At Cindy's Sweet Treats, Cookies Are Packaged In Boxes Of 8. Depending On The Cookie Flavor, The Most A Box Can Cost Is $ 16 \$16 $16 .Let X X X Represent How Much Each Cookie Costs. Which Inequality Describes The Problem?- $8x \leq

Introduction

At Cindy's Sweet Treats, cookies are packaged in boxes of 8. Depending on the cookie flavor, the most a box can cost is $\$16$. In this problem, we are tasked with finding the cost of each cookie, represented by the variable $x$. To do this, we need to set up an inequality that describes the situation.

Understanding the Problem

Let's break down the problem step by step. We know that the cost of each cookie is represented by the variable $x$. Since there are 8 cookies in a box, the total cost of the box is $8x$. We are also given that the most a box can cost is $\$16$. This means that the total cost of the box must be less than or equal to $\$16$.

Setting Up the Inequality

To set up the inequality, we need to translate the given information into mathematical terms. We know that the total cost of the box is $8x$, and this must be less than or equal to $\$16$. Therefore, we can write the inequality as:

$$8x \leq 16$$

This inequality states that the total cost of the box ($8x$) is less than or equal to $\$16$.

Solving the Inequality

To solve the inequality, we need to isolate the variable $x$. We can do this by dividing both sides of the inequality by 8:

$$\frac{8x}{8} \leq \frac{16}{8}$$

Simplifying the inequality, we get:

$$x \leq 2$$

This means that the cost of each cookie ($x$) must be less than or equal to $\$2$.

Conclusion

In this problem, we set up an inequality to describe the situation at Cindy's Sweet Treats. We found that the cost of each cookie ($x$) must be less than or equal to $\$2$. This is a classic example of a linear inequality, and it can be solved using basic algebraic techniques.

Key Takeaways

• The cost of each cookie is represented by the variable $x$.
• The total cost of the box is $8x$.
• The most a box can cost is $\$16$.
• The inequality $8x \leq 16$ describes the situation.
• Solving the inequality, we find that $x \leq 2$.

Practice Problems

1. A bakery sells boxes of 12 donuts. If the most a box can cost is $\$24$, what is the maximum cost of each donut?
2. A store sells boxes of 6 pens. If the most a box can cost is $\$18$, what is the maximum cost of each pen?

Answer Key

1. $x \leq 2$
2. $x \leq 3$

Additional Resources

For more practice problems and additional resources, visit the following websites:

• Khan Academy: Linear Inequalities
• Mathway: Linear Inequalities
• IXL: Linear Inequalities
  At Cindy's Sweet Treats: Q&A =============================

Frequently Asked Questions

Q: What is the cost of each cookie at Cindy's Sweet Treats? A: The cost of each cookie is represented by the variable $x$. We found that $x \leq 2$, which means that the cost of each cookie must be less than or equal to $\$2$.

Q: How many cookies are in a box at Cindy's Sweet Treats? A: There are 8 cookies in a box at Cindy's Sweet Treats.

Q: What is the maximum cost of a box of cookies at Cindy's Sweet Treats? A: The maximum cost of a box of cookies at Cindy's Sweet Treats is $\$16$.

Q: How do I set up an inequality to describe a situation like this? A: To set up an inequality, you need to translate the given information into mathematical terms. In this case, we knew that the total cost of the box was $8x$ and that this must be less than or equal to $\$16$. Therefore, we wrote the inequality as $8x \leq 16$.

Q: How do I solve an inequality like this? A: To solve an inequality, you need to isolate the variable. In this case, we divided both sides of the inequality by 8 to get $x \leq 2$.

Q: What is the difference between a linear inequality and a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1. For example, $2x + 3 = 5$ is a linear equation. A linear inequality is an inequality in which the highest power of the variable is 1. For example, $2x + 3 \leq 5$ is a linear inequality.

Q: Can I use the same methods to solve a linear inequality as I would to solve a linear equation? A: Yes, you can use the same methods to solve a linear inequality as you would to solve a linear equation. However, you need to be careful when dividing or multiplying both sides of the inequality by a negative number, as this can change the direction of the inequality.

Q: What are some common mistakes to avoid when solving linear inequalities? A: Some common mistakes to avoid when solving linear inequalities include:

• Dividing or multiplying both sides of the inequality by a negative number without changing the direction of the inequality.
• Forgetting to isolate the variable.
• Not checking the solution to make sure it satisfies the original inequality.

Q: How can I practice solving linear inequalities? A: You can practice solving linear inequalities by working through practice problems, such as those found in a textbook or online resource. You can also try solving inequalities on your own, using real-world examples or word problems.

Q: What are some real-world applications of linear inequalities? A: Linear inequalities have many real-world applications, including:

• Budgeting and finance: Linear inequalities can be used to model budget constraints and determine how much money is available for different expenses.
• Science and engineering: Linear inequalities can be used to model physical systems and determine the relationships between different variables.
• Business and economics: Linear inequalities can be used to model supply and demand curves and determine the optimal price and quantity of a product.

Conclusion

In this article, we have discussed the basics of linear inequalities and how to solve them. We have also answered some frequently asked questions and provided some practice problems and real-world applications. We hope that this article has been helpful in understanding linear inequalities and how to use them to model real-world situations.