Ariel is training for her pilot's license. The school requires students to learn from the teacher and learn in the simulator. Airplane tutoring costs $105 per hour, and the flight simulator costs $45 per hour. The school requires students to spend 4 more hours in airplane instruction than in the simulator. If Ariel can afford to spend $3870 on training, what is the maximum number of hours of training in an airplane and in a simulator she can afford in getting her license?

Simulator = 23 hours

Airplane = 27 hours

Step-by-step explanation:

Let the number of hours spent in the simulator be x.

Since the school requires students to spend 4 more hours in airplane instruction than in the simulator. Thai means that the number of hours spent in the airplane will be: x + 4

To determine the maximum number of hours of training in an airplane and in a simulator she can afford in getting her license will then be:

= 105(x+4) + 45(x) = 3870

105x + 420 + 45x = 3870

105x + 45x = 3870 - 420

150x = 3450

x = 3450/150

x = 23

Number of hours spent in simulator = 23 hours.

Number of hours used in airplane = 23 + 4 = 27 hours

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!

it has changed from the width and the height.

step-by-step explanation: