Complete The Table By Filling In The Missing Prices In Rands For The Given Number Of Pens.$[ \begin{tabular}{|l|l|l|l|l|} \hline \textbf{Number Of Pens} & \textbf{2} & \textbf{6} & \textbf{10} & \textbf{20} \ \hline \textbf{Price In Rands} & _ &
Mathematical Problem Solving: Completing the Table with Missing Prices
In this article, we will delve into a mathematical problem that involves completing a table with missing prices for a given number of pens. The problem requires us to use our mathematical skills to fill in the blanks and arrive at the correct solutions. We will break down the problem step by step, and provide a clear explanation of the mathematical concepts involved.
The problem is presented in the form of a table, with the number of pens on one axis and the price in rands on the other axis. The table has four rows, each representing a different number of pens: 2, 6, 10, and 20. However, the price in rands is missing for each of these rows. Our task is to fill in the missing prices.
To solve this problem, we need to use the concept of proportionality. Proportionality is a mathematical relationship between two or more quantities that are directly or inversely proportional to each other. In this case, we are given the price of 1 pen, and we need to find the price of 2, 6, 10, and 20 pens.
Step 1: Find the Price of 1 Pen
Let's assume that the price of 1 pen is x rands. We are not given the exact price, but we can represent it as a variable.
Step 2: Find the Price of 2 Pens
Since the price of 2 pens is twice the price of 1 pen, we can multiply the price of 1 pen by 2 to get the price of 2 pens. Therefore, the price of 2 pens is 2x rands.
Step 3: Find the Price of 6 Pens
Similarly, the price of 6 pens is six times the price of 1 pen. Therefore, the price of 6 pens is 6x rands.
Step 4: Find the Price of 10 Pens
The price of 10 pens is ten times the price of 1 pen. Therefore, the price of 10 pens is 10x rands.
Step 5: Find the Price of 20 Pens
Finally, the price of 20 pens is twenty times the price of 1 pen. Therefore, the price of 20 pens is 20x rands.
In conclusion, we have successfully completed the table with missing prices by using the concept of proportionality. We found the price of 2, 6, 10, and 20 pens by multiplying the price of 1 pen by the corresponding number of pens.
| Number of Pens | Price in Rands |
|---|---|
| 2 | 2x |
| 6 | 6x |
| 10 | 10x |
| 20 | 20x |
The problem presented in this article is a classic example of a mathematical problem that requires the use of proportionality. The concept of proportionality is a fundamental concept in mathematics that is used to describe the relationship between two or more quantities that are directly or inversely proportional to each other.
The concept of proportionality has numerous real-world applications. For example, in finance, proportionality is used to calculate the interest on a loan or investment. In physics, proportionality is used to describe the relationship between two or more physical quantities, such as the force and acceleration of an object.
When solving problems that involve proportionality, it's essential to remember the following tips and tricks:
- Always identify the proportional relationship between the quantities involved.
- Use the concept of proportionality to set up an equation or formula that describes the relationship between the quantities.
- Solve the equation or formula to find the missing value or quantity.
In conclusion, completing the table with missing prices is a mathematical problem that requires the use of proportionality. By following the steps outlined in this article, we can successfully fill in the missing prices and arrive at the correct solutions. The concept of proportionality is a fundamental concept in mathematics that has numerous real-world applications.
Mathematical Problem Solving: Completing the Table with Missing Prices - Q&A
In our previous article, we delved into a mathematical problem that involved completing a table with missing prices for a given number of pens. We used the concept of proportionality to fill in the missing prices and arrived at the correct solutions. In this article, we will provide a Q&A section to further clarify any doubts or questions that readers may have.
Q: What is proportionality?
A: Proportionality is a mathematical relationship between two or more quantities that are directly or inversely proportional to each other. In the context of the problem, we used proportionality to find the price of 2, 6, 10, and 20 pens by multiplying the price of 1 pen by the corresponding number of pens.
Q: How do I identify the proportional relationship between quantities?
A: To identify the proportional relationship between quantities, you need to look for a direct or inverse relationship between the quantities. In the problem, we were given the price of 1 pen, and we needed to find the price of 2, 6, 10, and 20 pens. We used the concept of proportionality to set up an equation that described the relationship between the quantities.
Q: What is the difference between direct and inverse proportionality?
A: Direct proportionality is a relationship between two or more quantities where an increase in one quantity results in a proportional increase in the other quantity. Inverse proportionality is a relationship between two or more quantities where an increase in one quantity results in a proportional decrease in the other quantity.
Q: How do I use proportionality to solve problems?
A: To use proportionality to solve problems, you need to follow these steps:
- Identify the proportional relationship between the quantities involved.
- Set up an equation or formula that describes the relationship between the quantities.
- Solve the equation or formula to find the missing value or quantity.
Q: What are some real-world applications of proportionality?
A: Proportionality has numerous real-world applications, including finance, physics, and engineering. For example, in finance, proportionality is used to calculate the interest on a loan or investment. In physics, proportionality is used to describe the relationship between two or more physical quantities, such as the force and acceleration of an object.
Q: How do I practice using proportionality to solve problems?
A: To practice using proportionality to solve problems, you can try the following:
- Start with simple problems that involve direct or inverse proportionality.
- Gradually move on to more complex problems that involve multiple quantities and relationships.
- Use online resources or practice problems to help you improve your skills.
In conclusion, completing the table with missing prices is a mathematical problem that requires the use of proportionality. By following the steps outlined in this article, we can successfully fill in the missing prices and arrive at the correct solutions. The concept of proportionality is a fundamental concept in mathematics that has numerous real-world applications. We hope that this Q&A section has helped to clarify any doubts or questions that readers may have.
For further practice and learning, we recommend the following resources:
- Khan Academy: Proportionality and Ratios
- Mathway: Proportionality and Ratios
- IXL: Proportionality and Ratios
When solving problems that involve proportionality, it's essential to remember the following tips and tricks:
- Always identify the proportional relationship between the quantities involved.
- Use the concept of proportionality to set up an equation or formula that describes the relationship between the quantities.
- Solve the equation or formula to find the missing value or quantity.
- Practice using proportionality to solve problems to improve your skills.