To find the percentage change from 100 to 150, we need to first calculate the difference between the two numbers.

Now, let's work through the steps to find the percent increase from 100 to 150:

The initial value is 100, because that's what we're starting with. The final value is 150, because that's where we end up.

Subtract the initial value from the final value. In this case, 150 (final value) - 100 (initial value) = 50. This gives us the amount of increase.

To find the percent increase, we need to divide the amount of increase by the original number and then multiply by 100 to convert it into a percentage. In other words, the formula for the percent increase is:

% Increase = (Increase / Original number) * 100

Here, our increase is 50 (from step 2) and the original number is 100.

So, let's plug these values into our formula:

% Increase = (50 / 100) * 100

Simplifying this gives us 50%.

So, there's a 50% increase from 100 to 150. This means that 150 is 50% more than 100. In other words, if we start with 100 and increase it by half of its value (which is 50), we end up with 150.

This process applies to any situation where you need to find the percent increase between two numbers.

The best way to truly understand a concept is by working through more problems, which allows you to see the procedure in action multiple times.

**Example 1**:

The population of a small town was 4,000 people last year. This year, the population is 4,600 people. What is the percent increase in population?

Solution:

Initial value = 4,000

Final value = 4,600

Difference (increase) = 4,600 - 4,000 = 600

% Increase = (600 / 4,000) * 100 = 15%

So, the population has increased by 15%.

**Example 2:**

A company's revenue last quarter was $1,000,000. This quarter, their revenue is $1,200,000. What is the percent increase?

**Solution:**

Initial value = $1,000,000

Final value = $1,200,000

Difference (increase) = $1,200,000 - $1,000,000 = $200,000

% Increase = ($200,000 / $1,000,000) * 100 = 20%

So, the company's revenue increased by 20% this quarter.

**Example 3:**

A car's speed was initially 60 miles per hour. The driver then accelerates to 75 miles per hour. What is the percent increase in the speed of the car?

Solution:

Initial value = 60 mph

Final value = 75 mph

Difference (increase) = 75 mph - 60 mph = 15 mph

% Increase = (15 / 60) * 100 = 25%

So, the speed of the car has increased by 25%.

**Example 4:**

A stock was worth $45 last month. Now, it's worth $54. What's the percent increase in the stock's value?

**Solution:**

Initial value = $45

Final value = $54

Difference (increase) = $54 - $45 = $9

% Increase = ($9 / $45) * 100 = 20%

So, the stock's value increased by 20%.