So a tip of $12.33 seems reasonable.
What are you asked to find? | the total amount of potassium recommended |
Choose a variable to represent it. | Let |
Write a sentence that gives the information to find it. | 85 mg is 2% of the total amount. |
Translate the sentence into an equation. |
|
Divide both sides by 0.02. | |
Simplify. | |
Check: Is this answer reasonable? | Yes. 2% is a small percent and 85 is a small part of 4,250. |
Write a complete sentence that answers the question. | The amount of potassium that is recommended is 4250 mg. |
What are you asked to find? | the percent of the total calories from fat |
Choose a variable to represent it. | Let |
Write a sentence that gives the information to find it. | What percent of 480 is 240? |
Translate the sentence into an equation. |
|
Divide both sides by 480. | |
Simplify. | |
Convert to percent form. | |
Check. Is this answer reasonable? | Yes. 240 is half of 480, so 50% makes sense. |
Write a complete sentence that answers the question. | Of the total calories in each brownie, 50% is fat. |
People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent .
To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.
HOW TO: Find Percent Increase
Step 1. Find the amount of increase.
Step 2. Find the percent increase as a percent of the original amount.
What are you asked to find? | the percent increase |
Choose a variable to represent it. | Let |
Find the amount of increase. |
|
Find the percent increase. | The increase is what percent of the original amount? |
Translate to an equation. |
|
Divide both sides by 26. | |
Round to the nearest thousandth. | |
Convert to percent form. | |
Write a complete sentence. | The new fees represent a |
TRY IT 10.1
TRY IT 10.2
Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.
HOW TO: Find Percent Decrease
What are you asked to find? | the percent decrease |
Choose a variable to represent it. | Let |
Find the amount of decrease. |
|
Find the percent of decrease. | The decrease is what percent of the original amount? |
Translate to an equation. |
|
Divide both sides by 3.71. | |
Round to the nearest thousandth. | |
Convert to percent form. | |
Write a complete sentence. | The price of gas decreased 1.9%. |
TRY IT 11.1
TRY IT 11.2
Access Additional Online Resources
In the following exercises, translate and solve.
1. What number is | 2. What number is |
3. What number is | 4. What number is |
5. | 6. |
7. | 8. |
9. | 10. |
11. | 12. |
13. | 14. |
15. | 16. |
17. What percent of | 18. What percent of |
19. What percent of | 20. What percent of |
21. | 22. |
23. | 24. |
In the following exercises, solve the applications of percents.
25. Geneva treated her parents to dinner at their favorite restaurant. The bill was | 26. When Hiro and his co-workers had lunch at a restaurant the bill was |
27. Trong has | 28. Cherise deposits |
29. One serving of oatmeal has | 30. One serving of trail mix has |
31. A bacon cheeseburger at a popular fast food restaurant contains | 32. A grilled chicken salad at a popular fast food restaurant contains |
33. The nutrition fact sheet at a fast food restaurant says the fish sandwich has | 34. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has |
35. Emma gets paid | 36. Dimple gets paid |
In the following exercises, find the percent increase or percent decrease.
37. Tamanika got a raise in her hourly pay, from | 38. Ayodele got a raise in her hourly pay, from |
39. According to Statistics Canada, annual international graduate student fees in Canada rose from about | 40. The price of a share of one stock rose from |
41. According to Time magazine | 42. In one month, the median home price in the Northeast rose from |
43. A grocery store reduced the price of a loaf of bread from | 44. The price of a share of one stock fell from |
45. Hernando’s salary was | 46. From |
47. In one month, the median home price in the West fell from | 48. Sales of video games and consoles fell from |
49. At the campus coffee cart, a medium coffee costs | 50. Alison was late paying her credit card bill of |
51. Without solving the problem | 52. Without solving the problem “What is |
53. After returning from vacation, Alex said he should have packed | 54. Because of road construction in one city, commuters were advised to plan their Monday morning commute to take |
1. 54 | 3. 26.88 | 5. 162.5 |
7. 18,000 | 9. 112 | 11. 108 |
13. $35 | 15. $940 | 17. 30% |
19. 36% | 21. 150% | 23. 175% |
25. $11.88 | 27. $259.80 | 29. 24.2 grams |
31. 2,407 grams | 33. 45% | 35. 25% |
37. 13.2% | 39. 15% | 41. 72.7% |
43. 2.5% | 45. 11% | 47. 5.5% |
49. 21.2% | 51. The original number should be greater than 44.80% is less than 100%, so when 80% is converted to a decimal and multiplied to the base in the percent equation, the resulting amount of 44 is less. 44 is only the larger number in cases where the percent is greater than 100%. | 53. Alex should have packed half as many shorts and twice as many shirts. |
This chapter has been adapted from “Solve General Applications of Percent” in Prealgebra (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a CC BY 4.0 Licence . Adapted by Izabela Mazur. See the Copyright page for more information.
