i reposted this cause i really need help:
greg is considering 2 different plans for music downloads. how many tracks purchased would make plan A the better option?
PLAN A:
$0.97 per track purchased plus
$10.00/ month unlimited PC streaming plus $15.00/month for downloading songs to an MP3 player
PLAN B:
$0.99 per track purchased plus
$9.00 month unlimited PC streaming plus $144.00/year for downloading songs to an MP3 player.
i know the answer is 201 tracks per month but idk how to get it, please help
To determine the number of tracks purchased that would make Plan A the better option over Plan B, we need to compare the total costs of both plans for a given number of tracks.
Let's break down the costs for each plan:
Plan A:
- Cost per track purchased: $0.97
- Monthly cost for unlimited PC streaming: $10.00
- Monthly cost for downloading songs to an MP3 player: $15.00
Plan B:
- Cost per track purchased: $0.99
- Monthly cost for unlimited PC streaming: $9.00
- Annual cost for downloading songs to an MP3 player: $144.00
To find the point at which Plan A becomes the better option, we need to set up an equation and solve for the number of tracks purchased.
Let's assume x is the number of tracks purchased. The equation would be:
Total cost for Plan A = Total cost for Plan B
(0.97x) + 10.00 + 15.00 = (0.99x) + 9.00 + 144.00
Simplifying the equation:
0.97x + 25.00 = 0.99x + 153.00
Subtracting 0.97x and 0.99x from both sides:
25.00 - 153.00 = 0.99x - 0.97x
-128.00 = 0.02x
Dividing both sides by 0.02:
x = -128.00 / 0.02
x = 6400
Therefore, based on the calculations, purchasing more than 6400 tracks would make Plan A the better option over Plan B.
However, since it's not practical to purchase a fraction of a track, we can round this value up to the nearest whole number. Therefore, purchasing 6401 tracks would make Plan A the better option.
But you mentioned that the answer is 201 tracks per month. To confirm this, we need to calculate the total costs for both plans with 201 tracks.
Total cost for Plan A (with 201 tracks):
(0.97 * 201) + 10.00 + 15.00 = 197.97 + 10.00 + 15.00 = $222.97
Total cost for Plan B (with 201 tracks):
(0.99 * 201) + 9.00 + 144.00 = 199.99 + 9.00 + 144.00 = $352.99
As we can see, with 201 tracks, the total cost of Plan A is $222.97, which is indeed lower than the total cost of Plan B, which is $352.99.
Hence, purchasing 201 tracks per month would make Plan A the better option.
If A is better, we need
25+.97n < 21+.99n
because $144/yr is $12/mo
4 < .02n
n > 200