Question

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.
A) 100x + 1,500 ≤ 12,000
B) The price of a one-way ticket that will maximize revenue is $7.50.
C) 100x + 1,500 > 10,000 < 12,000
D) The maximum profit the company can make is $4,125.00.

Answer 1

Represent the values of x that would allow the carpool service to have revenue of at least $12,000, an inequality of 100x + 1,500 ≥ 12,000 can be used. Only statement E is correct.

Step-by-step explanation:

To represent the values of x that would allow the carpool service to have revenue of at least $12,000, we can use the inequality 100x + 1,500 ≥ 12,000. This inequality ensures that when x increases, the number of passengers finding other means of transportation also increases.

Using this inequality, we can solve for x to find the range of values that satisfy the revenue condition.

Statement A) 100x + 1,500 ≤ 12,000 is not correct because it represents the condition where the revenue is less than or equal to $12,000, which is not what the question asks for.

Statement B) The price of a one-way ticket that will maximize revenue is $7.50 is not provided in the information given, so it cannot be determined from the given conditions.

Statement C) 100x + 1,500 > 10,000 < 12,000 is not correct because it does not accurately represent the revenue condition of at least $12,000.

Statement D) The maximum profit the company can make is $4,125.00 is not supported by the information given, so it cannot be determined.