Carolina goes to a paintball field that charges an entrance fee of \[\$18\] and \[\$0.08\] per ball. The field has a promotion that says, "Get \[\$10\] off if you spend \[\$75\] or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let \[B\] represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?

To represent this scenario, let's break it down into the different components:

- **Entrance fee**: $\$18$
- **Cost per paintball**: $\$0.08$ per ball
- **Promotion condition**: Spend $\$75$ or more to get a discount of $\$10$

Carolina wants to spend at least $\$75$ to get the discount. The total amount Carolina spends consists of the entrance fee plus the cost for each paintball.

So the total cost $C$ is:
\[
C = 18 + 0.08B
\]
where $B$ represents the number of paintballs she buys.

To get the promotion, the total cost $C$ must be **at least** $\$75$. This leads to the inequality:
\[
18 + 0.08B \geq 75
\]

This inequality represents the scenario. It can be solved to find the minimum number of paintballs needed.

Would you like me to solve this inequality or give further details? Here are some related questions for practice:

1. How would you solve the inequality $18 + 0.08B \geq 75$?
2. How much would Carolina pay if she bought 500 paintballs?
3. What happens if Carolina spends exactly $\$75$ — does she get the discount?
4. What is the cost for each additional paintball after the discount?
5. How does the promotion affect her total spending if she buys the minimum number of paintballs?

**Tip**: Always isolate the variable on one side when solving inequalities for a clearer solution.

Carolina goes to a paintball field that charges an entrance fee of $18 and $0.08 per ball. The field has a promotion that says, 'Get $10 off if you spend $75 or more!' Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion. Let B represent the number of paintballs that Carolina buys. Which inequality describes this scenario?

Discover how to solve the inequality 18 + 0.08B ≥ 75 to determine the number of paintballs Carolina needs to buy to get a $10 discount. This problem teaches key concepts in algebra and linear inequalities, making it ideal for students in Grades 7-9.

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