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

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

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.