Question

A commuter railway has 800 passengers a day and charges each one 2 dollars. For each 9 cents the fare is increased, 8 fewer people will ride the train. Express the income I from the train in terms of the ticket price p (in dollars).

Answer 1

To express the income I from the train in terms of the ticket price p, multiply the fare by the number of passengers and convert the result from cents to dollars.

Step-by-step explanation:

To express the income I from the train in terms of the ticket price p, we need to consider the relationship between the fare and the number of passengers. Based on the given information, we can determine that for each 9 cents the fare is increased, 8 fewer people will ride the train. Let's denote the initial fare as F (in cents) and the initial number of passengers as P. From the given data, we have:

F = $2 = 200 cents

P = 800 passengers

So, the income I can be calculated by multiplying the fare by the number of passengers:

I = F * P = 200 * 800 = 160,000 cents

Now, to express the income I in terms of the ticket price p (in dollars), we need to convert cents to dollars by dividing by 100:

I = 160,000 cents / 100 = $1600

Therefore, the income I from the train in terms of the ticket price p is $1600.