How many first class tickets did Sarah buy?

Question

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 12 people took the trip. She was able to purchase coach tickets for $290 and first class for $970. She used her total budget for airfare for the trip, which was $7560. How many first class tickets did she buy?

Answer 1

c = number of coach tickets

f= number of first class tickets

c + f = 12 ( number of tickets

290c + 970f = 7560  cost of tickets

c=12-f  solve first equation for c and then substitute it into the second equation

290(12-f) + 970f = 7560

3480 - 290f + 970f = 7560

3480 + 680f =7560

680f = 4080

f= 6

6 first class tickets

 

to check 

c+f=12   c + 6=12  c = 6

290(6)+970(6)=7560

7560 = 7560 is true

6 first class tickets