Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the trip. She was able to purchase coach tickets for $180 and first class tickets for $1160. She used her total budget for airfare for the trip, which was $8580. How many first class tickets did she buy? How many coach tickets did she buy?

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the trip.

She was able to purchase coach tickets for $180 and first class tickets for $1160. She used her total budget for airfare for the trip, which was $8580.

Now, to find the number of first class tickets and coach tickets.

Let the number of first class tickets be [tex]x.[/tex]

And the number of coach tickets be [tex]y.[/tex]

So, the total number of tickets she purchased for the trip:

[tex]x+y=15[/tex]

[tex]x=15-y.[/tex] ........( 1 )

Now, the total budget of airfare for the trip was:

[tex]x(1160)+y(180)=8580[/tex]

[tex]1160x+180y=8580[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]1160(15-y)+180y=8580[/tex]

[tex]17400-1160y+180y=8580[/tex]

[tex]17400-980y=8580[/tex]

Subtracting both sides by 17400 we get:

[tex]-980y=-8820[/tex]

Dividing both sides by -980 we get:

[tex]y=9.[/tex]

The number of coach tickets = 9.

Now, to get the number of first class tickets by substituting the value of [tex]y[/tex] in equation (1):

[tex]x=15-y\\x=15-9\\x=6.[/tex]

The number of first class tickets = 6.

Therefore, the number of first class tickets are 6 and coach tickets are 9.