Understanding the Concept of Increasing a Number by 25%: Solving the Equation x 0.25x 30

When dealing with numerical problems that involve increasing a number by a certain percentage, the key is to set up the right equation and solve it systematically. In this article, we explore how to solve the equation x 0.25x 30, which illustrates how increasing a number by 25% can result in a specific value.

Problem Statement

Let's denote the unknown number as x. The problem states that when this number is increased by 25% of itself, the result is 30. This can be expressed mathematically as:

x 0.25x 30

Step-by-Step Solution

Step 1: Combining Like Terms

First, we combine the like terms on the left side of the equation. The equation becomes:

1.25x 30

This step involves recognizing that x 0.25x can be simplified to 1.25x.

Step 2: Isolating the Variable

To find the value of x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.25:

x 30 / 1.25

This step shows the algebraic manipulation to solve for x.

Step 3: Calculating the Result

Now, let's perform the calculation:

x 30 / 1.25

To simplify this, convert 1.25 to a fraction: 1.25 5/4

x 30 × 4/5

Simplifying further:

x 24

This is the solution to the problem. The number that, when increased by 25% of itself, gives a result of 30 is 24.

Verification

To verify the solution, we can substitute x 24 back into the original equation:

24 0.25(24) 24 6 30

This confirms that the solution is correct.

Conclusion

In conclusion, the number that, when increased by 25% of itself, equals 30 is 24. By following the steps outlined in this article, we can solve a wide range of similar problems involving percentage increases and algebraic equations. This method can be applied to other similar scenarios to find the original value before a percentage increase or decrease.