Question

A 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

15 business classes and 12 economy classes

Explanation:

For this equation let x be the number of the amount of business classes and y be the amount of economy classes:

We are looking for 27 employees to attend the conference so:

x + 7 = 27

Then look for the amount of business classes and economy classes by how much is each seat so:

700x + 357y = 15,000 (The max limit)

Multiply the first equation by 700

700 * x + 700 * y = 700 * 27

700x + 700y = 18,900

Lets look for y by subtracting the second equation by the first equation:

700x + 357y = 15,000 - 700x + 700y = 18,900

700x - 700x = 0

0

357y - 700y = -325y

0 325y

Then 15,000 - 18,900 = -3,900

Meaning:

0 -325y = -3,900

To find y, we must divide -3,900 by -325y

-3900/-325 =

So y = 12

Then for x:

x + y = 27

Since y = 12

x + 12 = 27

Backwards formation:

27 - 12 = 15

x = 15

So there are 15 business classes and 12 economy classes