What Is The Unknown In The Problem?The Total Number Of Students In The Program, T T T .Given: 170 T = 85 % \frac{170}{t} = 85\% T 170 ​ = 85% Write The Percent As A Rate Per 100: 170 T = 85 100 \frac{170}{t} = \frac{85}{100} T 170 ​ = 100 85 ​

Introduction

When solving a problem, it's essential to identify the unknown variable or variables that need to be determined. In this case, we are given an equation involving the total number of students in a program, denoted as $t$. The equation is $\frac{170}{t} = 85\%$, and we need to find the value of $t$. In this article, we will explore the concept of identifying the unknown in a problem and how to solve it using algebraic techniques.

Understanding the Problem

The problem states that the total number of students in the program, $t$, is related to the equation $\frac{170}{t} = 85\%$. To begin solving this problem, we need to understand the given information and what is being asked. The equation $\frac{170}{t} = 85\%$ implies that the ratio of 170 to the total number of students, $t$, is equal to 85%. This means that 85% of the total number of students is equal to 170.

Writing the Percent as a Rate Per 100

To simplify the equation, we can write the percent as a rate per 100. This is done by dividing the numerator and denominator of the fraction by 100. Therefore, we can rewrite the equation as $\frac{170}{t} = \frac{85}{100}$.

Identifying the Unknown

Now that we have rewritten the equation, we can identify the unknown variable. In this case, the unknown variable is the total number of students in the program, denoted as $t$. We need to find the value of $t$ that satisfies the equation.

Solving the Equation

To solve the equation, we can start by cross-multiplying the fractions. This gives us $170 \times 100 = 85 \times t$. Simplifying the equation, we get $17000 = 85t$. Now, we can divide both sides of the equation by 85 to solve for $t$. This gives us $t = \frac{17000}{85}$.

Calculating the Value of $t$

To calculate the value of $t$, we can divide 17000 by 85. This gives us $t = 200$. Therefore, the total number of students in the program is 200.

Conclusion

In this article, we identified the unknown variable in the problem and solved it using algebraic techniques. We started by rewriting the percent as a rate per 100 and then cross-multiplying the fractions to solve for the unknown variable. The final answer is $t = 200$, which represents the total number of students in the program.

Discussion

The problem presented in this article is a classic example of a proportion problem. Proportion problems involve setting up a ratio of two quantities and solving for the unknown variable. In this case, we set up the ratio $\frac{170}{t} = \frac{85}{100}$ and solved for $t$. The solution to this problem demonstrates the importance of identifying the unknown variable and using algebraic techniques to solve for it.

Real-World Applications

The concept of identifying the unknown variable and solving for it has numerous real-world applications. In business, for example, managers may need to determine the total number of employees in a company based on a given ratio of employees to customers. In science, researchers may need to determine the concentration of a solution based on a given ratio of solute to solvent. In both cases, the ability to identify the unknown variable and solve for it is essential.

Tips for Solving Proportion Problems

When solving proportion problems, it's essential to follow these tips:

• Identify the unknown variable and what is being asked.
• Rewrite the percent as a rate per 100.
• Cross-multiply the fractions to solve for the unknown variable.
• Simplify the equation and solve for the unknown variable.
• Check the solution to ensure it is reasonable and makes sense in the context of the problem.

By following these tips, you can become proficient in solving proportion problems and apply the concept to real-world situations.

Common Mistakes to Avoid

When solving proportion problems, there are several common mistakes to avoid:

• Failing to identify the unknown variable and what is being asked.
• Not rewriting the percent as a rate per 100.
• Not cross-multiplying the fractions to solve for the unknown variable.
• Not simplifying the equation and solving for the unknown variable.
• Not checking the solution to ensure it is reasonable and makes sense in the context of the problem.

By avoiding these common mistakes, you can ensure that your solutions are accurate and make sense in the context of the problem.

Conclusion

In conclusion, identifying the unknown variable and solving for it is a crucial step in solving proportion problems. By following the tips outlined in this article and avoiding common mistakes, you can become proficient in solving proportion problems and apply the concept to real-world situations. The solution to the problem presented in this article demonstrates the importance of identifying the unknown variable and using algebraic techniques to solve for it.

Introduction

In our previous article, we explored the concept of identifying the unknown variable in a problem and solving it using algebraic techniques. In this article, we will answer some frequently asked questions (FAQs) related to identifying the unknown variable and solving proportion problems.

Q: What is the unknown variable in a problem?

A: The unknown variable is the quantity or value that we need to determine or solve for in a problem. It is the variable that is not given or is not known, and we need to find its value using the given information and algebraic techniques.

Q: How do I identify the unknown variable in a problem?

A: To identify the unknown variable, you need to read the problem carefully and understand what is being asked. Look for the variable that is not given or is not known, and make sure you understand what is being asked about that variable.

Q: What is a proportion problem?

A: A proportion problem is a type of problem that involves setting up a ratio of two quantities and solving for the unknown variable. It is a problem that involves finding the value of a variable that is related to a given ratio.

Q: How do I solve a proportion problem?

A: To solve a proportion problem, you need to follow these steps:

1. Identify the unknown variable and what is being asked.
2. Rewrite the percent as a rate per 100.
3. Cross-multiply the fractions to solve for the unknown variable.
4. Simplify the equation and solve for the unknown variable.
5. Check the solution to ensure it is reasonable and makes sense in the context of the problem.

Q: What are some common mistakes to avoid when solving proportion problems?

A: Some common mistakes to avoid when solving proportion problems include:

• Failing to identify the unknown variable and what is being asked.
• Not rewriting the percent as a rate per 100.
• Not cross-multiplying the fractions to solve for the unknown variable.
• Not simplifying the equation and solving for the unknown variable.
• Not checking the solution to ensure it is reasonable and makes sense in the context of the problem.

Q: How do I check my solution to ensure it is reasonable and makes sense in the context of the problem?

A: To check your solution, you need to make sure that it is reasonable and makes sense in the context of the problem. Ask yourself questions such as:

• Is the solution a whole number or a decimal?
• Is the solution positive or negative?
• Does the solution make sense in the context of the problem?

Q: What are some real-world applications of proportion problems?

A: Proportion problems have numerous real-world applications, including:

• Business: Managers may need to determine the total number of employees in a company based on a given ratio of employees to customers.
• Science: Researchers may need to determine the concentration of a solution based on a given ratio of solute to solvent.
• Finance: Investors may need to determine the return on investment based on a given ratio of investment to return.

Q: How can I practice solving proportion problems?

A: You can practice solving proportion problems by:

• Working on practice problems and exercises.
• Using online resources and tools to practice solving proportion problems.
• Joining a study group or working with a tutor to practice solving proportion problems.

Q: What are some tips for solving proportion problems?

A: Some tips for solving proportion problems include:

• Read the problem carefully and understand what is being asked.
• Identify the unknown variable and what is being asked.
• Rewrite the percent as a rate per 100.
• Cross-multiply the fractions to solve for the unknown variable.
• Simplify the equation and solve for the unknown variable.
• Check the solution to ensure it is reasonable and makes sense in the context of the problem.

Conclusion

In conclusion, identifying the unknown variable and solving proportion problems is a crucial step in solving many types of problems. By following the tips and avoiding common mistakes outlined in this article, you can become proficient in solving proportion problems and apply the concept to real-world situations.