Question

The cost of a hotel room is $50 per night plus a one-time fee of $10 for cleaning. For how many nights can the hotel room be booked if the total cost can be a maximum of $410?
Write an inequality to represent the situation. Use x to represent the number of nights.
You got it!
You just wrote an inequality to represent the situation. Now solve the associated equation, 10 + 50x = 410, to find the boundary for the inequality. Show your work or solve on paper.
10 + 50x ≤ 410
10+50x
=
410
−
−
=

x
=
Good work!
You found that x = 8 is the solution to the associated equation. Is x = 8 also included in the solutions to the inequality?
10 + 50x ≤ 410

Yes

No

Answer 1

Let's solve the inequality step by step.

1. **Set up the inequality**:
\[
10 + 50x \leq 410
\]

2. **Subtract 10 from both sides**:
\[
50x \leq 400
\]

3. **Divide both sides by 50**:
\[
x \leq 8
\]

The critical point, \( x = 8 \), indicates the maximum number of nights you can book the hotel room while staying within the budget of $410.

Now, to answer your question about whether \( x = 8 \) is included in the solutions to the inequality:

Since the inequality is \( \leq \) (less than or equal to), this means that \( x = 8 \) is indeed included as a solution in the inequality.

So the answer is **Yes**.