Question

Two competing passenger trains create a new marketing plan, charging passengers a fixed amount and then a rate per mile.Fast Track: $79.75 plus $0.30 a mileCheap Track: $179.50 plus $0.25 a mileA one-way train ride from Miami to San Francisco is 2,585 miles. If C is the cost of the ride and M is the number of miles one way, which train is the cheapest, what is the equation for the cheapest option, and how much money do you save?

Answer 1

Start by writing the equations

Fast track=FT

Cheap track=CT

`\begin{gathered} FT\colon C=79.75+0.3M \\ CT\colon C=179.5+0.25M \end{gathered}`

then replace the number of miles for the trip (2,585 miles) in both equations

`\begin{gathered} FT\colon \\ 79.75+0.3\cdot2585 \\ 855.25 \\ CT\colon \\ 179.5+0.25\cdot2585 \\ 825.75 \end{gathered}`

The cheap track is the cheapest by:

`855.25-825.75=29.5`

the correct answer option is the third one.