sides by 0.6, we get:
x < 6.67
Since we cannot purchase a fraction of a song, the maximum number of songs that can be purchased for Company A to be a better buy is 6 songs (D).