business has $15,000 to spend on airline tickets to travel to a conference. It wants 27 of its employees to attend. The business wants to buy as many business-class seats as possible. The business-class seats cost $700. The economy-class seats cost $375. Create a system of equations that models how many of each type of ticket the business should purchase.

Question

business has $15,000 to spend on airline tickets to travel to a conference. It wants 27 of its employees to attend. The business wants to buy as many business-class seats as possible. The business-class seats cost $700. The economy-class seats cost $375. Create a system of equations that models how many of each type of ticket the business should purchase.

Answer 1

Let x be the number of business-class seats and y be the number of economy-class seats.

We know that the business wants to buy as many business-class seats as possible, so we can start with the equation:

x + y = 27

We also know that the business has $15,000 to spend. The cost of each business-class seat is $700, so the cost of x business-class seats is 700x. Similarly, the cost of each economy-class seat is $375, so the cost of y economy-class seats is 375y. The total cost of all the tickets should be $15,000, so we can write:

700x + 375y = 15000

These two equations together form the system of equations that models how many of each type of ticket the business should purchase:

x + y = 27

700x + 375y = 15000