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
Let x be the number of songs purchased.
For Company A, the cost is $1.25 per song.
Cost for Company A = $1.25x
For Company B, the cost is $0.65 per song plus a $4 membership fee.
Cost for Company B = $0.65x + $4
We want to find the maximum number of songs for which Company A is a better buy. In other words, we want to find the point at which the cost for Company A is less than the cost for Company B.
So, $1.25x < $0.65x + $4
$1.25x - $0.65x < $4
$0.6x < $4
x < 6.67
Therefore, Jason can purchase a maximum of 6 songs for Company A to be a better buy. So, the answer is D. 6 songs.