Intermediate Algebra I Copyright © 2021 by Pooja Gupta is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.
What is a percent .
A percent is a way of expressing a number as a fraction of 100. The symbol "%" is used to denote a percent . For example, 25% means 25 out of 100.
To convert a percent to a decimal , divide the percent by 100. For example, 25% is equivalent to 0.25 as a decimal .
To convert a percent to a fraction , write the percent as a fraction with a denominator of 100 and simplify if possible. For example, 25% is equivalent to 25/100, which simplifies to 1/4.
To convert a decimal to a percent , multiply the decimal by 100. For example, 0.25 is equivalent to 25% as a percent .
To convert a decimal to a fraction , write the decimal as a fraction and simplify if possible. For example, 0.25 is equivalent to 25/100, which simplifies to 1/4.
To calculate a percentage of a number, multiply the number by the decimal equivalent of the percentage. For example, to find 25% of 80, you would calculate 0.25 * 80 = 20.
To calculate a percent increase, first find the difference between the new and original values. Then, divide the difference by the original value and multiply by 100. For example, if the original value is 50 and the new value is 65, the percent increase is ((65-50)/50) * 100 = 30%.
To calculate a percent decrease, use the same process as for percent increase, but with the difference being the original value minus the new value.
To calculate the sale price of an item after a discount, subtract the discount amount from the original price. For example, if an item is originally $80 and there is a 20% discount, the sale price would be $80 - (0.20 * $80) = $64.
To calculate the selling price of an item after a markup, add the markup amount to the original price. For example, if an item is originally $50 and there is a 25% markup, the selling price would be $50 + (0.25 * $50) = $62.50.
When solving percent word problems , it's important to carefully read the problem and identify the known values and the unknown value. Then, set up an equation and solve for the unknown value using the methods described above.
Good luck with your study of applying percents !
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Summary: solving general applications of percents, key concepts.
Home » Mathematics » Algebra 1 » Applications of Percents
Professor Fraser
Table of contents, algebra 1 applications of percents.
Section 2: Solving Linear Equations: Lecture 7 | 20:38 min
Dr. Fraser will cover Applications of Percents with examples of real life situations. You will learn about percentage of increase which is illustrated with sales tax, as well as percentage of decrease which can be understood as a discount.
Study guides, download lecture slides, related books.
Last reply by: jeffrey breci Post by Daniel Delapena on December 11, 2011 I believe Jeff is correct...and also, example 4 seems like it would be 25% of change, due to the 25% discount from the original price? The answer was in the question? | |
Last reply by: Stacy Amadio Post by Jeff Mitchell on January 23, 2011 Wow, I disagree with example one completely. if it changed from 50 to 70 it did not increase 140%. if it increased 100% it would have gone from 50 to 100. Since it did not go past 100 it is clearly less than 100% increase. | |
Post by SASHKA YAKIMOVA on January 1, 2010 In Example 4, shouldn't the percent of change be calculated by dividing the NEW VALUE by the ORIGINAL VALUE? |
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Markup, Discount, Tax, Tip, and Interest Practice Learn with flashcards, games, and more — for free.
Solve the equation using good algebra techniques. Step 5. Check the answer in the problem and make sure it makes sense. Step 6. Write a complete sentence that answers the question. Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications.
When working with division and multiplication together, we work left to right, first computing the fraction as a decimal, and then multiplying by 100: percent change ≈ 1.288461 × 100 = 128.8461 (2.4.10) The instructions were to round to the nearest tenth of a percent, so we will state the answer as 128.5%.
Solve the equation using good algebra techniques. Step 5. Check the answer in the problem and make sure it makes sense. Step 6. Write a complete sentence that answers the question. Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications.
