Finding the Maximum Number of Pairs

Oct 13, 2025 by talynt.org 63 views

Introduction

As a high school coach, buying new athletic shorts for the basketball team can be a daunting task, especially when there's a budget constraint. In this scenario, the coach needs to purchase shorts for 15 members of the team while spending less than $200. The question is, what is the maximum cost of each pair, $s$ , that the coach can buy? To answer this, we need to set up an inequality that represents the maximum cost.

Setting Up the Inequality

Let's denote the number of pairs of shorts as $n$ and the cost of each pair as $s$ . The total cost of the shorts is the product of the number of pairs and the cost of each pair, which is $ns$ . Since the coach wants to spend less than $200, we can set up the following inequality:

ns < 200

However, this inequality doesn't take into account the fact that the coach needs to buy shorts for 15 members of the team. To account for this, we need to find the maximum number of pairs that the coach can buy while staying within the budget.

Finding the Maximum Number of Pairs

Since the coach needs to buy shorts for 15 members of the team, the maximum number of pairs that the coach can buy is 15. However, this doesn't take into account the fact that the coach needs to stay within the budget of $200. To find the maximum number of pairs that the coach can buy, we need to divide the budget by the cost of each pair.

The Inequality

Let's denote the cost of each pair as $s$ . The maximum number of pairs that the coach can buy is 15, so we can set up the following inequality:

15s < 200

This inequality represents the maximum cost of each pair, $s$ , that the coach can buy.

Solving the Inequality

To solve the inequality, we need to isolate the variable $s$ . We can do this by dividing both sides of the inequality by 15:

s < \frac{200}{15}

Simplifying the fraction, we get:

s < 13.33

This means that the maximum cost of each pair of shorts that the coach can buy is $13.33.

Conclusion

In conclusion, the inequality that represents the maximum cost of each pair, $s$ , that the coach can buy is:

s < 13.33

This means that the coach can buy shorts for the basketball team while staying within the budget of $200.

Frequently Asked Questions

What is the maximum number of pairs of shorts that the coach can buy? The maximum number of pairs of shorts that the coach can buy is 15.
What is the maximum cost of each pair of shorts that the coach can buy? The maximum cost of each pair of shorts that the coach can buy is $13.33.
How can the coach stay within the budget of $200? The coach can stay within the budget of $200 by buying shorts for the basketball team that cost less than $13.33 per pair.

Final Thoughts

In conclusion, the coach needs to buy shorts for the basketball team while staying within the budget of $200. The inequality that represents the maximum cost of each pair, $s$ , that the coach can buy is:

s < 13.33

This means that the coach can buy shorts for the basketball team while staying within the budget of $200.

Introduction

In our previous article, we explored the scenario of a high school coach who needs to buy new athletic shorts for the basketball team while staying within a budget of $200. We set up an inequality to represent the maximum cost of each pair, $s$ , that the coach can buy. In this article, we'll answer some frequently asked questions related to this scenario.

Q&A

Q: What is the maximum number of pairs of shorts that the coach can buy?

A: The maximum number of pairs of shorts that the coach can buy is 15.

Q: What is the maximum cost of each pair of shorts that the coach can buy?

A: The maximum cost of each pair of shorts that the coach can buy is $13.33.

Q: How can the coach stay within the budget of $200?

A: The coach can stay within the budget of $200 by buying shorts for the basketball team that cost less than $13.33 per pair.

Q: What if the coach wants to buy more than 15 pairs of shorts?

A: If the coach wants to buy more than 15 pairs of shorts, they will need to spend more than $200. In this case, the coach will need to either reduce the number of pairs they buy or find a way to increase their budget.

Q: Can the coach buy shorts that cost more than $13.33 per pair?

A: Yes, the coach can buy shorts that cost more than $13.33 per pair. However, this will mean that they will need to spend more than $200, which is not within their budget.

Q: How can the coach ensure that they are staying within their budget?

A: The coach can ensure that they are staying within their budget by keeping track of the total cost of the shorts they buy and comparing it to their budget. They can also use a calculator or spreadsheet to help them stay within their budget.

Q: What if the coach wants to buy shorts that are of higher quality or have additional features?

A: If the coach wants to buy shorts that are of higher quality or have additional features, they may need to spend more than $13.33 per pair. In this case, the coach will need to decide whether the additional features or higher quality are worth the extra cost.

Conclusion

s < 13.33

This means that the coach can buy shorts for the basketball team while staying within the budget of $200. By answering these frequently asked questions, we hope to have provided more clarity on this scenario.

Additional Resources

Final Thoughts

In conclusion, the coach needs to be mindful of their budget when buying shorts for the basketball team. By staying within their budget and using the inequality to guide their purchasing decisions, the coach can ensure that they are getting the best value for their money.