Question

A commuter railway has 800

passengers a day and charges each one 2
dollars. For each 5
cents the fare is increased, 10
fewer people will ride the train. Express the income I
from the train in terms of the ticket price
(in dollars).

Answer 1

The income I of the commuter railway in terms of the ticket price p is expressed by the formula I = (800 - 10x) × (2 + 0.05x), where x is replaced with (p - 2)/0.05 to express the income as a function of p.

Step-by-step explanation:

The commuter railway income I in terms of the ticket price p (in dollars) can be expressed as the product of the number of passengers and the price per ticket. Initially, the railway has 800 passengers each day at $2 per ticket, so the income is $1600 when p = $2. The problem states that for each $0.05 increase in fare, 10 fewer passengers will ride the train. Let's denote the additional fare increase in terms of $0.05 increments as x. So, the new fare will be p = $2 + $0.05x and the number of passengers will be 800 - 10x. Therefore, the income can be expressed as:

I = (800 - 10x) × (2 + 0.05x)

To make this a function of p, we can substitute x with (p - 2)/0.05 since p = $2 + $0.05x. So:

I = (800 - 10((p - 2)/0.05)) × p

This expression now represents the railway's income in terms of the ticket price p.