Question

Mr.Kuszynski is choosing which music streaming service he should get. Spoofy has an introductory rate of $2, then charges $0.75 each month after the first. Pear Music has a promotion so the first month is $3 and all following months are $0.50. After how many months would Mr.Kuszynski pay the same amount? If Mr.Kuszynski wanted to subscribe for a year, which plan should he go with? Find the difference between the two plans after a year.

Answer 1

Let's first put the information that is given to us in a mathematical lenguage:

1. Define the variables

- Let S be the cost of streaming with Spoofy after x months

-Let P be the cost of streaming with Pear music after x months

- x is a number of months that is able to vary

2. Convert the conditions given in the problem into a mathematical lenguage:

- Since "Spoofy has an introductory rate of $2, then charges $0.75 each month after the first"

`S=2+0.75(x-1)`

we write (x-1) instead of x because it only counts after the first month.

-Since "Pear Music has a promotion so the first month is $3 and all following months are $0.50. "

`P=3+0.50(x-1)`

Then they ask us in what month (x represent the months) are those values equal, so we will proceed to equalize the equations P and S, and solve for x

`3+0.50(x-1)=2+0.75(x-1)\Rightarrow(0.75-0.50)(x-1)=3-2`

Then

`(x-1)=(1)/(0.25)\Rightarrow x=(1)/(0.25)+1=4+1=5`

So the answer is that after 5 months Mr.Kuszynski will pay the same amount in both streaming services.