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Solving Percent Change Problems

Math: basic tutorials : solving percent change problems.

• Introduction to Fractions
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• Multiplying Fractions
• Dividing Fractions
• Adding Fractions
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• Decimals and Rounding
• Introduction to Percentage
• Simple Operations with Percent
• Solving Percent Application Problems
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A percent change problem asks how much a quantity has increased or decreased compared to its original value, e.g. the population of a city increases from last year to this year. This section shows you how to calculate percent increase or decrease.

Solving Percent Change Application Problems

Click on the titles below to view each example.

The price of admission into a museum increased from 26 dollars to 36 dollars per person. Find the percent increase. Round your final answer to the nearest tenth of a percent.

Line 1: What are you being asked to find? We are being asked to find the percent increase.

Line 2: Choose a variable to represent it. Let p be the percent increase.

Line 3: Find the amount of the increase by subtracting the original amount from the new amount, so the increase is 36 minus 26 equals 10.

Line 4: Find the percent increase. 10 is what percent of 26?

Line 5: Translate into algebra so the equation is 10 equals p times 26.

Line 6: Divide both sides of the equation by 26 to solve for p, so the equation is 10 divided by 26 equals 26p divided by 26.

Line 7: Simplify and round to the nearest thousandth so 0 decimal 3 8 5 equals p.

Line 8: Convert to a percent by multiplying by 100 percent so 38 decimal 5 percent equals p.

Line 9: Write a statement that answers the question. Therefore, the new admission price represents a 38 decimal 5 percent increase over the old admission price

The population of a city was 672 000 in 2010. The population of the city in 2020 is 630 000. Find the percent decrease. Round your final answer to the nearest tenth of a percent.

Line 1: What are you being asked to find? We are being asked to find the percent decrease.

Line 2: Choose a variable to represent it. Let p be the percent decrease.

Line 3: Find the amount of the decrease by subtracting the new population from the original population, so the decrease is 672 000 minus 630 000 equals 42 000.

Line 4: Find the percent decrease. 42 000 is what percent of 672 000?

Line 5: Translate into algebra so the equation is 42 000 equals p times 672 000.

Line 6: Divide both sides of the equation by 672 000 to solve for p, so the equation is 42 000 divided by 672 000 equals 672 000p divided by 672 000.

Line 7: Simplify and round to the nearest thousandth so 0 decimal 0 6 3 equals p.

Line 8: Convert to a percent by multiplying by 100 percent so 6 decimal 3 percent equals p.

Line 9: Write a statement that answers the question. Therefore, the population decreased by 6.3 percent.

Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet

• Summary: Solving Percent Change Problems - PDF - Opens in a new window This document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
• Worksheet: Percent Change Problems - PDF - Opens in a new window This document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.

Attribution

Examples Source: " Prealgebra - opens in a new window " by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

• << Previous: Solving Percent Application Problems
• Next: Basic Algebra >>

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4.2: Percents Problems and Applications of Percent

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• Page ID 142718

• Morgan Chase
• Clackamas Community College via OpenOregon

You may use a calculator throughout this module.

Recall: The amount is the answer we get after finding the percent of the original number. The base is the original number, the number we find the percent of. We can call the percent the rate.

When we looked at percents in a previous module, we focused on finding the amount. In this module, we will learn how to find the percentage rate and the base.

\(\text{Amount}=\text{Rate}\cdot\text{Base}\)

\(A=R\cdot{B}\)

We can translate from words into algebra.

• “is” means equals
• “of” means multiply
• “what” means a variable

Solving Percent Problems: Finding the Rate

Suppose you earned \(56\) points on a \(60\)-point quiz. To figure out your grade as a percent, you need to answer the question “\(56\) is what percent of \(60\)?” We can translate this sentence into the equation \(56=R\cdot60\).

Exercises \(\PageIndex{1}\)

1. \(56\) is what percent of \(60\)?

2. What percent of \(120\) is \(45\)?

1. \(93\%\) or \(93.3\%\)

2. \(37.5\%\)

Be aware that this method gives us the answer in decimal form and we must move the decimal point to convert the answer to a percent.

Also, if the instructions don’t explicitly tell you how to round your answer, use your best judgment: to the nearest whole percent or nearest tenth of a percent, to two or three significant figures, etc.

Solving Percent Problems: Finding the Base

Suppose you earn \(2\%\) cash rewards for the amount you charge on your credit card. If you want to earn $ \(50\) in cash rewards, how much do you need to charge on your card? To figure this out, you need to answer the question “\(50\) is \(2\%\) of what number?” We can translate this into the equation \(50=0.02\cdot{B}\).

