Question

Downloading songs from Source A costs $2.00 a song plus a monthly fee of $5.50. Downloading songs from Source B costs $3.00 a song with no monthly fee. The monthly cost to download songs depends on the number of songs, s, downloaded. Which inequality represents the situation when the monthly cost from Source A is greater than the monthly cost from Source B?

Answer 1

Answer: 5.50 > s

Explanation:

Let C(A) represent the monthly cost from Source A, and C(B) represent the monthly cost from Source B.

For Source A, the monthly cost includes both a monthly fee of $5.50 and the cost per song, which is $2.00 times the number of songs downloaded (s). So, for Source A:

C(A) = $5.50 + $2.00s

For Source B, there is no monthly fee, but the cost per song is $3.00 times the number of songs downloaded (s). So, for Source B:

C(B) = $3.00s

To represent the situation where the monthly cost from Source A is greater than the monthly cost from Source B, you can write the inequality:

C(A) > C(B)

Now, substitute the expressions for C(A) and C(B):

$5.50 + $2.00s > $3.00s

Now, subtract $3.00s from both sides of the inequality:

$5.50 > $3.00s - $2.00s

$5.50 > $1.00s

Now, divide both sides by $1.00 to isolate s:

$5.50/$1.00 > $1.00s/$1.00

5.50 > s

So, the inequality that represents the situation when the monthly cost from Source A is greater than the monthly cost from Source B is:

5.50 > s