linear equations

Question

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

10

people took the trip. She was able to purchase coach tickets for

​$160

and first class tickets for

​$940

She used her total budget for airfare for the​ trip, which was

​$7060

How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answer 1

Let X and Y represent the number of coach and first class tickets, respectively. X+Y = 10

$7060 = $160X + $940Y

But Y can be expressed as 10-X, so

$7060 = $160X + $940(10-X)

7060 = 160X + 9400 - 940X

Combine X terms on left of equal sign and numbers to right

780X = 2340

Solve for X = 2340/780 = 3

Since 3+Y = 10, Y = 7

There were 3 coach tickets and 7 first class.