solve using two equations with two variables

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 tickets for $1150. She used her total budget for airfare for the trip, which was $10,700. How many first-class tickets did she buy?
How many coach tickets did she buy?

Question

solve using two equations with two variables

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 tickets for $1150.  She used her total budget for airfare for the trip, which was $10,700.  How many first-class tickets did she buy?
How many coach tickets did she buy?

anonymous · Answer

I need help in setting up my equations.

anonymous · Answer

I haven't done word problems like this, but this would be how I envision the setup:
You have x amount of people flying coach, and y amount of people flying first-class, with the total cost being $10,700.

250x+1150y=10700.

Now, because x and y have to add up to be 14,

x+y=14.

Now you can either use substitution; matrix manipulation; elimination, what have you, to solve this.

anonymous · Answer

I set it up like that and I am stuck solving the equation.  I am coming up with a bunch of fractions.

anonymous · Answer

Okay, try using substitution. In the second equation, set x = 14-y. Plug (14-y) into your first equation, in place of x, and you'll get a clean value for y. Then, you know how many first-class; which leads you to how many coach tickets.

anonymous · Answer

That's it.  Thanks!!

anonymous · Answer

Glad to help. :)