A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation. Let x represent the number of $1.00 increases in ticket price. Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. Then, use the inequality to select all the correct statements.

I can determine the inequality with the information provided. Then, from that you may select the correct statements given that you did not include them.

Determination of the inequality:

1) Revenue = number of riders * price of the ticket ≥ 12

2) number of riders = 2000 - 100x [x is the number of $1.00 increases on the price]

3) price = 5 - x

4) Equation, revenue = (2000 - 100x) (5 - x) = 10,000 - 2,000x - 500x + 100x^2

revenue = 10,000 - 2500x + 100x^2

5) Inequality 10,000 - 2500x + 100x^2 ≥ 12,000

6) Simplify the inequality:

10,000 - 12,000 - 2500x + 100x^2 ≥ 0

- 2,000 - 2500x + 100x^2 ≥ 0

-20 - 25x + x^2 ≥ 0

There you have to forms of the inequality. Sure, other equivalent forms can be displayed.

Analysis and conclusion:

From that you can determine that it is not possible to reach the revenue of 12,000 under the conditions given.

Note that the domain of x is 1, 2, 3, 4, 5.

When you solve the inequality, you realize that none value of x between 0 and 5 result in a revenue greater than or equal to 0.

So, the conclusion is that it is not possible to have a revenue of at least 12,000.