3. $ \(50\) is \(2\%\) of what number?

4. \(5\%\) of what number is \(36\)?

3. $ \(2,500\)

5. An \(18\%\) tip will be added to a dinner that cost $ \(107.50\). What is the amount of the tip?

6. The University of Oregon women’s basketball team made \(13\) of the \(29\) three-points shots they attempted during a game against UNC. What percent of their three-point shots did the team make?

7. \(45\%\) of the people surveyed answered “yes” to a poll question. If \(180\) people answered “yes”, how many people were surveyed altogether?

5. $ \(19.35\)

6. \(44.8\%\) or \(45\%\)

7. \(400\) people were surveyed

Solving Percent Problems: Percent Increase

When a quantity changes, it is often useful to know by what percent it changed. If the price of a candy bar is increased by \(50\) cents, you might be annoyed because it’s it’s a relatively large percentage of the original price. If the price of a car is increased by \(50\) cents, though, you wouldn’t care because it’s such a small percentage of the original price.

To find the percent of increase:

• Subtract the two numbers to find the amount of increase.
• Using this result as the amount and the original number as the base, find the unknown percent.

Notice that we always use the original number for the base, the number that occurred earlier in time. In the case of a percent increase, this is the smaller of the two numbers.

8. The price of a candy bar increased from $ \(0.89\) to $ \(1.39\). By what percent did the price increase?

9. The population of Portland in 2010 was \(583,793\). The estimated population in 2019 was \(654,741\). Find the percent of increase in the population. [1]

8. \(56.2\%\) increase

9. \(12.2\%\) increase

Solving Percent Problems: Percent Decrease

Finding the percent decrease in a number is very similar.

To find the percent of decrease:

• Subtract the two numbers to find the amount of decrease.

Again, we always use the original number for the base, the number that occurred earlier in time. For a percent decrease, this is the larger of the two numbers.

10. During a sale, the price of a candy bar was reduced from $ \(1.39\) to $ \(0.89\). By what percent did the price decrease?

11. The number of students enrolled at Clackamas Community College decreased from \(7,439\) in Summer 2019 to \(4,781\) in Summer 2020. Find the percent of decrease in enrollment.

10. \(36.0\%\) decrease

11. \(35.7\%\) decrease

Relative Error

In an earlier module, we said that a measurement will always include some error, no matter how carefully we measure. It can be helpful to consider the size of the error relative to the size of what is being measured. As we saw in the examples above, a difference of \(50\) cents is important when we’re pricing candy bars but insignificant when we’re pricing cars. In the same way, an error of an eighth of an inch could be a deal-breaker when you’re trying to fit a screen into a window frame, but an eighth of an inch is insignificant when you’re measuring the length of your garage.

The expected outcome is what the number would be in a perfect world. If a window screen is supposed to be exactly \(25\) inches wide, we call this the expected outcome, and we treat it as though it has infinitely many significant digits. In theory, the expected outcome is \(25.000000...\)

To find the absolute error , we subtract the measurement and the expected outcome. Because we always treat the expected outcome as though it has unlimited significant figures, the absolute error should have the same precision (place value) as the measurement , not the expected outcome .

To find the relative error , we divide the absolute error by the expected outcome. We usually express the relative error as a percent. In fact, the procedure for finding the relative error is identical to the procedures for finding a percent increase or percent decrease!

To find the relative error:

• Subtract the two numbers to find the absolute error.
• Using the absolute error as the amount and the expected outcome as the base, find the unknown percent.

Exercisew \(\PageIndex{1}\)

12. A window screen is measured to be \(25\dfrac{3}{16}\) inches wide instead of the advertised \(25\) inches. Determine the relative error, rounded to the nearest tenth of a percent.

13. The contents of a box of cereal are supposed to weigh \(10.8\) ounces, but they are measured at \(10.67\) ounces. Determine the relative error, rounded to the nearest tenth of a percent.

12. \(0.1875\div25\approx0.8\%\)

13. \(0.13\div10.8\approx1.2\%\)

The tolerance is the maximum amount that a measurement is allowed to differ from the expected outcome. For example, the U.S. Mint needs its coins to have a consistent size and weight so that they will work in vending machines. A dime (10 cents) weighs \(2.268\) grams, with a tolerance of \(\pm0.091\) grams. [2] This tells us that the minimum acceptable weight is \(2.268-0.091=2.177\) grams, and the maximum acceptable weight is \(2.268+0.091=2.359\) grams. A dime with a weight outside of the range \(2.177\leq\text{weight}\leq2.359\) would be unacceptable.

