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What is the percent increase from 250 to 900?


  1. Write the percent change formula for an increase:

$\text{Percent Increase} = \frac{\text{Amount of Increase}}{\text{Original Amount}}$


  1. Substitute the known quantities for the amount of the increase and the original amount:

$\text{Percent Increase} = \frac{900 - 250}{250}$


  1. Subtract:

$\text{Percent Increase} = \frac{650}{250}$


  1. Express the ratio as a percent: □

Verified Answer :

  • Identify the original value as \(250\) and the final value as \(900\).
  • Find the amount of increase: \(900 - 250 = 650\).
  • Divide the increase by the original amount: \(\frac{650}{250} = 2.6\).
  • Multiply by \(100\%\) to convert to a percentage: \(2.6 \times 100\% = \boxed{260\%}\).

Explanation

  1. Analyzing the Problem

The goal is to calculate the percent increase from an initial value of \(250\) to a final value of \(900\). The formula for percent increase is:
\[ \text{Percent Increase} = \left( \frac{\text{Final Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\% \]
We identify the original value as \(250\) and the final value as \(900\).

  1. Calculating the Amount of Increase

Next, we determine the actual amount of the increase by subtracting the original value from the final value:
\[ \text{Amount of Increase} = 900 - 250 = 650 \]
This represents the absolute change between the two values.

  1. Calculating the Percent Increase

Now, we find the ratio of this increase to the original value:
\[ \text{Ratio} = \frac{650}{250} \]
Performing this division, we find:
\[ \frac{650}{250} = 2.6 \]
To express this ratio as a percentage, we multiply by \(100\%\):
\[ 2.6 \times 100\% = 260\% \]
Thus, the percent increase from \(250\) to \(900\) is \(\boxed{260\%}\).

Examples

Percent increase is a vital concept for understanding growth in real-world scenarios. For example, if a store increases the price of an item from \(\$250\) to \(\$900\), calculating the percentage helps the consumer understand the magnitude of the change. This method is also widely used in business to track growth in sales, in finance to measure investment returns, and in science to analyze changes in experimental data. Understanding this concept allows for better decision-making by normalizing changes to a standard 100-point scale.

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