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Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for economy. If a fight had 52 passengers who paid a total of $1360, how many first class passengers were there?

User Esdes
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1 Answer

4 votes

Answer:

Number of first class passengers = 12

Explanation:

  • We will need a system of equations to determine the number of first class passengers.

For our system, we can allow:

  • E to represent the number of economy passengers,
  • and F to represent the number of first class passengers

First equation:

We know that the revenues earned from the first class and economy tickets equals the total revenue:

(economy fare * quantity) + (first class fare * quantity) = total revenue.

Since the economy fare is $25. the first class fare is $30, and the total revenue is $1360, our first equation is given by:

25E + 30F = 1360

Second equation:

We also know that the sum of the economy and first class passengers equals the total number of passengers:

economy passengers + first class passengers = total number of passengers

Since there are 52 passengers in total, our second equation is given by:

E + F = 52

Method to solve: Substitution:

We can start by isolating E in the second equation:

(E + F = 52) - F

E = -F + 52

Now we can solve for F (i.e., the number of first class passengers) by substituting -F + 52 for E in the first equation (i.e., 25E + 30F = 1360):

25(-F + 52) + 30F = 1360

-25F + 1300 + 30F = 1360

(5F + 1300 = 1360) - 1300

(5F = 60) / 5

F = 12

Thus, there were 12 first class passengers.

Optional Step 3: Check the validity of the answer:

Before we can check whether our answer is correct, we first need to find E (i.e., the number of economy passengers) by plugging in 12 for F in the second equation (i.e., E + F = 52):

(E + 12 = 52) - 12

E = 40

Thus, there were 40 economy passengers.

Now we can check that our answers are correct by plugging in 12 for F and 40 for E in both equations and seeing if we get the same answer on both sides:

Checking the validity of the answer with the first equation:

25(40) + 30(12) = 1360

1000 + 360 = 1360

1360 = 1360

Checking the validity of the answer with the second equation:

40 + 12 = 52

52 = 52

Thus, our answers are correct.

User Ataraxia
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