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 $370 and first class tickets for $1210. She used her total budget for airfare for the trip, which was $8640. How many first class tickets did she buy? How many coach tickets did she buy?
f + c = 12 so c = (12-f)
1210 f + 370 c = 8640
1210 f + 370(12-f) = 8640
1210 f - 370 f + 4440 = 8640
840 f = 4200
Your turn :)
To find the number of coach tickets Sarah bought, let's assume she bought 'x' coach tickets. Since there were a total of 12 people on the trip, the number of first-class tickets she bought can be found by subtracting 'x' from 12.
Let's calculate the cost of the coach tickets first. She bought 'x' tickets, and each coach ticket costs $370. So the total cost of the coach tickets is 370 * x = 370x.
Now let's calculate the cost of the first-class tickets. She bought (12 - x) first-class tickets, and each first-class ticket costs $1210. So the total cost of the first-class tickets is 1210 * (12 - x) = 1210(12 - x).
According to the information given, the total cost of airfare for the trip was $8640. Therefore, the sum of the cost of coach tickets and first-class tickets should be equal to $8640.
So we have the equation: 370x + 1210(12 - x) = 8640.
Simplifying the equation, we get:
370x + 14520 - 1210x = 8640.
Combine like terms:
-840x + 14520 = 8640.
Now isolate 'x' by moving 14520 to the other side of the equation:
-840x = 8640 - 14520.
-840x = -5880.
Divide both sides of the equation by -840 to solve for 'x':
x = -5880 / -840.
x = 7.
Therefore, Sarah bought 7 coach tickets and 12 - 7 = 5 first-class tickets.