A U.S. nickel (5 cents) weighs \(5.000\) grams with a tolerance of \(\pm0.194\) grams.

14. Determine the lowest acceptable weight and highest acceptable weight of a nickel.

15. Determine the relative error of a nickel that weighs \(5.21\) grams.

A U.S. quarter (25 cents) weighs \(5.670\) grams with a tolerance of \(\pm0.227\) grams.

16. Determine the lowest acceptable weight and highest acceptable weight of a quarter.

17. Determine the relative error of a quarter that weighs \(5.43\) grams.

14. \(4.806\) g; \(5.194\) g

15. \(0.21\div5.000=4.2\%\)

16. \(5.443\) g; \(5.897\) g

17. \(0.24\div5.670\approx4.2\%\)

• www.census.gov/quickfacts/fact/table/portlandcityoregon,OR,US/PST045219 ↵
• https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications and https://www.thesprucecrafts.com/how-much-do-coins-weigh-4171330 ↵

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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

Related Topics

• How to Find Percent of Increase and Decrease
• How to Find Discount, Tax, and Tip
• How to Do Percentage Calculations
• How to Solve Simple Interest Problems

Step by step guide to solve percent problems

• In each percent problem, we are looking for the base, or part or the percent.
• Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

• \(51\) is \(340\%\) of what?
• \(93\%\) of what number is \(97\)?
• \(27\%\) of \(142\) is what number?
• What percent of \(125\) is \(29.3\)?
• \(60\) is what percent of \(126\)?
• \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

• \(\color{blue}{15}\)
• \(\color{blue}{104.3}\)
• \(\color{blue}{38.34}\)
• \(\color{blue}{23.44\%}\)
• \(\color{blue}{47.6\%}\)
• \(\color{blue}{100}\)

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Percent Change

Hello, and welcome to this video about percent change ! Today we’ll learn how to solve problems involving percent increases and decreases and then we’ll see how this skill can help you in the real world.

Before we get started, let’s review a few things. First, change is the difference between two quantities over time. A percent is a part-to-whole ratio that’s expressed as a fraction of 100. For example, the percentage 80% means 80 out of \(100:\frac{80}{100}\). In this case, 80 is the part and 100 is the whole.

How to calculate percentage change?

Percent change is the difference between a new quantity and an old quantity, expressed as a percent. Percent change is calculated by finding the difference between the new quantity and the old quantity, and dividing the difference by the old quantity, then you multiply it by 100.

Let’s take a look at an example together.

The price of a container of laundry detergent went from $8 to $10. What is the percent change?

First, find the difference between the new quantity and the old quantity by subtracting. Since \(10-8=2\), the difference is 2.

Next, divide the difference, 2, by the old quantity, which is \(8: 2\div 8=0.25\).

Last, convert the decimal into a percentage by multiplying it by 100. \(0.25\times 100=25\), so the percent change is 25%. In other words, the cost of the laundry detergent changed by 25%.

Percent change can be calculated by using this formula:

Let’s use this formula to solve a percent change problem.

A company used to sell 12 oz smoothies but recently upgraded to 16 oz smoothies. What is the percent change between the smaller and larger smoothie sizes?

First, we identify the old value and the new value in the word problem. The old value, which is the original smoothie size given, is 12 ounces. And the new value is 16 ounces.

From here, substitute these numbers into our formula and solve.

  \(\frac{4}{12}\) simplifies to \(\frac{1}{3}\) by dividing both the numerator and denominator by 4.

If you plug \(\frac{1}{3}\) into a calculator, you’ll get an estimate of 0.33. It’s really 0.3, but we can round it to two digits. So we’re going to round to 0.33 and multiply by 100, which will give us 33 percent.

So our percent change for this problem is 33%.

Now it’s your turn. Consider the following percent change problem:

A ticket to a basketball game went from $50 to $56. What is the percent change?

Pause the video here, substitute the values into the formula, and solve. When you’re done, resume the video and we’ll go over it together.

Now that you’ve tried this one on your own, let’s take a look at it together.

First, we want to identify the old value and the new value in the word problem. The old value, which is the original ticket price, is $50. And the new value is $56.

