Question

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 $290 each and first-class tickets for $1270 each. She used her total budget for airfare for the trip, which was $6420. How many first-class tickets did she buy? How many coach tickets did she buy?

Let's use some variables to solve this. Let C represent the number of coach tickets and F represent the number of first-class tickets.
We know the following:
The total number of people on the trip is 12, including Sarah, so C + F = 12.
The cost of each coach ticket is $290, so 290C represents the total cost of coach tickets.
The cost of each first-class ticket is $1270, so 1270F represents the total cost of first-class tickets.
The total budget for airfare is $6420, so 290C + 1270F = 6420.

Answer 1

To solve the problem, use a system of equations. The solution is 3 first-class tickets and 9 coach tickets.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let C represent the number of coach tickets and F represent the number of first-class tickets. We know that C + F = 12, since the total number of people on the trip is 12.

We also know that 290C + 1270F = 6420, since the total cost of coach tickets and first-class tickets is $6420. We can use these equations to solve for the values of C and F.

One way to solve this system of equations is by substitution. We can solve the first equation for C and substitute it into the second equation:

C = 12 - F

Substituting this into the second equation:

290(12 - F) + 1270F = 6420

Expanding the equation:

3480 - 290F + 1270F = 6420

Combining like terms:

980F = 2940

Dividing by 980:

F = 3

Plugging this value back into the first equation, we find that C = 12 - 3 = 9.

Therefore, Sarah bought 3 first-class tickets and 9 coach tickets for the trip.