Percent Increase and Decrease Word Problems

Summary

This video script offers a comprehensive guide on calculating the percent of change. It explains the formula, which is the new value minus the original value, divided by the original value and multiplied by 100. The script uses various examples, such as changes in gas prices and savings account balances, to demonstrate how to determine whether the change is an increase or decrease. It also covers word problems involving population changes and student dropouts to illustrate the application of the formula in real-world scenarios.

Takeaways

• 📐 The formula for calculating percent of change is: (New Value - Original Value) / Original Value * 100%.
• 🔢 When the New Value is greater than the Original Value, the percent change is a positive number, indicating an increase.
• 🔽 Conversely, when the New Value is less than the Original Value, the percent change is negative, indicating a decrease.
• 💯 The percent change is always expressed as a percentage, showing how much the value has increased or decreased relative to the original.
• 📉 A negative percent change signifies a decrease, while a positive percent change signifies an increase in value.
• 💡 The script provides practical examples, such as changes in gas prices, savings account balances, cat populations, and student enrollment, to illustrate the calculation of percent change.
• 📈 The percent change can be used to measure the relative change in various quantities over time, such as prices, populations, or account balances.
• 💼 In the example of John's savings account, adding money to the account results in a positive percent change, calculated by the formula.
• 🏫 The script also covers how to calculate percent change when there's a decrease in quantity, such as students dropping a course, using the same formula but resulting in a negative value.
• 🌐 The concept of percent change is applicable across different contexts and can be used to analyze data and make comparisons in various fields.

Q & A

What is the formula for calculating the percent of change?

The formula for calculating the percent of change is: (New Value - Original Value) / Original Value * 100%.

How do you interpret a positive percent change?

A positive percent change indicates an increase from the original value to the new value.

What does a negative percent change signify?

A negative percent change signifies a decrease from the original value to the new value.

If a number changes from 30 to 42, what is the percent change?

The percent change is 40%. (42 - 30) / 30 * 100% = 0.4 * 100% = 40%.

What is the percent change when a value increases from 40 to 70?

The percent change is 75%. (70 - 40) / 40 * 100% = 0.75 * 100% = 75%.

How do you calculate the percent change when a value goes from 30 to 55?

The percent change is 83.3%. (55 - 30) / 30 * 100% ≈ 0.833 * 100% = 83.3%.

What is the percent change when the price of gas increases from $2.24 to $2.56?

The percent change is approximately 14.29%. (2.56 - 2.24) / 2.24 * 100% ≈ 0.142857 * 100% = 14.29%.

If John had $2500 in his savings and added $400, what is the percent change in his savings?

The percent change is 16%. (2900 - 2500) / 2500 * 100% = 0.16 * 100% = 16%.

What is the percent change in the population of cats on Island X if it grew from 1500 to 1750?

The percent change is 16.7%. (1750 - 1500) / 1500 * 100% ≈ 0.167 * 100% = 16.7%.

How do you calculate the percent change in the number of students in a chemistry course if 140 students dropped out from 500?

The percent change is -28%. (360 - 500) / 500 * 100% = -0.28 * 100% = -28%.

What is the significance of the sign (positive or negative) in the percent change calculation?

The sign in the percent change calculation indicates whether there has been an increase (positive) or a decrease (negative) in the value.