So from here, we’re going to substitute these numbers into our formula and solve. So remember, our percent change formula is:

Remember, our new value is the larger price, so 56, and our old value is the original price, which is 50.

Plug \(\frac{6}{50}\) into a calculator to get:

So the percent change for this problem is 12%.

A percent change can indicate an increase or a decrease. A percent increase means that the new value is greater than the old value. All of the examples we’ve looked at so far have involved percent increases.

A percent decrease means that the new value is less than the original value. Let’s take a look at an example together involving percent decrease.

Mrs. Slater started the school day with 150 pencils in her classroom. At the end of the day, there were only 120 pencils in her classroom. What is the percent change in the number of pencils from the start of the day to the end of the day?

First, we want to identify the old value and the new value in the word problem. The old value, which is the number of pencils at the beginning of the day, is 150. And the new value, which is the amount of pencils at the end of the day, is 120.

Now, we can substitute these values into our formula and solve:

Remember, our old value is the larger number, and the new value is the smaller number, in this one. So our new value is 120 and our old value is 150.

This simplifies to:

Which, as a decimal is:

This shows a percent change of -20%.

Let’s take a look at what’s different about this percent change problem. Notice that the new value is less than the old value, so the numerator is a negative number. This negative number results in a negative percentage, indicating that there is a percent decrease from the original value.

In the other percent change problems we’ve looked at today, the results were positive percentages, indicating that there was a percent increase from the original value.

A coffee shop had 550 customers on Wednesday and 300 customers on Thursday. What is the percent change in the number of customers from Wednesday to Thursday? Is the change a percent increase or decrease? Round to the nearest tenth.

First, identify the old value and the new value in the word problem. The old value, which is the number of customers on Wednesday, is 550. The new value, which is the number of customers on Thursday, is 300.

From here, substitute these numbers into the formula and solve.

  Remember, our new value in this instance was 300, and our old value was 550.

If we plug this number into a calculator, we’ll get -0.45, so we’re going to round this to -0.455 and then multiply by 100.

This gives us a percent change of -45.5%. Since the percent change is negative, it indicates a percent decrease. Therefore, there was a 45.5% decrease in customers at the coffee shop from Wednesday to Thursday.

Great work!

When solving word problems involving percent change, it’s really important to consider the wording of the question being asked. Let’s take a look at why this is necessary.

Consider the following percent change problem.

A video game usually costs $60, but Max used a coupon to get the game for $51. What is the percent decrease from the original cost to the coupon cost?

First, we’re going to identify the old value and the new value in the word problem. The old value, which is the original cost of the video game, is $60. And the new value, which is the discounted cost of the game, is $51.

From here, substitute these numbers into the formula and solve. So let’s write out our formula again. Remember, writing out our formula helps us memorize it so it’s always helpful to do.

Our new value is 51, because that’s the discounted price of the game, and the old value is 60.

Which can be simplified to:

Which, when we plug this into a calculator, we get:

So our percent change is -15%. But let’s take another look at the way this question is phrased.

A video game usually costs $60, but Max used a coupon to get the game for $51. What is the percent decrease?

This question asks us for what the percent decrease is. Notice that this problem is not asking for the percent change. Instead, it’s asking for the percent decrease. Since the word “decrease” already indicates that the percent change is negative, there is no need to include the negative sign in your final answer. So the percent decrease in the cost of the video game is 15%.

Percent change is something you’ll encounter often in the real world. When a quantity changes over a period of time, it can be expressed as percent change. Calculating percent change is a regular occurrence in fields such as finance, physics, and sales.

I have one more problem for you to try. This one is a little more difficult, but I know you can solve it! Consider the following percent change problem.

On Monday, Starz Movie Theater sold 436 matinee tickets, and on Tuesday, they sold 321 tickets. Because of the matinee special on Wednesdays, Starz sold 590 tickets on Wednesday. What is the percent change from Monday to Tuesday and from Tuesday to Wednesday? Round your answers to the nearest whole number.

Pause the video here, substitute the values into the formula, and solve to answer both questions. When you’re done, resume the video and we’ll go over it together.

Let’s start by finding the percent change from Monday to Tuesday. Identify the old value and the new value in the word problem. The old value, which is the number of tickets sold on Monday, is 436. And the new value, which is the number of tickets sold on Tuesday, is 321.

So, from Monday to Tuesday:

So this is equal to the new number, which is 321, minus our old number, which is 436, because that’s the number of tickets sold on Monday.

Which, we can then plug this into our calculator and we’ll get a decimal value that can be rounded to 0.26.

