Question

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM. There were 35,000 people at a ball game in Atlanta. The day's receipts were $290,000. How many people paid $14 for reserved seats and how many paid $6 for general admission? Let x represent the number of reserved seats and y represent the number of general admission seats. A. 14x + 6y = 290,000 x + y = 35,000 OB. 25,000x + 14y = 35,000 x + y = 290,000 O C. 20,000x + 14y = 6 x + y = 15,000 OD. 15,000x + 14y = 20,000 x + y = 6

Answer 1

The system of equations to model the problem is A. 14x + 6y = 290,000 and x + y = 35,000.

Step-by-step explanation:

The system of equations to model the problem is:

A. 14x + 6y = 290,000

x + y = 35,000

To find the number of people who paid $14 for reserved seats and the number of people who paid $6 for general admission, we use the variables x and y. x represents the number of reserved seats and y represents the number of general admission seats. The first equation represents the total amount of money collected from both types of seats, while the second equation represents the total number of people who attended the ball game.

Answer 2

The number of people who paid for reserved seats and people who paid for general admission is 10,000 and 25,000 respectively

How many paid $6 for general admission?

Let x represent the number of reserved seats

y represent the number of general admission seats.

x + y = 35,000

14x + 6y = 290,000

From (1)

x = 35000 - y

Substitute into (2)

14x + 6y = 290,000

14(35,000 - y) + 6y = 290,000

490,000 - 14y + 6y = 290,000

- 14y + 6y = 290,000 - 490,000

-8y = -200,000

Divide both sides by -8

y = -200,000/-8

y = 25,000

Substitute y = 25,000 into (1)

x + y = 35,000

x + 25,000 = 35,000

x = 35,000 - 25,000

x = 10,000

Hence, 10,000 people paid for reserved seat and 25,000 people paid for general admission