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There are 120 seats on an airplane. If a passenger reserved a seat at least two weeks early the passenger paid $150 for the flight. Other passengers paid $200. All 120 seats were sold and thr total amount paid by the passengers was $22,550. How many passengers paid the lower fee?

1 Answer

5 votes

What we need to do first in this type of problems is to identify clearly the variables, to do that we must read the final of the question, what they asks us to find is the number of passengers that will pay a lower feed, so it will be one of our varibles, let's define the variables now:

TW= number of passengers that reserved a seat at least two weeks early (they are the passengers that paid a lower fee)

OW= the other passengers

since we know that there are 120 seats on the airplane, and all the seats were sold we infer that:


TW+OW=120

and since we know that the total amount paid by the passengers was $22,550. we know that:


150TW+200OW=22,550

then we have a system of two equations with two variables, then it has a unique solution:

we can despejate OW from the first equation, obtaining:


OW=120-TW

Then we replace OW by 120-TW in the second equation:


150TW+200(120-TW)=22,550
150TW+24,000-200TW=22,550
-50TW=-1450
50TW=1450
TW=(1450)/(50)=29

Then the final answer is that 29 passengers of the airplane paid the lower fee.

User Davidavr
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