So this gives us a percent change of -26%. Since the percent change is a negative value, it is a percent decrease. So this shows that from Monday to Tuesday, the movie theater had a percent decrease of 26%.

Now let’s find the percent change from Tuesday to Wednesday. Identify the old value and the new value in the word problem. The old value, which is the number of tickets sold on Tuesday, is 321. And the new value, is the number of tickets sold on Wednesday, so 590.

So if we plug this into our formula, we’ll get:

When we plug \(\frac{269}{321}\) into our calculator, we can round to get a decimal value of about 0.84.

Therefore, the percent change in ticket sales from Tuesday to Wednesday is 84%. Since the percent change is a positive value, it is a percent increase.

I hope this video about percent change was helpful. Thanks for watching, and happy studying!

Percent Change Practice Questions

  What is the percent change from 180 to 189?

8% increase

5% increase

9% increase

5.5% increase

The percent change formula is \(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\). In this case, the new value is 189, and the old value is 180. Substitute these values into the formula.

\(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\) \(\text{% change}=\frac{189-180}{180}\times 100\) \(\text{% change}=5\%\)

The percent change is positive because the new value is larger than the old value. The scenario represents a 5% increase.

  What is the percent change from 12.5 to 3.6?

71.9% decrease

78.0% decrease

71.2% decrease

78.4% decrease

The percent change formula is \(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\). In this scenario, 12.5 is the old value, and 3.6 is the new value. Substitute these values into the formula.

\(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\) \(\text{% change}=\frac{3.6-12.5}{12.5}\times 100\) \(\text{% change}=-71.2\%\)

  Which set of values shows a 62.5% increase?

The percent change formula is \(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\). Substitute the old value, 8, and the new value, 13, into the percent change formula.

\(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\) \(\text{% change}=\frac{13-8}{8}\times 100\) \(\text{% change}=62.5\%\)

The result is 62.5%. So, when 8 increases to 13 a 62.5% increase occurs.

  A fundraiser earns $75 on Saturday and $525 on Sunday. What is the percent change in money earned from Saturday to Sunday?

450% increase

60% increase

500% increase

600% increase

The percent change formula is \(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\). $75 represents the old value, and $525 represents the new value. When the values are substituted into the formula, it becomes:

\(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\) \(\text{% change}=\frac{525-75}{75}\times 100\) \(\text{% change}=600\%\)

The percent change is positive because the amount of money increases from Saturday to Sunday. The scenario represents a 600% increase.

  A pair of shoes are on sale. The original price was $120. The new sale price is $90. What is the percent change for the price of the shoes?

25% increase

35% decrease

25% decrease

15% decrease

The percent change formula is \(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\). The old price of the shoes was $120, and the new price of the shoes is $90. Substitute these values into the formula.

\(\text{% change}=\frac{\text{new value-old value}}{\text{old value}}\times 100\) \(\text{% change}=\frac{90-120}{120}\times 100\) \(\text{% change}=-25\%\)

The percent change is negative, so the scenario represents a 25% percent decrease.

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Solving problems with percentages

• Price difference I
• Price difference II
• How many students?

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{b}=\frac{x}{100}$$

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=\frac{x}{100}\cdot b$$

x/100 is called the rate.

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?

$$a=r\cdot b$$

$$47\%=0.47a$$

$$=0.47\cdot 34$$

$$a=15.98\approx 16$$

16 of the students wear either glasses or contacts.

We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.

The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?

We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

$$240-150=90$$

Then we find out how many percent this change corresponds to when compared to the original number of students

$$90=r\cdot 150$$

$$\frac{90}{150}=r$$

$$0.6=r= 60\%$$

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.

$$1.6-1=0.6$$

$$0.6=60\%$$

As you can see both methods gave us the same answer which is that the student body has increased by 60%

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A skirt cost $35 regulary in a shop. At a sale the price of the skirtreduces with 30%. How much will the skirt cost after the discount?

Solve "54 is 25% of what number?"

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Course: 7th grade   >   Unit 2

Solving percent problems.

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• Percent word problem: magic club
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• Percent word problems: tax and discount
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Video transcript

Objective 1

Applications involving percents, learning objectives.

• Calculate discounts and markups using percent
• Calculate interest earned or owed
• Read and interpret data from pie charts as percents

Percent Change

Percents have a wide variety of applications to everyday life, showing up regularly in taxes, discounts, markups, and interest rates. We will look at several examples of how to use percent to calculate markups, discounts, and interest earned or owed.

