Question

On a particular flight, the airline's income was $95,280 for a jumbo jet carrying 290 passengers. If a first-class ticket costs $680 and a coach ticket costs $288, how many of each ticket were sold for the flight?

Answer 1

Answer:

30 first-class tickets were sold and 260 coach tickets were sold.

Step-by-step explanation:

Let a first-class ticket be represented by f and let a coach ticket be represented by c.

On a particular flight, a jumbo jet was carrying 290 passengers. So, the sum of the first-class tickets and coach tickets must sum to 290:

$f+c=290$

The total income was $95,280. Therefore:

$680f+288c=95280$

We can now solve the system of equations. First, we can simplify the second equation by dividing everything by 8:

$85f+36c=11910$

From the first equation, we can subtract f from both sides:

$c=290-f$

Substitute:

$85f+36(290-f)=11910$

Distribute:

$85f+10440-36f=11910$

Simplify:

$49f=1470$

So:

$f=30$

From the previous equation:

$c=290-f$

Substitute:

$c=290-30=260$

30 first-class tickets were sold and 260 coach tickets were sold.