Question

tyra's family is spending the afternoon in millersville. they plan to see a movie that is over 2 hours long and then explore the town. The movie will cost the family $36, and parking costs $4 per hour. how long will the family be able to spend in millersville if they don't have any other expenses and want to spend less than $60? modeled in a inequality.

Answer 1

To determine how long Tyra's family will be able to spend in Millersville while staying within their budget of less than $60, we can set up an inequality.

Let \( h \) be the number of hours they spend parking. The total cost for the outing can be represented as the sum of the movie cost and the parking cost:

- Cost of the movie: $36
- Parking cost: $4 per hour, so for \( h \) hours, it will be \( 4h \).

The total cost can be expressed as:

\[
\text{Total Cost} = 36 + 4h
\]

We want this total to be less than $60:

\[
36 + 4h < 60
\]

Now, we can solve this inequality step-by-step:

1. Subtract 36 from both sides:

\[
4h < 60 - 36
\]

\[
4h < 24
\]

2. Divide both sides by 4:

\[
h < 6
\]

This means the family can spend less than 6 hours on parking. Since they also need to consider that the movie is over 2 hours long, the total time spent in Millersville will be the movie time plus parking time.

If we denote the time spent watching the movie as \( m \) (where \( m > 2 \)), the total time spent in Millersville will be:

\[
\text{Total time} = m + h
\]

Given that \( h < 6 \):

- If \( m \) is at least 2 hours long, the family has at least \( 2 + h < 2 + 6 = 8 \) hours total in Millersville, with some total time slightly longer than 8 hours (if they watch a movie that is just over 2 hours).

In conclusion, the inequality for the parking hours is \( h < 6 \), meaning the family has a total of less than 8 hours in Millersville, factoring in the movie duration as well.