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1. “Systems of Linear Equations”
American Airlines sold a certain number of tickets from Los Angeles to Hawaii. They charged $90
for flight x and the remaining tickets for $250 for flight y. If the airline sold 120 tickets and
collected a total of $27,600 from the sale of those tickets:
a) Set up the System of Linear Equations
b) How many tickets of each flight were sold?
c) How much money was made from each flight?

1. “Systems of Linear Equations” American Airlines sold a certain number of tickets from Los Angeles to Hawaii. They charged $90 for flight x and the remaining class=

Answer :

xKelvin

Answer:

Part A)

[tex]\begin{aligned} x+y&=120 \\ 90x+250y&=27600\end{aligned}[/tex]

Part B)

Flight X sold 15 tickets and Flight Y sold 105 tickets.

Part C)

Flight X made $1,350 and Flight Y made $26,250.

Step-by-step explanation:

Let the amount of tickets sold by Flight X be represented by x and the amount of tickets sold by Flight Y be represented by y.

Part A)

The airline sold 120 tickets in total. Hence:

[tex]x+y=120[/tex]

Each x ticket costs $90 and each y ticket costs 250. The total income was $27,600. Thus:

[tex]90x+250y=27600[/tex]

Our system of equations is:

[tex]\begin{aligned} x+y&=120 \\ 90x+250y&=27600\end{aligned}[/tex]

Part B)

Solve the system of equations. We can use substitution. From the first equation, subtract y from both sides:

[tex]x=120-y[/tex]

In the second equation, we can divide everything by 10 and substitute in x:

[tex]9(120-y)+25y=2760[/tex]

Simplify:

[tex]16y+1080=2760[/tex]

So:

[tex]y=105\text{ tickets}[/tex]

Using the equation above:

[tex]x=120-(105)=15\text{ tickets}[/tex]

Flight X sold 15 tickets and Flight Y sold 105 tickets.

Part C)

Since each ticket of Flight X sold for $90 and Flight X sold 15 tickets, Flight X made $1,350.

Then it follows that Flight Y made $26,250.

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