2021-01-10

Two groups of students bought airline tickets to go to a conference. One group bought two tickets from Airline 1 and three tickets from Airline 2 and their total was $900 before taxes and fees. The other group bought one ticket from Airline 1 and four tickets from Airline 2, and their total was$950 before taxes and fees. How much does a ticket cost of each airline?

Jayden-James Duffy

Let x be the cost of a ticket on Airline 1 and y be the cost of a ticket on Airline 2.
Two tickets from Airline 1 and three tickets from Airline 2 cost $900: $2x+3y=900$(1) One ticket from Airline 1 and four tickets from Airline 2 cost$950:
$x+4y=950$(2)
Solve by substitution. Solve for xx using (2) to obtain (3):
$x=950-4y$(3)
Substitute (3) to (1) and solve for yy:
$2\left(950-4y\right)+3y=900$
$1900-8y+3y=900$
$-5y=-1000$
$y=200$
Solve for x using (3):
$x=950-4\left(200\right)$
$x=950-800$
$x=150$
The cost of a ticket on Airline 1 is $150, and the cost of a ticket on Airline 2 is$200.

Jeffrey Jordon