Terms in this set (25) Study with Quizlet and memorize flashcards containing terms like Percent, 4/5 is what percent?, 1.2 is what percent? and more.
We'll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application. When Aolani and her friends ate dinner at a restaurant, the bill came to $80. $80. They wanted to leave a 20% 20% tip. What amount would the tip be? To solve this, we want to find what amount is 20% 20% of $80. $80.
Step 5. Solve the equation using good algebra techniques. Step 6. Check the answer in the problem and make sure it makes sense. Step 7. Answer the question with a complete sentence. Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications.
Percents can be used in many types of problems and situations. The following applications are the most common basic types. To determine percent of a number, change the percent to a fraction or decimal (whichever is easier for you) and multiply. Remember: The word of means multiply. Find the percents of the following numbers.
The base usually follows "percent of" or "% of". In application problems this may not be a number, but a phrase which tells you where to go find the number. 3. Any remaining number will be the amount. It will often be with the word "is". EXAMPLE: A company's budget for advertising is $15,000. This is 5% of their total budget. What is their ...
This page titled 4.2: Percents Problems and Applications of Percent is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Morgan Chase via source content that was edited to the style and standards of the LibreTexts platform.
Examples, solutions, and videos that will help GMAT students review percents and their applications. The following diagram gives the formula to find the percent of change. Scroll down the page for more examples and solutions. While exercising, Martha's heart rate is about 180 beats per minute. After exercising, Martha takes a nap, during ...
Skills Practiced. This quiz and worksheet test the following skills: Problem solving - use acquired knowledge to solve practice problems involving percents. Distinguishing differences - compare ...
Answers. 51. The original number should be greater than 44.80% is less than 100%, so when 80% is converted to a decimal and multiplied to the base in the percent equation, the resulting amount of 44 is less. 44 is only the larger number in cases where the percent is greater than 100%. 53.
What is a Percent? A percent is a way of expressing a number as a fraction of 100. The symbol "%" is used to denote a percent. For example, 25% means 25 out of 100. Converting Between Percents, Decimals, and Fractions. To convert a percent to a decimal, divide the percent by 100. For example, 25% is equivalent to 0.25 as a decimal.
Money earns interest. Repay amount plus interest. Fixed percent of the principle. Start studying Lesson 5.3 applications of percent. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
Write a complete sentence that answers the question. Check the answer in the problem and make sure it makes sense. Find percent increase. Find the amount of increase: increase = new amount−original amount increase = new amount − original amount. Find the percent increase as a percent of the original amount. Find percent decrease.
15 = Q ⋅ 50. Percent. The missing factor is the percent. Percent, we know, means per 100, or part of 100. In 15 = Q ⋅ 50. Q indicates what part of 50 is being taken or considered. Specifically, 15 = Q ⋅ 50 means that if 50 was to be divided into 100 equal parts, then Q indicates 15 are being considered. In problem 3, one of the factors ...
Solve the equation using good algebra techniques. Write a complete sentence that answers the question. Check the answer in the problem and make sure it makes sense. Find percent increase. Find the amount of increase: increase = new amount−original amount increase = new amount − original amount. Find the percent increase as a percent of the ...
To find the rate, we use the simple interest formula, substitute in the given values for the principal and time, and then solve for the rate. Example 3.3.28 3.3. 28. Loren loaned his brother $3,000 to help him buy a car. In 4 years his brother paid him back the $3,000 plus $660 in interest.
Sales tax is a familiar example of a percent of increase. Discount is an example of a percent of decrease. When solving these kinds of problems, always write the percent as either a fraction with a denominator of 100 or a decimal equivalent to the percent. Time-saving lesson video on Applications of Percents with clear explanations and tons of ...
The correct way to think about this is 880 = 0.88 ⋅ B 880 = 0.88 ⋅ B. Dividing 880 880 by 0.88 0.88 gives us the answer 1, 000 1, 000, which is clearly correct because we can find that 12% 12 % of 1, 000 1, 000 is 120 120, making the new amount 880 880. The original price was $ 1, 000 1, 000. To summarize, we cannot add 12% 12 % to the new ...
Definition: Basic Percent Equation. The equation that describes all relationships involving percents is. percent × whole = part (2.3.3) (2.3.3) percent × whole = part. We will call this the Basic Percent Equation. It will be used to solve all basic percent problems.