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](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
where
slope of line
y-intercept
Let linear function to calculate total cost of gym be:
![c(n)=mn+b](https://tex.z-dn.net/?f=c%28n%29%3Dmn%2Bb)
where
total cost of gym
cost per month (slope)
number of months
start-up fee (y-intercept)
For Gym 1
,
![c(n)=20n+12](https://tex.z-dn.net/?f=c%28n%29%3D20n%2B12)
For Gym 2
,
![c(n)=22n+4](https://tex.z-dn.net/?f=c%28n%29%3D22n%2B4)
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)](https://tex.z-dn.net/?f=%28n%29)
![20n+12=22n+4](https://tex.z-dn.net/?f=20n%2B12%3D22n%2B4)
![\\\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}](https://tex.z-dn.net/?f=%5C%5C%5Ctextrm%7BSubtracting%2022n%20from%20both%20sides%7D%5C%5C20n-22n%2B12%3D22n-22n%2B4%5C%5C-2n%2B12%3D4%5C%5C%5Ctextrm%7BSubtracting%2012%20from%20both%20sides%7D%5C%5C-2n%2B12-12%3D4-12%5C%5C-2n%3D-8%5C%5C%5Ctextrm%7BDividing%20both%20sides%20by%20-2%7D%5C%5C%5Cfrac%7B-2%7D%7B-2%7Dn%3D%5Cfrac%7B-8%7D%7B-2%7D%5C%5Cn%3D4%5Ctextrm%7B%20months%7D)
So,
In 4 months the cost of both gyms will be the same.
Answer:
Therefore, x is 1 and 2.
Step-by-step explanation:
As you plot both equations on the same graph, you will get something like this, shown in the graph.
Then, you have to find the x solutions where they intersect.
So, both equations intersect at x = 1 and 2.
Answer:
(4,7)
Step-by-step explanation:
B is the correct answer I think