Question

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 14 people took the trip. She was able to purchase coach tickets for ​$240 and first class tickets for ​$1130. She used her total budget for airfare for the​ trip, which was ​$10,480. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answer 1

$\left\{{{240x+1130y=10480,}\atop{x+y=14;}}\right \left\{{{240x+1130y=10480,}\atop{y=14-x;}}\right \\\left\{{{240x+1130(14-x)=10480,}\atop{y=14-x;}}\right \left\{{{240x+15820-1130x=10480,}\atop{y=14-x;}}\right \\\left\{{{-890x+15820=10480,}\atop{y=14-x;}}\right \left\{{{-890x=10480-15820,}\atop{y=14-x;}}\right \\\left\{{{-890x=-5340,}\atop{y=14-x;}}\right \left\{{{890x=5340,}\atop{y=14-x;}}\right \\\left\{{{x=6,}\atop{y=14-6;}}\right \left\{{{x=6,}\atop{y=8;}}\right$

The answers to your specific question is Sarah bought 6 coach tickets and 8 first class tickets.