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.