4 Σ A Jug Contains 1 Litre Of Juice. Dani Pours A Drink For Each Of Her Friends. 1 Litre After Dani Has Poured Out 4 Glasses, The Jug Is Half Full. Form An Equation And Solve It To Find The Capacity Of Each Glass. The Rectangle Has The Same Area As The

Feb 26, 2025 by ADMIN 253 views

**Mathematical Problem Solving: Finding the Capacity of Each Glass**

Introduction

Mathematics is a fascinating subject that involves problem-solving, critical thinking, and logical reasoning. In this article, we will delve into a mathematical problem that involves forming an equation and solving it to find the capacity of each glass. The problem is as follows: A jug contains 1 litre of juice. Dani pours a drink for each of her friends. After Dani has poured out 4 glasses, the jug is half full. We need to form an equation and solve it to find the capacity of each glass.

Understanding the Problem

Let's break down the problem and understand what is being asked. We have a jug that contains 1 litre of juice. Dani pours out 4 glasses, and after that, the jug is half full. This means that the amount of juice left in the jug is 0.5 litres. Since Dani poured out 4 glasses, the total amount of juice poured out is 0.5 litres. We need to find the capacity of each glass.

Forming the Equation

Let's denote the capacity of each glass as x. Since Dani poured out 4 glasses, the total amount of juice poured out is 4x. We know that the amount of juice left in the jug is 0.5 litres, and the total amount of juice in the jug is 1 litre. Therefore, we can form the following equation:

4x + 0.5 = 1

Solving the Equation

To solve the equation, we need to isolate the variable x. We can start by subtracting 0.5 from both sides of the equation:

4x = 1 - 0.5 4x = 0.5

Next, we can divide both sides of the equation by 4:

x = 0.5 / 4 x = 0.125

Interpretation of the Result

The result x = 0.125 means that the capacity of each glass is 0.125 litres. This is equivalent to 125 millilitres.

Conclusion

In this article, we formed an equation and solved it to find the capacity of each glass. The problem involved understanding the given information, forming an equation, and solving it to find the solution. The result showed that the capacity of each glass is 0.125 litres, which is equivalent to 125 millilitres.

Real-World Applications

This problem has real-world applications in various fields such as:

Cooking: When cooking, it's essential to know the capacity of each glass to measure the right amount of ingredients.
Science: In scientific experiments, knowing the capacity of each glass is crucial to measure the right amount of substances.
Industry: In industrial settings, knowing the capacity of each glass is essential to measure the right amount of materials.

Tips and Tricks

Here are some tips and tricks to help you solve similar problems:

Read the problem carefully: Before starting to solve the problem, read it carefully to understand what is being asked.
Form an equation: Form an equation based on the given information and the problem statement.
Solve the equation: Solve the equation to find the solution.
Check the units: Make sure to check the units of the solution to ensure that they are correct.

Frequently Asked Questions

Here are some frequently asked questions related to this problem:

What is the capacity of each glass? The capacity of each glass is 0.125 litres, which is equivalent to 125 millilitres.
How do I form an equation to solve this problem? To form an equation, you need to understand the given information and the problem statement. Then, you can form an equation based on the given information and the problem statement.
How do I solve the equation? To solve the equation, you need to isolate the variable x. You can start by subtracting 0.5 from both sides of the equation, then divide both sides of the equation by 4.

Conclusion

In conclusion, this problem involves forming an equation and solving it to find the capacity of each glass. The result showed that the capacity of each glass is 0.125 litres, which is equivalent to 125 millilitres. This problem has real-world applications in various fields such as cooking, science, and industry. By following the tips and tricks provided, you can solve similar problems and become proficient in mathematical problem-solving.

Introduction

In our previous article, we solved a mathematical problem involving finding the capacity of each glass. In this article, we will provide a Q&A section to help you understand the problem and its solution better. We will answer some frequently asked questions related to the problem and provide additional information to help you grasp the concept.

Q&A

Q: What is the capacity of each glass?

A: The capacity of each glass is 0.125 litres, which is equivalent to 125 millilitres.

Q: How do I form an equation to solve this problem?

A: To form an equation, you need to understand the given information and the problem statement. Then, you can form an equation based on the given information and the problem statement. In this case, the equation is 4x + 0.5 = 1, where x is the capacity of each glass.

Q: How do I solve the equation?

A: To solve the equation, you need to isolate the variable x. You can start by subtracting 0.5 from both sides of the equation, then divide both sides of the equation by 4. This will give you the value of x, which is the capacity of each glass.

Q: What if I have a different problem with a different number of glasses?

A: If you have a different problem with a different number of glasses, you can follow the same steps to form an equation and solve it. The only difference will be the number of glasses and the amount of juice left in the jug.

Q: Can I use this method to solve problems with different units?

A: Yes, you can use this method to solve problems with different units. However, you need to make sure that you are using the correct units and that you are converting them correctly.

Q: What if I get stuck while solving the equation?

A: If you get stuck while solving the equation, don't worry! You can try breaking down the equation into smaller parts and solving each part separately. You can also try using different methods, such as graphing or using a calculator, to help you solve the equation.

Q: Can I use this method to solve problems with multiple variables?

A: Yes, you can use this method to solve problems with multiple variables. However, you need to make sure that you are using the correct equations and that you are solving for the correct variables.

Additional Tips and Tricks

Here are some additional tips and tricks to help you solve similar problems:

Read the problem carefully: Before starting to solve the problem, read it carefully to understand what is being asked.
Form an equation: Form an equation based on the given information and the problem statement.
Solve the equation: Solve the equation to find the solution.
Check the units: Make sure to check the units of the solution to ensure that they are correct.
Use different methods: Try using different methods, such as graphing or using a calculator, to help you solve the equation.
Break down the equation: Try breaking down the equation into smaller parts and solving each part separately.

Conclusion

In conclusion, this Q&A section provides additional information and answers to frequently asked questions related to the problem of finding the capacity of each glass. By following the tips and tricks provided, you can solve similar problems and become proficient in mathematical problem-solving.

Real-World Applications

This problem has real-world applications in various fields such as:

Cooking: When cooking, it's essential to know the capacity of each glass to measure the right amount of ingredients.
Science: In scientific experiments, knowing the capacity of each glass is crucial to measure the right amount of substances.
Industry: In industrial settings, knowing the capacity of each glass is essential to measure the right amount of materials.

Frequently Asked Questions

Here are some frequently asked questions related to this problem:

What is the capacity of each glass? The capacity of each glass is 0.125 litres, which is equivalent to 125 millilitres.
How do I form an equation to solve this problem? To form an equation, you need to understand the given information and the problem statement. Then, you can form an equation based on the given information and the problem statement.
How do I solve the equation? To solve the equation, you need to isolate the variable x. You can start by subtracting 0.5 from both sides of the equation, then divide both sides of the equation by 4.