Sarah took the advertising department from her company on a round trip to meet with a
potential client. Including Sarah a total of 16 people took the trip. She was able to
purchase coach tickets for $220 and first class tickets for $1260. She used her total
budget for airfare for the trip, which was $12,880. How many first class tickets did she
buy? How many coach tickets did she buy?
Let's solve this problem using algebra.
Let's assume Sarah purchased x first class tickets and y coach tickets.
According to the given information:
x + y + 1 = 16 (including Sarah, a total of 16 people took the trip)
x * $1260 + y * $220 = $12,880 (the total budget for airfare for the trip was $12,880)
We have a system of equations:
x + y = 15
1260x + 220y = 12880
Solving this system of equations, we can find the values of x and y.
Using the first equation to solve for x, we get x = 15 - y.
Substituting this value of x into the second equation, we get:
1260(15 - y) + 220y = 12880
18900 - 1260y + 220y = 12880
-1040y = -6020
y = 5
Substituting the value of y back into the equation x = 15 - y, we get x = 10.
Therefore, Sarah bought 10 first class tickets and 5 coach tickets.