To find the percentage change from 50 to 80, we need to first calculate the difference between the two numbers.

It is a valuable tool for analyzing changes and trends in various contexts, such as financial growth, population increase, or academic improvement.

These are the following step to solve this problem:

**Step 1:** Determine the initial value.

First, let's identify the initial value. In this case, the initial value is 50.

**Step 2:** Determine the final value.

Now, let's find the final value, which is 80.

**Step 3:** Calculate the increase in value.

To find the increase, subtract the initial value from the final value:

Increase = Final Value - Initial Value

Increase = 80 - 50

**Step 4:** Calculate the percent increase.

To calculate the percent increase, divide the increase by the initial value and multiply by 100:

Percent Increase = (Increase / Initial Value) * 100

Percent Increase = (30 / 50) * 100

**Step 5:** Simplify the fraction (if necessary).

Let's simplify the fraction 30/50. Both the numerator and denominator are divisible by 10, so we get:

Percent Increase = (3 / 5) * 100

**Step 6:** Calculate the percent.

Now, let's calculate the percent increase using a calculator or by dividing and multiplying:

Percent Increase = (0.6) * 100

Percent Increase = 60%

So, the percent increase from 50 to 80 is 60%.

In our example, we were given an initial value of 50 and a final value of 80. By following the step-by-step approach, we calculated the percent increase to be 60%.

This means that the quantity increased by 60% relative to its initial value. In other words, it experienced significant growth or expansion.

Let’s take a look at some more relevant examples:

**Example 1: Population Growth**

Suppose a town had a population of 10,000 people five years ago. Today, the population has grown to 15,000 people. What is the percentage increase in the population?

**Step 1: **Determine the initial value.

The initial population is 10,000.

**Step 2:** Determine the final value.

The current population is 15,000.

**Step 3:** Calculate the increase in value.

Increase = Final Value - Initial Value

Increase = 15,000 - 10,000

Increase = 5,000

**Step 4:** Calculate the percent increase.

Percent Increase = (Increase / Initial Value) * 100

Percent Increase = (5,000 / 10,000) * 100

Percent Increase = 0.5 * 100

Percent Increase = 50%

Therefore, the population has increased by 50% over the past five years.

**Example 2:** Sales Growth

Suppose a company made $500,000 in sales last year, and this year it made $700,000 in sales. What is the percentage increase in sales?

**Step 1: Determine the initial value.**

The sales of the company last year were $500,000.

**Step 2: Determine the final value.**

The sales of the company this year were $700,000.

**Step 3: Calculate the increase in value.**

Increase = Final Value - Initial Value

Increase = $700,000 - $500,000

Increase = $200,000

**Step 4: Calculate the percent increase.**

Percent Increase = (Increase / Initial Value) * 100

Percent Increase = ($200,000 / $500,000) * 100

Percent Increase = 0.4 * 100

Percent Increase = 40%

Therefore, the company's sales increased by 40% compared to the previous year.

**Example 3: Test Score Improvement**

Suppose a student scored 75% on a math test and then improved to 90% on the next test. What is the percentage increase in the test score?

**Step 1: Determine the initial value.**

The initial test score was 75%.

**Step 2: Determine the final value.**

The improved test score is 90%.

**Step 3: Calculate the increase in value.**

Increase = Final Value - Initial Value

Increase = 90% - 75%

Increase = 15%

**Step 4: Calculate the percent increase.**

Percent Increase = (Increase / Initial Value) * 100

Percent Increase = (15% / 75%) * 100

Percent Increase = 0.2 * 100

Percent Increase = 20%

Therefore, the student's test score increased by 20%.

Understanding percent increase allows us to assess the magnitude of changes and make meaningful comparisons.

For instance, in financial terms, it helps us analyze investment returns or sales growth. In academic settings, it helps us evaluate improvements in test scores or grades. In population studies, it helps us understand population growth rates.