Final answer:
Sarah bought 4 first class tickets and 6 coach tickets for her advertising department on a round trip. This was determined by solving the system of linear equations formed by the total cost and the number of tickets purchased.
Step-by-step explanation:
The problem presented is a system of equations question where Sarah is buying a total of 10 tickets for her advertising department, split between coach and first class tickets. First class tickets cost $1060 each, and coach tickets cost $200 each. The total cost for all tickets is $5440. The task is to find out how many first class and coach tickets Sarah purchased.
Let's define two variables: let x be the number of first class tickets and let y be the number of coach tickets. We have two equations based on the information given:
- The total number of tickets is 10: x + y = 10
- The total amount spent on tickets is $5440: 1060x + 200y = 5440
By solving this system of equations, we can find the values of x and y.
First, we can solve the first equation for y: y = 10 - x. Next, we substitute this expression for y into the second equation: 1060x + 200(10 - x) = 5440. Simplify and solve for x:
1060x + 2000 - 200x = 5440
860x = 3440
x = 4
There are 4 first class tickets purchased. Now we can find y using the first equation: y = 10 - 4, hence y = 6. This means that 6 coach tickets were purchased.