Samantha wants to join a gym. Gym A: $15 joining fee $35 monthly charge. Gym B: No joining fee $40 monthly charge. Enter the number of months for the total cost of both gyms to be equal.

3 months

Step-by-step explanation:

Given data

Gym A

$15 joining fee $35 monthly charge

let the number of months be x

and the total charges for x months be y

the expression for the total charges will be given as

y= 15+35x1

Gym B: No joining fee $40 monthly charge

let the number of months be x

and the total charges for x months be y

the expression for the total charges will be given as

y= 40x2

Equate 1 and 2

15+35x= 40x

collect like terms

15= 40x-35x

15= 5x

divide both sides by 5

x= 15/5

x= 3

Hence the number of months is 3 months

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

the correct answer is x/3+10≥32

hope this !