Respuesta :
Answer:
In 4 months the cost of both gyms will be the same.
Step-by-step explanation:
At first we need to model the function to calculate the cost of the 2 gyms.
Slope-intercept equation of linear function
[tex]f(x)=mx+b[/tex]
where
[tex]m\rightarrow[/tex] slope of line
[tex]b\rightarrow[/tex] y-intercept
Let linear function to calculate total cost of gym be:
[tex]c(n)=mn+b[/tex]
where
[tex]c\rightarrow[/tex] total cost of gym
[tex]m\rightarrow[/tex] cost per month (slope)
[tex]n\rightarrow[/tex] number of months
[tex]b\rightarrow[/tex] start-up fee (y-intercept)
For Gym 1
[tex]m=20[/tex] , [tex]b=12[/tex]
[tex]c(n)=20n+12[/tex]
For Gym 2
[tex]m=22[/tex] , [tex]b=4[/tex]
[tex]c(n)=22n+4[/tex]
In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months [tex](n)[/tex]
[tex]20n+12=22n+4[/tex]
[tex]\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}[/tex]
So,
In 4 months the cost of both gyms will be the same.
