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

66
people took the trip. She was able to purchase coach tickets for
​$150150
and first class tickets for
​$11601160.
She used her total budget for airfare for the​ trip, which was
​$49404940.
How many first class tickets did she​ buy? How many coach tickets did she​ buy?

your prices make no sense

To determine the number of first-class and coach tickets Sarah bought, we can set up a system of equations based on the given information:

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

The total number of people who took the trip is 66, including Sarah:
x + y + 1 (Sarah) = 66

The cost of each first-class ticket is $1160, and the cost of each coach ticket is $150:
1160x + 150y = 4940

We can now solve this system of equations to find the values of x and y.

To start, let's rearrange the first equation to solve for x + y:
x + y = 66 - 1
x + y = 65

Now we have a system of equations:
x + y = 65 (Equation 1)
1160x + 150y = 4940 (Equation 2)

To solve this system, we can use the method of substitution or elimination. Let's use the substitution method.

From Equation 1, we can rearrange it to solve for x:
x = 65 - y

Now we substitute this value of x into Equation 2:
1160(65 - y) + 150y = 4940

Expanding and rearranging the equation:
75400 - 1160y + 150y = 4940
-1010y = 4940 - 75400
-1010y = -70460

Dividing both sides of the equation by -1010 to solve for y:
y = (-70460) / (-1010)
y = 70

Now that we have the value of y, we can substitute it back into Equation 1 to solve for x:
x + 70 = 65
x = 65 - 70
x = -5

From this result, we can determine that Sarah bought -5 first-class tickets, which is not possible. It means there must be an error in the problem statement or the given information.

Please double-check the information and make any necessary corrections.