Respuesta :
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"
[tex]S=2+0.75(x-1)[/tex]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. "
[tex]P=3+0.50(x-1)[/tex]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
[tex]3+0.50(x-1)=2+0.75(x-1)\Rightarrow(0.75-0.50)(x-1)=3-2[/tex]Then
[tex](x-1)=\frac{1}{0.25}\Rightarrow x=\frac{1}{0.25}+1=4+1=5[/tex]So the answer is that after 5 months Mr.Kuszynski will pay the same amount in both streaming services.
