Question

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 ​$150 and first class tickets for ​$920. She used her total budget for airfare for the​ trip, which was ​$4730. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answer 1

Set up a system of equations:
x = # of coach seats
y= # of 1st class seats
Each coach seat (x) cost 150
Each 1st class seat (y) cost 920
Total spent is 4730
150x + 920y = 4730

Total seats (coach + 1st class) is 11
x + y = 11

System of equations:
150x + 920y = 4730
x + y = 11
Substitute (11- y) for x in the first equation:
150 (11 - y) + 920y = 4730 Distribute
1650 - 150y + 920y = 4730 Subtract 1650, add like terms
770y = 3080
y = 4
4 first-class seats were booked
Plug y = 4 into the other equation:
x + y = 11
x+ 4 = 11
x = 7

Answer is (7,4)
7 coach seats, 4 first class seats