Pregunta
- Airline fares for a flight from Dallas to Austin are
for first class and
for tourist class. If a
flight had 52 passengers who paid
, how many first class and tourist class passengers were
there?
flight had 52 passengers who paid
there?
Ask by Mejia Pollard. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
There were 12 first class passengers and 40 tourist class passengers on the flight.
Solución
To determine the number of first class and tourist class passengers on the flight from Dallas to Austin, we can set up a system of equations based on the given information.
Let:
-
= number of first class passengers -
= number of tourist class passengers
Given:
- The total number of passengers is 52:
- The total revenue from fares is $1360:
Steps to Solve:
-
Solve Equation 1 for
: -
Substitute
into Equation 2: -
Expand and simplify:
-
Solve for
: -
Find
using the value of :
Conclusion:
- First Class Passengers: 12
- Tourist Class Passengers: 40
Verification:
- Total passengers:
✓ - Total revenue:
✓
Answer:
There were 12 first class passengers and 40 tourist class passengers on the flight.
There were 12 first class passengers and 40 tourist class passengers on the flight.
Respondido por UpStudy AI y revisado por un tutor profesional
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Beyond the Answer
To find out how many first class and tourist class passengers were on the flight, we can set up a system of equations. Let
be the number of first class passengers and
be the number of tourist class passengers.
We have two equations based on the problem:
-
(total passengers) -
(total fare)
Now we can solve these equations:
From the first equation, we can express
as:
Next, substitute
in the second equation:
Expanding this gives:
Combining like terms, we have:
Subtracting 1300 from both sides results in:
Now, divide by 5:
Using the value of
to find
:
Thus, there were 12 first class passengers and 40 tourist class passengers on the flight.
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