Answer:
The best option depends on how many songs you plan to purchase.
Option 1 will be the best option if you wish to purchase an unlimited amount of songs or more than 16 per month for the total cost of one year of $245. It's modeled by the equation y=10x+125 where x is months and y is total annual cost.
Option 2 will be the best option if you wish to purchase less than 16 songs a month. This would be 16(12) = 192 songs a year. To stay under the cost of option 1 you can buy only 195 songs in a year. Paying for each song individually at $1 plus a lower annual fee will result in you spending $242 dollars a year or less if you purchase less songs. It's modeled by the equation y=1s+50 where s is the number of songs downloaded in a year and y is total annual cost.
Because your average of 14 songs a month is less than 16 songs a month, option 2 is your best option. You will download all the songs you normally do and pay less than option 1. Your cost under Option 1 would be $245. Your cost under Option 2 would be $218.
Step-by-step explanation:
Each option in the electronic music club represents a linear function. Each option has a constant rate of change charged per month or song. This is your slope. Each option has a one time annual fee charged. This is your y-intercept.
Option 1 has a constant rate (m) of $10 per month with an annual fee (b) of $125. Using Slope-Intercept form, y=mx+b, we can write the function y=10x+125 where x is number of months and y is total cost in 12 months.
Option 2 has a constant rate (s) of $1 per song with an annual fee (b) of $50. Using Slope-Intercept form, y=mx+b, we can write the function y=1s+50 where s is number of songs and y is total cost in 12 months.
We know the total annual cost of Option 1 by substituting x=12 months to represent a year.
y=10(12)+125=120+125=245.
We find when Option 2 will be the same cost by substituting y=245 into y=1s+50 and solve for s.
245=1s+50
245-50=1s+50-50
195=1s
This means that both options will be the same cost for one year if we purchase 195 songs that year. If we purchase more, than Option 1 is the best choice. If we purchase less than 195, Option 2 remains the best choice.
Lastly, if your average number of songs is 14 per month, we can find 14(12)=168 songs in a year. This is lower than 195. Thus option 2 is the best answer for you.
