Question

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for ​$160 and first class tickets for ​$1230. She used her total budget for airfare for the​ trip, which was ​$6950. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answer 1

Explanation:

c + f = 10 (the coach tickets + first class tickets = 10)...there is 10 people

160c + 1230f = 6950....each coach ticket is 160 and each first class ticket is 1230.....and when added, they equal 6950 (for the airfare)

c + f = 10.....c = 10 - f

160c + 1230f = 6950

sub in 10 - f for c

160(10 - f) + 1230f = 6950

distribute the 160 thru the parenthesis

1600 - 160f + 1230f = 6950

combine like terms

1600 + 1070f = 6950

subtract 1600 from both sides

1070f = 6950 - 1600

1070f = 5350

divide both sides by 1070

f = 5350/1070

f = 5 <===== she bought 5 first class tickets

c + f = 10

we found f to be 5...so sub in 5 for f and find c, the coach tickets

c + 5 = 10

c = 10 - 5

c = 5 .......and she bought 5 coach tickets

check...

160c + 1230f = 6950

160(5) + 1230(5) = 6950

800 + 6150 = 6950

6950 = 6950 (correct)....so it checks out

5 coach and 5 first class