10 Questions
If a car's value drops by 40%, what percentage increase would be needed to bring it back to its original value?
30%
A company's profits decreased by 15%. What percentage increase would be required to recover the initial profit amount?
17%
If a shirt was originally priced at $50 and experiences a 20% price increase, what is the new price of the shirt?
$65
In a test, a student scored 80 out of 100. If this score is a 25% increase from the previous test, what was the student's score in the previous test?
64
If a company's expenses increased by 10%, but its revenue increased by 15%, what is the overall percentage change in profit for the company?
+15%
If a product's original price was $80 and it undergoes a 20% price increase, what is the new price?
$96
To determine the percent decrease, you should take the reciprocal of which value and multiply by 100?
Fraction of decrease
If an investment had a 15% return, what was the original amount if the final value was $11,500?
$10,000
Which scenario does NOT commonly involve the concept of percent increase or decrease?
Measuring distance traveled
If a product's price decreased by 40%, what is the percentage increase needed to bring it back to its original price?
66.67%
Study Notes
Solving Problems Involving Percent of Increase or Decrease
Imagine you've just bought a new car, and a year later its value has dropped by 25%. Or perhaps you're a small business owner tracking a rise in customer satisfaction, which has increased by 18%. These scenarios involve percentages of increase or decrease, mathematical concepts that are essential in everyday problem-solving. In this article, we'll dive into calculating new amounts after an increase or decrease, finding percent decrease, finding percent increase, and real-world applications of these concepts.
Calculating the New Amount After Increase or Decrease
Let's say you're analyzing sales figures and discover the company experienced a 30% increase. To find the new amount, you multiply the original value by 1 plus the percent of increase. For example, if the original sales figure was $100,000, the new sales figure would be:
[ 100,000 \times (1 + 0.30) = 100,000 \times 1.30 = $130,000 ]
Conversely, if there's a decrease, you multiply the original value by 1 minus the percent of decrease:
[ 100,000 \times (1 - 0.25) = 100,000 \times 0.75 = $75,000 ]
Finding the Percent Decrease
To find the percent decrease, you take the reciprocal of the fraction that represents the decrease, then multiply by 100:
[ \text{Percent Decrease} = \frac{1 - \text{fraction of decrease}}{1 - 0} \times 100 = \frac{1 - 0.25}{1} \times 100 = 75 % ]
Finding the Percent Increase
To find the percent increase, you take the reciprocal of the fraction that represents the increase, then subtract 1 and multiply by 100:
[ \text{Percent Increase} = \frac{\text{fraction of increase}}{1 - \text{fraction of increase}} \times 100 - 100 = \frac{0.3}{1 - 0.3} \times 100 - 100 = 30 % ]
Real-World Applications
From a car's depreciation to a company's stock price, percent increase or decrease is a common concept in various scenarios:
- Economic growth
- Investment returns
- Annual sales data
- Price changes in goods and services
- Population fluctuations
A Final Note
While the examples used here are numerical, these concepts can also be applied to fractions, decimals, or ratios when working with percentages of increase or decrease. By understanding the basics and applications of these mathematical concepts, you'll be equipped to tackle real-world problems with ease!
Learn how to calculate new amounts after an increase or decrease, find percent decrease, find percent increase, and explore real-world applications of percent changes. From analyzing sales figures to tracking stock prices, these mathematical concepts are crucial in problem-solving across various scenarios.
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