Sarah took the advertising department from her company on a round trip to meet with a potential client. including sarah a total of 11 people took the trip. she was able to purchase coach tickets for $210 and first class tickets for $1200. she used her total budget for airfare for the trip, which was $10,230. how many first class tickets did she buy? how many coach tickets did she buy?

You can set up a system of equations for this problem. x= number of coach tickets and y = number of first class tickets.

$210x + $1200y = $10,230 (cost of coach ticket plus cost of first class tickets is total budget)

x + y = 11 (number of coach tickets plus number of first class tickets is total number of people)

Solve the second equation for y to get y = 11 - x, then plug that into the first equation and solve for x:

$210x + $1200(11 - x) = $10,230

$210x + $13,200 - $1200x = $10,230

-$990x + $13,200 = $10,230

-$990x = $2,970

x = 3

Sarah bought x = 3 coach tickets. Plug that into the second equation and solve for y:

3 + y = 11

y = 8

Sarah bought y = 8 first class tickets.