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?
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 :
`therefore x = 14-8`
Therefore there are 6 coach tickets and 8 first class tickets purchased