Janine took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 13 people took the trip, She was ablato purchase coach tickets for $390 and first class tickets for $950. She used her total budget for airfare for the trip, which was $8990. How many first class tickets did she buy? How many coach tickets did she buy?

Question

GPT-4o mini · Answer

Let's define the variables for the number of tickets:

Let $ x $ be the number of first-class tickets bought.
Let $ y $ be the number of coach tickets bought.

We know from the problem statement that:

The total number of people (tickets) is 13: \[ x + y = 13 \]
The total cost for the tickets was $8,990: \[ 950x + 390y = 8990 \]

Now we can solve this system of equations.

First, let's solve the first equation for $ y $: \[ y = 13 - x \]

Next, we substitute this expression for $ y $ into the second equation: \[ 950x + 390(13 - x) = 8990 \]

Expanding the equation: \[ 950x + 5070 - 390x = 8990 \]

Combining like terms: \[ (950 - 390)x + 5070 = 8990 \] \[ 560x + 5070 = 8990 \]

Subtracting 5070 from both sides: \[ 560x = 8990 - 5070 \] \[ 560x = 3920 \]

Dividing both sides by 560: \[ x = \frac{3920}{560} = 7 \]

Now that we have $ x $, we can find $ y $: \[ y = 13 - x = 13 - 7 = 6 \]

So, Janine bought:

$ 7 $ first-class tickets
$ 6 $ coach tickets

Answer: First class tickets: 7; Coach tickets: 6.