What is the percent increase from 60 to 84?
The objective is to find the percent increase from an original value of \(60\) to a new value of \(84\). A percent increase measures the relative growth of a quantity, calculated as the ratio of the increase to the original value, expressed as a percentage. The formula for percent increase is:
\[\text{Percent Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\%\]
First, identify the original value and the new value from the provided data.
Next, determine the absolute increase in value by subtracting the original value from the new value:
\[84 - 60 = 24\]
The value has increased by \(24\) units.
Now, determine the ratio of this increase to the original value:
\[\frac{24}{60}\]
Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is \(12\):
\[\frac{24 \div 12}{60 \div 12} = \frac{2}{5} = 0.4\]
The ratio of increase is \(0.4\).
Finally, convert the decimal ratio to a percentage by multiplying it by \(100\%\):
\[0.4 \times 100\% = 40\%\]
Therefore, the percent increase from \(60\) to \(84\) is \(\boxed{40\%}\).
Percent increase is widely used in everyday life, such as calculating price hikes in items, percentage growth in a company's revenue, or calculating the improvement in test scores. For instance, if a local store increases the price of a \$60 coffee machine to \$84, understanding that this is a 40% increase helps customers evaluate the impact on their budget and make informed purchasing decisions.