One Day In A Sporting Goods Store, 34 People Made Purchases While 14 People Did Not Buy Anything. What Is The Unsimplified Ratio, As A Fraction, Of The Number Of People Who Made A Purchase To The Number Of People Who Came Into The Store?A)

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In this article, we will delve into the world of mathematics, specifically ratios, and explore a real-world scenario that involves making purchases in a sporting goods store. We will examine the given information, calculate the unsimplified ratio of the number of people who made a purchase to the number of people who came into the store, and present the solution in the form of a fraction.

The Scenario: A Sporting Goods Store

Imagine walking into a bustling sporting goods store on a busy Saturday afternoon. As you enter the store, you notice a steady stream of customers browsing through the various sections, from athletic wear to equipment and accessories. The store is filled with the sounds of chatter, the rustling of packaging, and the occasional beep of a cash register.

The Data: 34 People Made Purchases, 14 Did Not Buy Anything

According to the store's records, a total of 34 people made purchases during the day, while 14 people did not buy anything. This information provides us with the necessary data to calculate the ratio of the number of people who made a purchase to the number of people who came into the store.

Calculating the Ratio: A Step-by-Step Approach

To calculate the ratio, we need to follow a simple step-by-step approach:

  1. Identify the number of people who made a purchase: In this case, the number of people who made a purchase is 34.
  2. Identify the number of people who did not make a purchase: The number of people who did not make a purchase is 14.
  3. Calculate the total number of people who came into the store: To find the total number of people who came into the store, we need to add the number of people who made a purchase to the number of people who did not make a purchase. total_people = 34 + 14 = 48
  4. Calculate the ratio: Now that we have the total number of people who came into the store, we can calculate the ratio of the number of people who made a purchase to the number of people who came into the store. ratio = 34 / 48

Simplifying the Ratio: A Fraction

To simplify the ratio, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 34 and 48 is 2. We can simplify the ratio by dividing both the numerator and the denominator by the GCD:

ratio = (34 ÷ 2) / (48 ÷ 2) ratio = 17 / 24

Conclusion: The Unsimplified Ratio

In conclusion, the unsimplified ratio of the number of people who made a purchase to the number of people who came into the store is 34 / 48. However, we can simplify this ratio by dividing both the numerator and the denominator by their greatest common divisor, which is 2. The simplified ratio is 17 / 24.

Real-World Applications of Ratios

Ratios are an essential concept in mathematics, and they have numerous real-world applications. In the context of the sporting goods store scenario, ratios can be used to:

  • Analyze sales data: By calculating the ratio of the number of people who made a purchase to the number of people who came into the store, the store can gain insights into their sales performance and identify areas for improvement.
  • Optimize inventory management: By understanding the ratio of the number of people who made a purchase to the number of people who came into the store, the store can optimize their inventory management and ensure that they have the right products in stock.
  • Make informed business decisions: By analyzing the ratio of the number of people who made a purchase to the number of people who came into the store, the store can make informed business decisions and develop strategies to increase sales and revenue.

Final Thoughts

In our previous article, we explored the concept of ratios and their real-world applications in the context of a sporting goods store. We calculated the unsimplified ratio of the number of people who made a purchase to the number of people who came into the store and simplified it to 17 / 24. In this article, we will address some frequently asked questions related to ratios and their applications.

Q: What is a ratio?

A ratio is a comparison of two numbers or quantities. It is a way to express the relationship between two values. Ratios can be expressed as a fraction, a decimal, or a percentage.

Q: How do I calculate a ratio?

To calculate a ratio, you need to identify the two values you want to compare. Then, you can express the ratio as a fraction by dividing the first value by the second value.

Q: What is the difference between a ratio and a proportion?

A ratio is a comparison of two values, while a proportion is a statement that two ratios are equal. For example, if we say that the ratio of boys to girls in a class is 3:5, we are expressing a ratio. If we say that the ratio of boys to girls in a class is equal to the ratio of boys to girls in another class, we are expressing a proportion.

Q: How do I simplify a ratio?

To simplify a ratio, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, you can divide both the numerator and the denominator by the GCD to simplify the ratio.

Q: What are some real-world applications of ratios?

Ratios have numerous real-world applications in fields such as business, economics, science, and engineering. Some examples include:

  • Sales data analysis: By calculating the ratio of the number of people who made a purchase to the number of people who came into a store, businesses can gain insights into their sales performance and identify areas for improvement.
  • Inventory management: By understanding the ratio of the number of people who made a purchase to the number of people who came into a store, businesses can optimize their inventory management and ensure that they have the right products in stock.
  • Engineering design: By using ratios to compare the dimensions of different components, engineers can design more efficient and effective systems.
  • Scientific research: By using ratios to compare the concentrations of different substances, scientists can gain insights into the behavior of complex systems.

Q: How do I use ratios in my everyday life?

Ratios are used in many everyday situations, such as:

  • Cooking: By using ratios to compare the amounts of different ingredients, cooks can create delicious and balanced meals.
  • Finance: By using ratios to compare the performance of different investments, investors can make informed decisions about their portfolios.
  • Health and wellness: By using ratios to compare the amounts of different nutrients, individuals can make informed decisions about their diets and exercise routines.

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

Some common mistakes to avoid when working with ratios include:

  • Not simplifying the ratio: Failing to simplify the ratio can lead to inaccurate conclusions and poor decision-making.
  • Not considering the context: Failing to consider the context in which the ratio is being used can lead to misinterpretation and poor decision-making.
  • Not using the correct units: Failing to use the correct units can lead to inaccurate conclusions and poor decision-making.

Conclusion

In conclusion, ratios are a powerful tool for comparing and analyzing different values. By understanding how to calculate and simplify ratios, individuals can gain insights into complex systems and make informed decisions about their lives. Whether you are a business owner, an engineer, or a scientist, ratios are an essential concept to master.