Not defining the variables

Oct 13, 2025 by windailys.com 109 views

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Introduction

As a student, it's not every day that you get to apply mathematical concepts to real-world problems, especially those as unique as creating a salt water solution to imitate the ocean. In this scenario, we have a student who wants to create a 3.5% salt water solution by mixing two different salt water solutions: a 2% salt water solution and a 7% salt water solution. The student needs 1 liter of the 3.5% salt water solution and wants to determine the amount of each solution to mix in order to achieve the desired concentration.

The Problem

Let's break down the problem and define the variables:

x: the amount of 2% salt water solution needed
y: the amount of 7% salt water solution needed
1 liter: the total amount of solution needed (1 liter = 1000 mL)

The student wants to create a 3.5% salt water solution, which means that the total amount of salt in the final solution should be 3.5% of 1 liter. Since the student has two different salt water solutions, we need to calculate the amount of salt in each solution and then mix them together to achieve the desired concentration.

Calculating the Amount of Salt in Each Solution

To calculate the amount of salt in each solution, we need to multiply the concentration of each solution by the amount of each solution.

Amount of salt in 2% solution: 0.02x
Amount of salt in 7% solution: 0.07y

Setting Up the Equation

Since the student wants to create a 3.5% salt water solution, the total amount of salt in the final solution should be 3.5% of 1 liter. We can set up an equation to represent this:

0.02x + 0.07y = 0.035(1000)

Simplifying the equation, we get:

0.02x + 0.07y = 35

Solving the Equation

To solve the equation, we can use the substitution method or the elimination method. Let's use the substitution method.

First, we can isolate x by subtracting 0.07y from both sides of the equation:

0.02x = 35 - 0.07y

Next, we can divide both sides of the equation by 0.02 to solve for x:

x = (35 - 0.07y) / 0.02

x = 1750 - 3.5y

Finding the Value of y

Since the student needs 1 liter of the 3.5% salt water solution, the total amount of solution needed is 1000 mL. We can set up an equation to represent this:

x + y = 1000

Substituting the expression for x from the previous equation, we get:

1750 - 3.5y + y = 1000

Combine like terms:

1750 - 2.5y = 1000

Subtract 1750 from both sides:

-2.5y = -750

Divide both sides by -2.5:

y = 300

Finding the Value of x

Now that we have the value of y, we can substitute it into the expression for x:

x = 1750 - 3.5y

x = 1750 - 3.5(300)

x = 1750 - 1050

x = 700

Conclusion

In this scenario, the student needs 700 mL of the 2% salt water solution and 300 mL of the 7% salt water solution to create a 3.5% salt water solution. By applying mathematical concepts to real-world problems, we can solve complex equations and find the solution to the problem.

Final Answer

The final answer is:

x = 700 mL: the amount of 2% salt water solution needed
y = 300 mL: the amount of 7% salt water solution needed

Discussion

This problem is a great example of how mathematical concepts can be applied to real-world problems. By using algebraic equations and solving for the unknown variables, we can find the solution to the problem. This type of problem is commonly seen in chemistry and physics, where the concentration of a solution is an important factor in determining the properties of the solution.

Real-World Applications

This problem has many real-world applications, such as:

Chemistry: in chemistry, the concentration of a solution is an important factor in determining the properties of the solution. By applying mathematical concepts to real-world problems, chemists can create solutions with specific concentrations.
Physics: in physics, the concentration of a solution is an important factor in determining the properties of the solution. By applying mathematical concepts to real-world problems, physicists can create solutions with specific concentrations.
Biology: in biology, the concentration of a solution is an important factor in determining the properties of the solution. By applying mathematical concepts to real-world problems, biologists can create solutions with specific concentrations.

Future Work

In the future, we can explore more complex problems that involve the concentration of a solution. For example, we can consider problems that involve multiple solutions with different concentrations, or problems that involve the creation of a solution with a specific concentration using multiple methods.

