An online music club has a one-time registration fee of $20 and charges $0.50 for each song download. If Ella has $50.00 to join the club and buy songs, which inequality gives the maximum number of songs, s, she can buy?

To determine the maximum number of songs Ella can buy, let's break down the problem.

1. **Registration fee**: The club charges a one-time fee of \$20.
2. **Cost per song**: Each song download costs \$0.50.
3. **Total amount Ella has**: She has \$50.00 in total.

### Step-by-Step Setup

- Let $ s $ represent the number of songs Ella can buy.
- The total cost includes both the registration fee and the cost of the songs:
  
  \[
  \text{Total Cost} = 20 + 0.50s
  \]

- Ella has at most \$50.00 to spend, so the total cost must be less than or equal to 50:

  \[
  20 + 0.50s \leq 50
  \]

### Solve the Inequality

1. Subtract 20 from both sides:

   \[
   0.50s \leq 50 - 20
   \]
   \[
   0.50s \leq 30
   \]

2. Divide both sides by 0.50:

   \[
   s \leq \frac{30}{0.50}
   \]
   \[
   s \leq 60
   \]

### Conclusion
The inequality that gives the maximum number of songs Ella can buy is:

\[
s \leq 60
\]

This means Ella can buy at most 60 songs.

Would you like further clarification, or do you have any questions?

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Here are 5 related questions to expand on this:

1. What happens if the cost per song increases to \$0.75? How does that change the inequality?
2. How many songs can Ella buy if she only has \$40 to spend instead of \$50?
3. If the registration fee was removed, how many songs could she buy with \$50?
4. How would the inequality change if Ella had \$100 to spend?
5. What if the registration fee doubled to \$40? How many songs could she buy?

**Tip**: When working with inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Discover how to determine the maximum number of songs Ella can buy with $50 using an inequality. This problem involves key algebraic concepts like linear inequalities and basic cost formulas, perfect for students in Grades 6-8.

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