Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 5 people took the trip. She was able to purchase coach tickets for $120 and first class tickets for $990. She used her total budget for airfare for the trip, which was $3210. How many first class tickets did she buy? How many coach tickets did she buy? ​

See below.

Step-by-step explanation:

Let “x” be a coach ticket.

Let “y” be a first class ticket.

Let’s set up a system of equations.

120x + 990y = 3210

x + y = 5

120x = 3210 - 990y

x = 26.75 - 8.25y

26.75 - 8.25y + y = 5

- 7.25y = -21.75

y = 3

120x + 990 * 3 = 3210

120x = 240

x = 2

She bought 2 coach tickets and 3 first class tickets.

first class tickets = 3

coach tickets = 2

Step-by-step explanation:

let number of coach tickets = x

and

number of first class tickets = y

coach tickets + first class tickets = total tickets

x + y = 5 > equation A

now

total cost of coach tickets = cost per coach tickets * number of coach tickets

= 120 * x

and

total cost of first class tickets = cost per first class ticket * number of first class tickets

= 990 * y

cost of coach tickets + cost of first class tickets = total cost of tickets

120x + 990y = 3210 > equation B

equation B - 120 times equation A gives

120x + 990y - 120 (x + y) = 3210 - 120 * 5

120x + 990y - 120x - 120y = 3210 - 600

870y = 2610

y = 3

thus x + 3 = 5

or x = 2

the image of (6, 9) under a dilation is (4, 6). the scale factor is