A Company Conducted A Survey To Determine Whether Its New Toothpaste Was More Popular With Children Or Adults. Of The Children Surveyed, $28\%$ Use The Toothpaste. Compare This With The Percentage Of Adults Who Use The

Feb 28, 2025 by ADMIN 219 views

**A Company's Toothpaste Survey: Uncovering the Preferences of Children and Adults**

Introduction

In the world of consumer products, understanding the preferences of different demographics is crucial for businesses to make informed decisions about their marketing strategies. A company recently conducted a survey to determine whether its new toothpaste was more popular with children or adults. The survey revealed that $28\%$ of children use the toothpaste, but what about the percentage of adults who use it? In this article, we will delve into the survey results and compare the usage of the toothpaste among children and adults.

The Survey Results

The survey conducted by the company revealed that $28\%$ of children use the new toothpaste. However, the percentage of adults who use the toothpaste is not explicitly stated in the problem. To compare the usage of the toothpaste among children and adults, we need to assume a certain percentage of adults who use the toothpaste.

Assumptions

Let's assume that the percentage of adults who use the toothpaste is $x\%$ . We can then compare the usage of the toothpaste among children and adults by calculating the difference between the two percentages.

Calculating the Difference

To calculate the difference between the percentage of children who use the toothpaste and the percentage of adults who use it, we can use the following formula:

Difference = (Percentage of children who use the toothpaste) - (Percentage of adults who use the toothpaste)

Substituting the given values, we get:

Difference = $28\%$ - $x\%$

Simplifying the Expression

To simplify the expression, we can convert the percentages to decimal form by dividing by $100$ . This gives us:

Difference = $0.28$ - $x/100$

Finding the Value of x

Since we want to find the value of $x$ , we can set up an equation using the difference. Let's assume that the difference is $y$ . Then, we can write:

$y = 0.28 - x/100$

Solving for x

To solve for $x$ , we can isolate the variable $x$ on one side of the equation. Multiplying both sides by $100$ , we get:

$100y = 28 - x$

Subtracting $28$ from both sides, we get:

$100y - 28 = -x$

Multiplying both sides by $-1$ , we get:

$x = 28 - 100y$

Interpreting the Results

Now that we have found the value of $x$ , we can interpret the results. The value of $x$ represents the percentage of adults who use the toothpaste. Since we assumed that the difference between the percentage of children who use the toothpaste and the percentage of adults who use it is $y$ , we can substitute the value of $y$ into the equation to find the value of $x$ .

Conclusion

In conclusion, the survey conducted by the company revealed that $28\%$ of children use the new toothpaste. By assuming a certain percentage of adults who use the toothpaste, we can compare the usage of the toothpaste among children and adults. The value of $x$ represents the percentage of adults who use the toothpaste, and it can be found by solving the equation $x = 28 - 100y$ , where $y$ is the difference between the percentage of children who use the toothpaste and the percentage of adults who use it.

The Mathematics Behind the Survey

The survey conducted by the company is a classic example of a statistical problem. The problem involves comparing the usage of the toothpaste among children and adults, and it requires the use of mathematical concepts such as percentages, decimals, and algebraic equations.

The Importance of Statistics in Business

Statistics plays a crucial role in business, and it is used to make informed decisions about marketing strategies, product development, and customer satisfaction. The survey conducted by the company is a great example of how statistics can be used to understand customer preferences and make data-driven decisions.

Real-World Applications of the Survey

The survey conducted by the company has several real-world applications. For example, the company can use the survey results to develop targeted marketing campaigns that appeal to children and adults. The company can also use the survey results to improve the product by making changes to the toothpaste formula or packaging.

Conclusion

Q&A: Understanding the Survey Results

Q: What was the main goal of the survey conducted by the company? A: The main goal of the survey was to determine whether the company's new toothpaste was more popular with children or adults.

Q: What percentage of children use the toothpaste? A: According to the survey results, $28\%$ of children use the toothpaste.

Q: What percentage of adults use the toothpaste? A: The percentage of adults who use the toothpaste is not explicitly stated in the problem. However, we can assume a certain percentage of adults who use the toothpaste and compare it with the percentage of children who use it.

Q: How can we compare the usage of the toothpaste among children and adults? A: We can compare the usage of the toothpaste among children and adults by calculating the difference between the two percentages. Let's assume that the percentage of adults who use the toothpaste is $x\%$ . Then, we can calculate the difference as follows:

Difference = (Percentage of children who use the toothpaste) - (Percentage of adults who use the toothpaste)

Substituting the given values, we get:

Difference = $28\%$ - $x\%$

Q: How can we simplify the expression and find the value of x? A: To simplify the expression, we can convert the percentages to decimal form by dividing by $100$ . This gives us:

Difference = $0.28$ - $x/100$

We can then solve for $x$ by isolating the variable $x$ on one side of the equation.

Q: What is the equation to find the value of x? A: The equation to find the value of $x$ is:

$x = 28 - 100y$

where $y$ is the difference between the percentage of children who use the toothpaste and the percentage of adults who use it.

Q: What is the importance of statistics in business? A: Statistics plays a crucial role in business, and it is used to make informed decisions about marketing strategies, product development, and customer satisfaction. The survey conducted by the company is a great example of how statistics can be used to understand customer preferences and make data-driven decisions.

Q: What are some real-world applications of the survey? A: The survey conducted by the company has several real-world applications. For example, the company can use the survey results to develop targeted marketing campaigns that appeal to children and adults. The company can also use the survey results to improve the product by making changes to the toothpaste formula or packaging.

Q: What can we conclude from the survey results? A: In conclusion, the survey conducted by the company revealed that $28\%$ of children use the new toothpaste. By assuming a certain percentage of adults who use the toothpaste, we can compare the usage of the toothpaste among children and adults. The value of $x$ represents the percentage of adults who use the toothpaste, and it can be found by solving the equation $x = 28 - 100y$ , where $y$ is the difference between the percentage of children who use the toothpaste and the percentage of adults who use it.

Frequently Asked Questions

Q: What is the main goal of the survey? A: The main goal of the survey is to determine whether the company's new toothpaste is more popular with children or adults.

Q: What percentage of children use the toothpaste? A: $28\%$ of children use the toothpaste.

Q: What percentage of adults use the toothpaste? A: The percentage of adults who use the toothpaste is not explicitly stated in the problem.

Q: What is the equation to find the value of x? A: The equation to find the value of $x$ is:

$x = 28 - 100y$

Q: What are some real-world applications of the survey? A: The survey conducted by the company has several real-world applications, including developing targeted marketing campaigns and improving the product.