Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 16 people took the trip. She was able to purchase coach tickets for $260 and first class tickets for $970. She used her total budget for airfare for the trip, which was $10,550. How many first class tickets did she buy? How many coach tickets did she buy?

Let x equal the # of coach tickets

Let y equal the # of first class tickets

x + y = 16

260x + 970y = 10,550

Solve and state the answer. Use the substitution method to solve this system. Solve the first equation for x.

x + y = 16

x = 16 - y

Now substitute the resulting expression into the other equation and solve for y.

260 (16 - y) + 970y = 10,550

4160 - 260y + 970y = 10,550

Combine like terms

4160 + 710y = 10,550

Subtract 4160 from both sides

710y = 6390

divide by 710

y = 9

Substitute the value of y into the equation that we solved for x, x=17-y.

x = 17 - 9

x = 8

Therefore the answer is, 8 coach tickets and 9 first class tickets.