The Soccer Team Is Conducting A Fundraiser Selling Long-sleeved T-shirts For $\$14$ And Short-sleeved T-shirts For $\$10$. So Far, The Team Has Sold Less Than $\$200$ Worth Of The Two Types Of T-shirts. Which Inequality Best

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Introduction

The soccer team is conducting a fundraiser by selling long-sleeved T-shirts for $14\$14 and short-sleeved T-shirts for $10\$10. The team has sold less than $200\$200 worth of the two types of T-shirts. In this scenario, we need to determine which inequality best represents the situation. We will analyze the given information and create an inequality to model the situation.

Given Information

  • Long-sleeved T-shirts are sold for $14\$14 each.
  • Short-sleeved T-shirts are sold for $10\$10 each.
  • The team has sold less than $200\$200 worth of the two types of T-shirts.

Creating the Inequality

Let's assume the number of long-sleeved T-shirts sold is represented by xx and the number of short-sleeved T-shirts sold is represented by yy. The total amount of money raised from selling the T-shirts can be represented by the equation:

14x+10y≤20014x + 10y \leq 200

This equation represents the total amount of money raised from selling the T-shirts, which is less than $200\$200. We can rewrite this equation as an inequality to represent the situation:

14x+10y<20014x + 10y < 200

Understanding the Inequality

The inequality 14x+10y<20014x + 10y < 200 represents the situation where the total amount of money raised from selling the T-shirts is less than $200\$200. This means that the sum of the cost of the long-sleeved T-shirts and the short-sleeved T-shirts is less than $200\$200.

Simplifying the Inequality

We can simplify the inequality by dividing both sides by the greatest common divisor of 1414 and 1010, which is 22. This gives us:

7x+5y<1007x + 5y < 100

Graphing the Inequality

We can graph the inequality on a coordinate plane to visualize the situation. The inequality 7x+5y<1007x + 5y < 100 represents a region in the coordinate plane where the sum of the cost of the long-sleeved T-shirts and the short-sleeved T-shirts is less than $100\$100.

Conclusion

In conclusion, the inequality 14x+10y<20014x + 10y < 200 represents the situation where the soccer team has sold less than $200\$200 worth of the two types of T-shirts. We can simplify the inequality to 7x+5y<1007x + 5y < 100 and graph it on a coordinate plane to visualize the situation. This inequality provides a mathematical model for the situation and helps us understand the relationship between the number of long-sleeved T-shirts sold, the number of short-sleeved T-shirts sold, and the total amount of money raised.

Real-World Applications

This inequality has real-world applications in various scenarios, such as:

  • Business: A company is selling two types of products, and the total revenue is less than a certain amount. The inequality can be used to model the situation and determine the maximum number of products that can be sold.
  • Finance: An individual is investing in two types of assets, and the total return is less than a certain amount. The inequality can be used to model the situation and determine the optimal investment strategy.
  • Science: A scientist is conducting an experiment with two variables, and the total effect is less than a certain amount. The inequality can be used to model the situation and determine the optimal experimental design.

Final Thoughts

Introduction

In our previous article, we discussed the soccer team fundraiser inequality, which represents the situation where the team has sold less than $200\$200 worth of the two types of T-shirts. In this article, we will answer some frequently asked questions about the inequality and provide additional insights.

Q: What is the purpose of the inequality?

A: The purpose of the inequality is to model the situation where the soccer team has sold less than $200\$200 worth of the two types of T-shirts. It helps us understand the relationship between the number of long-sleeved T-shirts sold, the number of short-sleeved T-shirts sold, and the total amount of money raised.

Q: How do I use the inequality in real-world scenarios?

A: The inequality can be used in various real-world scenarios, such as:

  • Business: A company is selling two types of products, and the total revenue is less than a certain amount. The inequality can be used to model the situation and determine the maximum number of products that can be sold.
  • Finance: An individual is investing in two types of assets, and the total return is less than a certain amount. The inequality can be used to model the situation and determine the optimal investment strategy.
  • Science: A scientist is conducting an experiment with two variables, and the total effect is less than a certain amount. The inequality can be used to model the situation and determine the optimal experimental design.

Q: How do I simplify the inequality?

A: The inequality can be simplified by dividing both sides by the greatest common divisor of the coefficients of the variables. For example, if the inequality is 14x+10y<20014x + 10y < 200, we can simplify it by dividing both sides by 2, which gives us 7x+5y<1007x + 5y < 100.

Q: How do I graph the inequality?

A: The inequality can be graphed on a coordinate plane to visualize the situation. The inequality 7x+5y<1007x + 5y < 100 represents a region in the coordinate plane where the sum of the cost of the long-sleeved T-shirts and the short-sleeved T-shirts is less than $100\$100.

Q: What are some common mistakes to avoid when working with the inequality?

A: Some common mistakes to avoid when working with the inequality include:

  • Not simplifying the inequality: Failing to simplify the inequality can make it difficult to understand and work with.
  • Not graphing the inequality: Failing to graph the inequality can make it difficult to visualize the situation and understand the relationship between the variables.
  • Not considering the constraints: Failing to consider the constraints of the inequality can lead to incorrect solutions.

Q: How do I apply the inequality in different contexts?

A: The inequality can be applied in different contexts, such as:

  • Linear programming: The inequality can be used to model linear programming problems, where the objective is to maximize or minimize a linear function subject to linear constraints.
  • Optimization: The inequality can be used to model optimization problems, where the objective is to find the optimal solution that satisfies a set of constraints.
  • Data analysis: The inequality can be used to model data analysis problems, where the objective is to understand the relationship between variables and make predictions.

Conclusion

In conclusion, the soccer team fundraiser inequality is a powerful tool for modeling real-world scenarios and understanding the relationship between variables. By simplifying the inequality, graphing it, and considering the constraints, we can gain valuable insights and make informed decisions. We hope this Q&A article has provided you with a better understanding of the inequality and its applications.