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.

A) 700x + 375y = 27
x + y = 15,000
B) x + 375y = 15,000
700x + y = 27
C) 700x + y = 15,000
x + 375y = 27
D) 700x + 375y = 15,000
x + y = 27

Answer 1

Answer: C) 15 business class seats and 12 economy class seats

Answer 2

`D) \left \{ {{700x+375y = 15000} \atop {x+y=27}} \right`

Explanation:

Given:

Total employees to attend business = 27

Let the number of employees who will travel by business- class be 'x'

Let the Number of employees who will travel by economy- class be 'y'

Hence Total Number of employees will be equal to sum of the number of employees who will travel by business- class and the Number of employees who will travel by economy- class.

Framing in equation form we get;

`x+y=27`

Also Given:

Total Money need to spend = $15,000

Cost of Business- class seat = $700.

Cost of Economy- class seat = $375.

Hence Total money Need to spend will be will be equal to sum of the number of employees who will travel by business- class multiplied by Cost of Business- class seat and the Number of employees who will travel by economy- class multiplied by Cost of Economy- class seat.

Framing in equation form we get;

`700x+375y = 15000`

Hence the System of equation will be
`\left \{ {{700x+375y = 15000} \atop {x+y=27}} \right.`