Ariel plane is training for her pilot's license. Airplane instruction costs $105 per hour, and the flight simulator costs $45 per hour. The school requires students to spend 4 more hours in airplane instructions 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?
Answer Choices Are:
a) 27 hours of instructions and 23 hours of simulator.
b) 25 hours of instructions and 29 hours of simulator.
c) 29 hours of instructions and 25 hours of simulator.
d) 23 hours of instructions and 27 hours of simulator.
e) 62 hours of instructions and 58 hours of simulator.

PLEASE HELP!!!!!!!

The maximum number of hours of training in an airplane and in a simulator she can afford in getting her license is (a) 27 hours of instructions and 23 hours of simulator.

Represent the time spent in airplane instructions with x, and the time spent in flight simulation with y.

So, we have the following equations

[tex]105x + 45y = 3870[/tex] -- the total amount spent

[tex]x = 4 + y[/tex] --- the relationship between the time spent

Substitute 4 + y for x in the first equation

[tex]105*(4 + y) + 45y = 3870[/tex]

[tex]420 + 105y + 45y = 3870[/tex]

[tex]420 + 150y = 3870[/tex]

Subtract 420 from both sides

[tex]150y = 3450[/tex]

Divide both sides by 150

[tex]y = 23[/tex]

Recall that:

[tex]x =4 + y[/tex]

So, we have:

[tex]x =4 + 23[/tex]

[tex]x =27[/tex]

Hence, the maximum number of hours of training are (a) 27 hours of instructions and 23 hours of simulator.

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