a bus company charges two dollars for each trip. It also sells monthly passes for $50. Write and solve an inequality to find how many trips you could make before the monthly pass is cheaper.

Answer 1

To determine how many trips you can make before the monthly pass becomes cheaper than paying for each individual trip, we can set up an inequality.

Let \( x \) represent the number of trips taken in a month. The cost for \( x \) trips at $2 per trip is given by:

\[ C_{\text{trips}} = 2x \]

The cost of the monthly pass is simply:

\[ C_{\text{pass}} = 50 \]

We want to find when the monthly pass becomes less expensive than the cost of paying for individual trips. This can be expressed as:

\[ C_{\text{trips}} > C_{\text{pass}} \]

Substituting the costs into the inequality, we get:

\[ 2x > 50 \]

Now, to solve for \( x \):

1. Divide both sides by 2: \[ x > 25 \]

This means that if you take more than 25 trips, the monthly pass becomes the cheaper option. Therefore, you can make up to 25 trips before the monthly pass is cheaper.