Solve For The Original Amount { T $}$ If It Is Increased By { 35% $}$ To Become { 160,000 $}$.

Mar 12, 2025 by ADMIN 95 views

**Solving for the Original Amount: A Step-by-Step Guide**

Introduction

In this article, we will delve into the world of mathematics and explore a common problem that involves calculating the original amount of money before it is increased by a certain percentage. We will use a real-world example to illustrate the concept and provide a step-by-step guide on how to solve for the original amount.

The Problem

Let's say we have a certain amount of money, denoted as ${$ t $}$, which is increased by ${$ 35% $}$ to become ${$ 160,000 $}$. Our goal is to find the original amount, ${$ t $}$, before it was increased.

Understanding the Concept of Percentage Increase

Before we dive into the solution, let's understand the concept of percentage increase. When a certain amount is increased by a percentage, it means that the new amount is the original amount plus a certain percentage of the original amount. In this case, the original amount is increased by ${$ 35% $}$, which means that the new amount is ${$ 100% $}$ (the original amount) plus ${$ 35% $}$ (the increase).

Step 1: Set Up the Equation

To solve for the original amount, we need to set up an equation that represents the situation. Let's denote the original amount as ${$ t $}$. Since the amount is increased by ${$ 35% $}$, the new amount can be represented as:

${$ t + 0.35t = 160,000 $}$

Step 2: Simplify the Equation

Now that we have set up the equation, let's simplify it by combining like terms. We can do this by adding the two terms on the left-hand side of the equation:

${$ 1.35t = 160,000 $}$

Step 3: Solve for the Original Amount

Now that we have simplified the equation, let's solve for the original amount, ${$ t $}$. We can do this by dividing both sides of the equation by ${$ 1.35 $}$:

${$ t = \frac{160,000}{1.35} $}$

Step 4: Calculate the Original Amount

Now that we have the equation, let's calculate the original amount:

${$ t = \frac{160,000}{1.35} = 117,593.33 $}$

Conclusion

In this article, we have solved for the original amount of money before it was increased by ${$ 35% $}$ to become ${$ 160,000 $}$. We have used a step-by-step approach to set up the equation, simplify it, and solve for the original amount. The original amount is ${$ 117,593.33 $}$.

Real-World Applications

This problem has many real-world applications, such as calculating the original price of an item before it was discounted, or calculating the original amount of money in a savings account before it was increased by interest.

Tips and Tricks

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

Always set up an equation that represents the situation.
Simplify the equation by combining like terms.
Solve for the unknown variable by dividing both sides of the equation by the coefficient of the variable.
Use a calculator to calculate the value of the unknown variable.

Common Mistakes

Here are some common mistakes to avoid when solving similar problems:

Not setting up an equation that represents the situation.
Not simplifying the equation by combining like terms.
Not solving for the unknown variable by dividing both sides of the equation by the coefficient of the variable.
Not using a calculator to calculate the value of the unknown variable.

Conclusion

Introduction

In our previous article, we explored the concept of solving for the original amount of money before it is increased by a certain percentage. We provided a step-by-step guide on how to set up the equation, simplify it, and solve for the original amount. In this article, we will answer some of the most frequently asked questions about solving for the original amount.

Q&A

Q: What is the formula for solving for the original amount?

A: The formula for solving for the original amount is:

${$ t = \frac{A}{1 + r} $}$

where ${$ t $}$ is the original amount, ${$ A $}$ is the new amount, and ${$ r $}$ is the rate of increase.

Q: How do I set up the equation to solve for the original amount?

A: To set up the equation, you need to identify the new amount, the rate of increase, and the original amount. Then, you can use the formula above to set up the equation.

Q: What is the difference between the rate of increase and the percentage increase?

A: The rate of increase is the decimal equivalent of the percentage increase. For example, if the percentage increase is 35%, the rate of increase is 0.35.

Q: How do I simplify the equation to solve for the original amount?

A: To simplify the equation, you need to combine like terms. In this case, you can multiply the rate of increase by the original amount to get the new amount.

Q: What is the formula for calculating the new amount?

A: The formula for calculating the new amount is:

${$ A = t(1 + r) $}$

where ${$ A $}$ is the new amount, ${$ t $}$ is the original amount, and ${$ r $}$ is the rate of increase.

Q: How do I calculate the original amount if the new amount is $160,000 and the rate of increase is 35%?

A: To calculate the original amount, you can use the formula:

${$ t = \frac{A}{1 + r} $}$

Substituting the values, you get:

${$ t = \frac{160,000}{1 + 0.35} $}$

Simplifying the equation, you get:

${$ t = \frac{160,000}{1.35} $}$

Calculating the value, you get:

${$ t = 117,593.33 $}$

Q: What are some common mistakes to avoid when solving for the original amount?

A: Some common mistakes to avoid when solving for the original amount include:

Not setting up the equation correctly
Not simplifying the equation by combining like terms
Not solving for the original amount by dividing both sides of the equation by the coefficient of the variable
Not using a calculator to calculate the value of the original amount

Conclusion

In conclusion, solving for the original amount of money before it is increased by a certain percentage is a common problem that involves calculating the original amount. We have provided a step-by-step guide on how to set up the equation, simplify it, and solve for the original amount. We have also answered some of the most frequently asked questions about solving for the original amount. We hope that this article has provided you with a clear understanding of how to solve similar problems.

Real-World Applications

Tips and Tricks

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

Always set up an equation that represents the situation.
Simplify the equation by combining like terms.
Solve for the unknown variable by dividing both sides of the equation by the coefficient of the variable.
Use a calculator to calculate the value of the unknown variable.

Common Mistakes

Here are some common mistakes to avoid when solving similar problems:

Not setting up an equation that represents the situation.
Not simplifying the equation by combining like terms.
Not solving for the unknown variable by dividing both sides of the equation by the coefficient of the variable.
Not using a calculator to calculate the value of the unknown variable.