Question

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 was able to purchase coach tickets for $390and first class tickets for $1130. She used her total budget for airfare for the trip, which was $10950. How many first class tickets did she buy? How many coach tickets did she buy?

Answer 1

Sarah bought 9 first class tickets and 2 coach tickets. We solved a system of linear equations using substitution to find out the number of each type of ticket she purchased.

Step-by-step explanation:

To determine how many first class and coach tickets Sarah bought, we need to set up a system of linear equations based on the given information. Let x be the number of first class tickets and y be the number of coach tickets. The two equations representing the situation are:

• x + y = 11 (since there are 11 people including Sarah)
• 1130x + 390y = 10950 (the total cost of the tickets)

We can solve this system of equations by substitution or elimination. Let's use substitution in this case:

1. From the first equation, we can express y as y = 11 - x.
2. Substitute y in the second equation: 1130x + 390(11 - x) = 10950.
3. This simplifies to 1130x + 4290 - 390x = 10950.
4. Combining like terms, we get 740x = 6660.
5. Dividing both sides by 740, we find that x = 9.
6. Substitute x back into y = 11 - x to get y = 11 - 9, so y = 2.

Sarah purchased 9 first class tickets and 2 coach tickets for the trip.