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Travka [436]
3 years ago
12

At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

but after that, each month at the gym costs $22. After how many months will the cost of both gyms be thge same?
Mathematics
1 answer:
mart [117]3 years ago
5 0

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

f(x)=mx+b

where

m\rightarrow slope of line

b\rightarrow y-intercept

Let linear function to calculate total cost of gym be:

c(n)=mn+b

where

c\rightarrow total cost of gym

m\rightarrow cost per month (slope)

n\rightarrow number of months

b\rightarrow start-up fee (y-intercept)

For Gym 1

m=20 , b=12

c(n)=20n+12

For Gym 2

m=22 , b=4

c(n)=22n+4

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 (n)

20n+12=22n+4

\\\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}

So,

In 4 months the cost of both gyms will be the same.

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