# Sarah took the advertising department from her company on a round trip to Chicago to meet with a potential client.Including Sarah, a total of 14 people took the trip. She was able to purchase coach...

Sarah took the advertising department from her company on a round trip to Chicago to meet with a potential client.Including Sarah, a total of 14 people took the trip.

She was able to purchase coach tickets for $250 and first-class for $1150. The total budget for airfare for the trip was $10,700.How many first-class tickets did she buy?How many coach tickets did she buy?

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We need to create a system of simultaneous equations as we have more than one unknown quantity (amount)

Let x = tickets for those in coach and y= 1st class tickets and we know we need 14 tickets:

- `therefore x + y = 14`

We also know the budget was $10 700 and the cost for each type:

2. `therefore 250x + 1150y = 10700`

Now we multiply 1. by ( - 250) so that we can eliminate one of our unknowns:

3. `- 250x- 250y = -3500`

Now add 2 to 3

`0x + 900y= 7200`

`therefore y = 7200/900`

`therefore y = 8`

Now subsitute into one of your previous equations to find x :

`x+y=14`

`therefore x = 14-8`

`therefore x=6`

**Therefore there are 6 coach tickets and 8 first class tickets purchased**

**Sources:**