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 $230 and first class tickets for $980. She used her total budget for airfare for the trip, which was $7780. How many first class tickets did she buy? How many coach tickets did she buy? number of first class tickets bought? number of coach tickets bought?

Sarah purchased 4 coach tickets and 7 First class tickets.

Step-by-step explanation:

Let the total number of coach tickets brought = x

Let the total number of first class ticket purchased = y

⇒ x + y = 11

Also, cost of 1 coach ticket = $230

So, the cost of x coach tickets = x ($230) = 230 x

And, cost of 1 first class ticket = $980

So, the cost of y first class tickets = y ($980) = 980 y

The total allowance for the trip is = $7780

⇒ 230 x + 980y = $7780

Solving the given system of equation:

x + y = 11

230 x + 980 y = $7780

Substitute the value y = 11 - x in the second equation.

we get:

230 x + 980 y = $7780 ⇒ 230 x + 980 (11 - x) = $7780

or, 230 x + 10,780 - 980 x = 7780

or, - 750 x = - 3000

or, x = 3000/750 = 4

or, x = 4

⇒ y = 11 - x = 11 - 4 = 7

or, x = 4, y = 11 is the solution of the system.

Hence, Sarah purchased 4 coach tickets and 7 First class tickets.