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Chapter 8: Problem 64

Describe how to find percent decrease and give an example.

Short Answer

Expert verified
Percent decrease is calculated by subtracting the new number from the original number, dividing this value by the original number and then multiplying by 100. For example, if the original number was 120 and it decreased to 90, the percent decrease would be 25 percent.

Step by step solution

01

Identify the Original and New Values

First, identify the initial (original) value and the final (new) value. You need two numbers to find the percent decrease. The original number is the larger of the two and the new number is the smaller one. Let's say the original value is 120 and the new value is 90.
02

Calculate the Difference

Subtract the smaller number (new value) from the larger number (original value). In this example, the difference is calculated as: 120 (original value) - 90 (new value) = 30.
03

Divide and Multiply by 100

Next, divide this difference by the original number, and then multiply the result by 100 to turn it into a percentage. Here, the calculation would be: (30 / 120) * 100 = 25.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calculating Percent Decrease
Understanding how to calculate percent decrease is a fundamental mathematical skill that can be applied to a wide range of scenarios, from finance to daily shopping. It tells us by what percentage an amount has reduced over time. To calculate a percent decrease, follow these simple steps:
  • Identify the initial (original) value: This is the larger number that represents the original status before the decrease.
  • Find the final (new) value: This is the smaller number post-decrease.
  • Compute the difference: Subtract the new value from the original value.
  • Calculate the percentage: Divide the difference by the original value and then multiply by 100 to find the percent decrease.
For example, if a product originally costs \(120 and is now selling for \)90, the percent decrease is calculated as follows: \begin{align*}\text{Difference} &= 120 - 90 = 30,\text{Percent Decrease} &= \frac{30}{120} \times 100 = 25\text{%}.ewlineewlineThis calculation indicates a 25% decrease in the product's price.
Identifying Original and New Values
The most crucial step in computing percent changes, whether it's an increase or decrease, involves correctly identifying the original and new values. The original value signifies the starting point or initial condition before any change has occurred, while the new value signifies the result or endpoint after the change has taken effect.Here is how you should approach it:
  • Initial condition: This could be an original price, quantity, score, etc.
  • Final condition: This represents the adjusted price, quantity, score, etc., after a certain event has occurred.
It's important to ensure that these values are based on the same units or quantities for the calculation to make sense. Once the correct values are identified, calculating the percent change becomes a matter of following the right formula.
Percent Change Mathematical Concepts
The concept of percent change is integral in mathematics and is used to express the degree of change over time. This can apply to increases or decreases. The formula for percent change is a tool that allows one to compare the relative change between two numbers.Here's a closer look at the mathematical concept:
  • Numerator - The Difference: The numerator in the percent change formula is the difference between the original and new values. Reflecting how much has been lost or gained.
  • Denominator - The Original Value: The denominator is the original value, which normalizes the change and relates it to the initial condition, providing a relative measure of change.
  • Multiplying by 100: This step is essential to convert the decimal obtained from the division into a percentage, which is easier for comparative and intuitive understanding.
By understanding and applying the percent change concept, one can quickly analyze fluctuations in data across various fields such as economics, science, and everyday life activities. The beauty of percent change lies in its universality and ability to convey changes effectively.

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Most popular questions from this chapter

The price of a color printer is reduced by \(30 \%\) of its original price. When it still does not sell, its price is reduced by \(20 \%\) of the reduced price. The salesperson informs you that there has been a total reduction of \(50 \%\). Is the salesperson using percentages properly? If not, what is the actual percent reduction from the original price?

What is the future value of a loan and how is it determined?

In Exercises 1-10, a. Find the value of each annuity. Round to the nearest dollar b. Find the interest. $$ \begin{array}{|l|l|l|} \hline \begin{array}{l} \$ 1200 \text { at the end of } \\ \text { every three months } \end{array} & \begin{array}{l} 3.25 \% \text { compounded } \\ \text { quarterly } \end{array} & \text { 6 years } \\ \hline \end{array} $$

You decide to work part-time at a local supermarket. The job pays \(\$ 8.50\) per hour and you work 20 hours per week. Your employer withholds \(10 \%\) of your gross pay for federal taxes, \(5.65 \%\) for FICA taxes, and \(3 \%\) for state taxes. a. What is your weekly gross pay? b. How much is withheld per week for federal taxes? c. How much is withheld per week for FICA taxes? d. How much is withheld per week for state taxes? e. What is your weekly net pay? f. What percentage of your gross pay is withheld for taxes? Round to the nearest tenth of a percent.

If a three-year car loan has the same interest rate as a six-year car loan, how do the monthly payments and the total interest compare for the two loans?
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