Solving a Quadratic Equation to Find One Third of a Number

In this article, we will solve a quadratic equation to find the value of a certain number, and then determine one third of that number. This process involves several steps, from setting up the equation to finding the square root and performing division. Let's go through the problem step by step.

The Problem

We are given that the product of 2 of a number and 5 of the same number is 152.1. Mathematically, this can be written as:

0.02x * 0.05x 152.1

Step 1: Simplify the Equation

We will start by simplifying the left side of the equation:

0.02x * 0.05x 0.001x^2

Thus, our equation becomes:

0.001x^2 152.1

Step 2: Isolate the Variable

To isolate x^2, we multiply both sides of the equation by 1000:

x^2 152100

Step 3: Solve for x

Next, we take the square root of both sides to find the value of x:

x √152100

x 390

Step 4: Find One Third of the Number

Now, to find one third of this number, we divide 390 by 3:

1/3 * 390 130

Therefore, one third of the number is 130.

Step-by-Step Solution

Let's assume the unknown number is x. We are given the following equation:

0.02x * 0.05x 152.1

Simplifying the left side of the equation gives:

0.001x^2 152.1

Multiplying both sides by 1000 to isolate x^2:

x^2 152100

Taking the square root of both sides to find x:

x √152100

x 390

To find one third of x, we divide 390 by 3:

1/3 * 390 130

Hence, one third of the number is 130.

Additional Practice

When solving such problems, it's helpful to write out the steps clearly. Here is another approach to solving the same problem:

Let's assume the unknown number is n. We are given the following equation:

0.02nx * 0.05nx 152.1

Multiplying the terms on the left side:

0.001n^2 152.1

Isolating n^2 by multiplying both sides by 1000:

n^2 152100

Solving for n by taking the square root:

n √152100 390

To find one third of n, we divide 390 by 3:

1/3 * 390 130

Thus, the final answer is 130.

Conclusion

In this article, we have explored how to solve a quadratic equation to find the value of a number and then determine one third of that number. This process involves several algebraic steps, from simplifying the equation to taking the square root and performing division. By following these steps, we can accurately solve similar problems and find the required result. Whether it's for practice or in your academic studies, understanding these steps will be invaluable.