Select The Best Answer For The Question.Heldi, A Jewelry Salesperson, Earns A Commission Of $\$ 55$ Every Time She Sells A Diamond Ring. How Many Rings Does She Have To Sell To Earn $\$ 605$? Choose The Equation That Correctly

Understanding the Commission Structure

As a jewelry salesperson, Heldi earns a commission of $\$ 55$ every time she sells a diamond ring. This commission structure is a key factor in determining how many rings she needs to sell to reach a specific earnings target. In this scenario, Heldi aims to earn $\$ 605$. To find out how many rings she must sell to achieve this goal, we need to establish a mathematical equation that relates her commission earnings to the number of rings sold.

Establishing the Equation

Let's denote the number of rings Heldi needs to sell as $x$. Since each ring earns her a commission of $\$ 55$, the total commission earned from selling $x$ rings can be represented as $55x$. This is the amount she needs to reach her target earnings of $\$ 605$. Therefore, we can set up the following equation:

$$55x = 605$$

Solving for x

To find the number of rings Heldi needs to sell, we need to solve for $x$ in the equation $55x = 605$. We can do this by dividing both sides of the equation by $55$:

$$x = \frac{605}{55}$$

Calculating the Number of Rings

Now, let's calculate the value of $x$:

$$x = \frac{605}{55} = 11$$

Conclusion

Based on the commission structure and the target earnings, Heldi needs to sell $\boxed{11}$ diamond rings to earn $\$ 605$.

Alternative Equation Options

While the equation $55x = 605$ is the correct representation of the commission earnings and target earnings, there are other equation options that may seem plausible but are incorrect. Let's examine some of these alternatives:

• Option 1: $55x + 605 = 0$

  This equation is incorrect because it represents a scenario where Heldi's commission earnings and target earnings are set to zero, which is not relevant to the problem.

• Option 2: $x = 55 + 605$

  This equation is incorrect because it represents a scenario where Heldi's commission earnings and target earnings are added together, which is not relevant to the problem.

• Option 3: $55x - 605 = 0$

  This equation is incorrect because it represents a scenario where Heldi's commission earnings and target earnings are set to zero, which is not relevant to the problem.

Choosing the Correct Equation

When faced with multiple equation options, it's essential to carefully analyze each one to determine which one accurately represents the problem. In this case, the correct equation is $55x = 605$, which relates Heldi's commission earnings to the number of rings she needs to sell to reach her target earnings.

Real-World Applications

Understanding commission structures and how to establish equations to represent them is crucial in various real-world scenarios, such as sales, marketing, and finance. By applying mathematical concepts to real-world problems, individuals can make informed decisions and achieve their goals.

Conclusion

In conclusion, Heldi needs to sell $\boxed{11}$ diamond rings to earn $\$ 605$. The correct equation to represent this scenario is $55x = 605$, which relates her commission earnings to the number of rings she needs to sell. By understanding commission structures and how to establish equations to represent them, individuals can make informed decisions and achieve their goals.

Understanding Commission Structures

As a jewelry salesperson, Heldi earns a commission of $\$ 55$ every time she sells a diamond ring. This commission structure is a key factor in determining how many rings she needs to sell to reach a specific earnings target. In this scenario, Heldi aims to earn $\$ 605$. To find out how many rings she must sell to achieve this goal, we need to establish a mathematical equation that relates her commission earnings to the number of rings sold.

Q&A: Commission Earnings and Diamond Ring Sales

Q: What is the commission structure for Heldi's diamond ring sales?

A: Heldi earns a commission of $\$ 55$ every time she sells a diamond ring.

Q: What is Heldi's target earnings?

A: Heldi aims to earn $\$ 605$.

Q: How many rings does Heldi need to sell to earn $\$ 605$?

A: Heldi needs to sell $\boxed{11}$ diamond rings to earn $\$ 605$.

Q: What is the correct equation to represent Heldi's commission earnings and target earnings?

A: The correct equation is $55x = 605$, where $x$ represents the number of rings Heldi needs to sell.

Q: What is the significance of understanding commission structures and establishing equations to represent them?

A: Understanding commission structures and establishing equations to represent them is crucial in various real-world scenarios, such as sales, marketing, and finance. By applying mathematical concepts to real-world problems, individuals can make informed decisions and achieve their goals.

Q: What are some common mistakes to avoid when establishing equations to represent commission earnings and target earnings?

A: Some common mistakes to avoid include:

• Representing commission earnings and target earnings as a sum or difference, rather than a product.
• Setting commission earnings and target earnings to zero, rather than a specific value.
• Failing to establish a clear relationship between commission earnings and the number of rings sold.

Conclusion

In conclusion, Heldi needs to sell $\boxed{11}$ diamond rings to earn $\$ 605$. The correct equation to represent this scenario is $55x = 605$, which relates her commission earnings to the number of rings she needs to sell. By understanding commission structures and how to establish equations to represent them, individuals can make informed decisions and achieve their goals.

Real-World Applications

Understanding commission structures and how to establish equations to represent them is crucial in various real-world scenarios, such as sales, marketing, and finance. By applying mathematical concepts to real-world problems, individuals can make informed decisions and achieve their goals.

Additional Resources

For further information on commission structures and how to establish equations to represent them, consider the following resources:

• Mathematics textbooks: Many mathematics textbooks cover commission structures and how to establish equations to represent them.
• Online tutorials: Websites such as Khan Academy and Mathway offer tutorials and examples on commission structures and how to establish equations to represent them.
• Professional development courses: Consider taking professional development courses or workshops on commission structures and how to establish equations to represent them.

Conclusion

In conclusion, Heldi needs to sell $\boxed{11}$ diamond rings to earn $\$ 605$. The correct equation to represent this scenario is $55x = 605$, which relates her commission earnings to the number of rings she needs to sell. By understanding commission structures and how to establish equations to represent them, individuals can make informed decisions and achieve their goals.