Let x = the amount of months you pay for each subscription.
Let y = the amount you pay per song downloaded.
If Store 1 makes you pay $10 a month plus $1 per song, your equation is 10x + 1y or just 10x + y
If Store 2 makes you pay $30 a month but no extra cost per song, your equation here is 30x + 0y or just 30x (since anything times 0 is zero, we can just take it away completely).
<u>A)</u> Now we set them equal to each other and solve for y, the amount of songs you'd need to download.
10x + y = 30x
Subtract 10x from both sides and combine like terms:
y = 30x - 10x
y = 20x
You would need to download 20 times the amount of months you are paying for for the cost of the first store to equal that of the second store. So if you were to pay for 3 months, you'd need to buy 60 songs. 4 months = 80 songs. 1 month = 20 songs, and so on. Without a specific amount of months in the question, you'll get a linear answer like this with no definitive ending answer.
<u>B)</u> Now we set y = 15 for each equation separately, then we compare which one would be more cost-efficient (which one is the least expensive).
10x + 1(15) = 10x + 15
30x + 0(15) = 30x
Store 1 is looking like the better store. If you pay for 1 month, you're only paying $25 as opposed to $30. If you pay for 2 months, you pay $35 at Store 1, $60 at Store 2. 3 months = $45 at Store 1, $90 at Store 2.
