Question

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 ​$120 and first class tickets for ​$950. She used her total budget for airfare for the​ trip, which was ​$7610. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answer 1

7 first-class tickets and 7 coach tickets.

Explanation:

Let's assume Sarah bought x coach tickets and y first-class tickets.

The cost of each coach ticket is $120, so the total cost of coach tickets is 120x.

The cost of each first-class ticket is $950, so the total cost of first-class tickets is 950y.

According to the given information, the total number of people who took the trip, including Sarah, is 15. So we have the equation:

x + y + 1 = 15

Simplifying the equation, we get:

x + y = 14

The total budget for airfare was $7610, so we have the equation:

120x + 950y = 7610

Now we can solve these two equations simultaneously to find the values of x and y.

Using the first equation, we can express x in terms of y:

x = 14 - y

Substituting this value of x into the second equation, we get:

120(14 - y) + 950y = 7610

Expanding and simplifying the equation:

1680 - 120y + 950y = 7610

830y = 5930

Dividing both sides by 830:

y = 7

Substituting this value of y back into the first equation, we can find x:

x + 7 = 14

x = 7

Therefore, Sarah bought 7 first-class tickets and 7 coach tickets.