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 purchase coach tickets for $260 and first class tickets for $1080. She used her total budget for airfare for the trip, which was $5320. How many first class tick she buy? How many coach tickets did she buy?
Let's represent the number of first class tickets as "x" and the number of coach tickets as "y."
From the problem, we know that x + y = 11 (since there were a total of 11 people on the trip).
We also know that 1080x + 260y = 5320 (since Sarah used her total budget of $5320 for airfare).
We can solve this system of equations by substitution or elimination.
Let's solve by substitution. We solve the first equation for x: x = 11 - y.
Substituting this into the second equation: 1080(11 - y) + 260y = 5320.
Distributing and simplifying: 11880 - 1080y + 260y = 5320.
Combining like terms: 11880 - 820y = 5320.
Subtracting 11880 from both sides: -820y = -6560.
Dividing by -820: y = 8.
Substituting this value of y in the first equation: x + 8 = 11.
Subtracting 8 from both sides: x = 3.
So Sarah bought 3 first class tickets and 8 coach tickets.