References

[1] "Algebra and Trigonometry" by Michael Sullivan
[2] "Chemistry: The Central Science" by Theodore L. Brown
[3] "Physics for Scientists and Engineers" by Paul A. Tipler

Note: The references provided are for illustrative purposes only and are not actual references used in this article.

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Introduction

In our previous article, we explored the problem of creating a 3.5% salt water solution by mixing two different salt water solutions: a 2% salt water solution and a 7% salt water solution. We defined the variables, calculated the amount of salt in each solution, and set up an equation to represent the problem. We then solved the equation to find the amount of each solution needed to create the desired concentration.

Q&A

Q: What is the main goal of the student in this problem?

A: The main goal of the student is to create a 3.5% salt water solution by mixing two different salt water solutions: a 2% salt water solution and a 7% salt water solution.

Q: What are the variables defined in this problem?

A: The variables defined in this problem are:

x: the amount of 2% salt water solution needed
y: the amount of 7% salt water solution needed

Q: How do we calculate the amount of salt in each solution?

A: To calculate the amount of salt in each solution, we multiply the concentration of each solution by the amount of each solution.

Amount of salt in 2% solution: 0.02x
Amount of salt in 7% solution: 0.07y

Q: What is the equation that represents the problem?

A: The equation that represents the problem is:

0.02x + 0.07y = 0.035(1000)

Simplifying the equation, we get:

0.02x + 0.07y = 35

Q: How do we solve the equation?

A: We can use the substitution method or the elimination method to solve the equation. In this case, we used the substitution method.

Q: What is the value of y?

A: The value of y is 300.

Q: What is the value of x?

A: The value of x is 700.

Q: What is the final answer?

A: The final answer is:

x = 700 mL: the amount of 2% salt water solution needed
y = 300 mL: the amount of 7% salt water solution needed

Common Mistakes

Not defining the variables: Make sure to define the variables clearly and concisely.
Not calculating the amount of salt in each solution: Make sure to calculate the amount of salt in each solution correctly.
Not setting up the equation correctly: Make sure to set up the equation correctly and simplify it as needed.
Not solving the equation correctly: Make sure to solve the equation correctly using the substitution method or the elimination method.

Tips and Tricks

Use a diagram to visualize the problem: A diagram can help you visualize the problem and make it easier to understand.
Check your units: Make sure to check your units and ensure that they are consistent throughout the problem.
Use a calculator to check your work: A calculator can help you check your work and ensure that you have the correct answer.

Conclusion

In this Q&A article, we explored the problem of creating a 3.5% salt water solution by mixing two different salt water solutions: a 2% salt water solution and a 7% salt water solution. We defined the variables, calculated the amount of salt in each solution, and set up an equation to represent the problem. We then solved the equation to find the amount of each solution needed to create the desired concentration. We also discussed common mistakes and provided tips and tricks to help you solve similar problems.

Final Answer

The final answer is:

x = 700 mL: the amount of 2% salt water solution needed
y = 300 mL: the amount of 7% salt water solution needed

Discussion

Real-World Applications

This problem has many real-world applications, such as:

Chemistry: in chemistry, the concentration of a solution is an important factor in determining the properties of the solution. By applying mathematical concepts to real-world problems, chemists can create solutions with specific concentrations.
Physics: in physics, the concentration of a solution is an important factor in determining the properties of the solution. By applying mathematical concepts to real-world problems, physicists can create solutions with specific concentrations.
Biology: in biology, the concentration of a solution is an important factor in determining the properties of the solution. By applying mathematical concepts to real-world problems, biologists can create solutions with specific concentrations.

Future Work

References

[1] "Algebra and Trigonometry" by Michael Sullivan
[2] "Chemistry: The Central Science" by Theodore L. Brown
[3] "Physics for Scientists and Engineers" by Paul A. Tipler

Note: The references provided are for illustrative purposes only and are not actual references used in this article.