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price .

How much is 15% of $220?

Identify the percent, the base, and the amount.

Percent: 15% Base: 220 Amount: n

Write the percent equation.

[latex]\begin{array}{c}\text{Percent}\cdot\text{Base}=\text{Amount}\\15\%\cdot220=n\end{array}[/latex]

Convert 15% to 0.15, then multiply by 220. 15% of $220 is $33.

[latex]0.15\cdot220=33[/latex]

The coupon will take $33 off the original price.

The example video that follows shows how to use the percent equation to find the amount of a discount from the price of a phone.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

[latex]\begin{array}{c}10\%\,\,\text{of}\,\,220=0.1\cdot220=22\\20\%\,\,\text{of}\,\,220=0.2\cdot220=44\end{array}[/latex]

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

When a person takes out a loan, most lenders charge interest on the loan. Interest is a fee or change for borrowing money, typically a percent rate charged per year. We can compute simple interest by finding the interest rate percentage of the amount borrowed, then multiply by the number of years interest is earned.

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• Dan\:bought\:bagels\:and\:left\:a\:25%\:tip\:of\:4.00.\:What\:was\:the\:price\:of\:the\:bagels,\:before\:tip?
• A\:salesman\:earns\:15%\:commisson.\:Find\:the\:amount\:he\:will\:earn\:when\:he\:sells\:goods\:worth\:2500.
• A\:computer\:with\:an\:original\:price\:of\:850\:is\:on\:sale\:at\:15%\:off.\:What\:is\:the\:discount\:amount?

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Grade 6 Mathematics Module: Solving Problems Involving Percent

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.

This module was designed and written with you in mind. It is here to help you master the lessons on solving percent problems such as percent of increase or decrease (discounts, original price, rate of discount, sale price, marked-up price), commission, sales tax, and simple interest. The scope of this module permits it to be used in many different learning situations. The language used recognizes your diverse vocabulary level as student. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.

The module is divided into three lessons, namely:

• Lesson 1 – Solving Percent Problems Involving Percent of Increase or Decrease
• Lesson 2 – Solving Percent Problems Involving Markups and Discounts
• Lesson 3 – Solving Percent Problems Involving Commission, Sales Tax, and Simple Interest

After going through this module, you are expected to solve problems involving percent which can be used in real-life situations, specifically to:

1. identify and analyze the elements of problems or situations involving percent and understand the process in solving each component;

2. visualize problems about percent using illustration to show better understanding in the given situation; and,

3. solve different problems involving percent such as change of percent, markup, discount, commission, sales tax, and simple interest.

Grade 6 Mathematics Quarter 2 Self-Learning Module: Solving Problems Involving Percent

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Amy's family has a Texas Red Lacy named Hank. The amount of food Hank eats each week increased from 48 lbs. to 54 lbs. What percentage did Hank increase the amount of food he eats? Hint Possible Solutions

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• Click on the following links for interactive games.   Understanding Ratios   Percents in Word Problems   Percent of Change Word Problems   Percent of a Number: Taxes   Sales Price Multi-Step Problems Involving Percents   Equivalent Ratios Word Problems
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• Readiness Standard 7.4 Proportionality. The student applies mathematical process standards  to represent and solve problems involving proportional relationships. The student is expected to: (D) solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

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The Sunday Read: ‘What Deathbed Visions Teach Us About Living’

Researchers are documenting a phenomenon that seems to help the dying, as well as those they leave behind..

By Phoebe Zerwick

Read by Samantha Desz

Produced by Jack D’Isidoro and Aaron Esposito

Narration produced by Anna Diamond and Emma Kehlbeck

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Chris Kerr was 12 when he first observed a deathbed vision. His memory of that summer in 1974 is blurred, but not the sense of mystery he felt at the bedside of his dying father. Throughout Kerr’s childhood in Toronto, his father, a surgeon, was too busy to spend much time with his son, except for an annual fishing trip they took, just the two of them, to the Canadian wilderness. Gaunt and weakened by cancer at 42, his father reached for the buttons on Kerr’s shirt, fiddled with them and said something about getting ready to catch the plane to their cabin in the woods. “I knew intuitively, I knew wherever he was, must be a good place because we were going fishing,” Kerr told me.

Kerr now calls what he witnessed an end-of-life vision. His father wasn’t delusional, he believes. His mind was taking him to a time and place where he and his son could be together, in the wilds of northern Canada.

Kerr followed his father into medicine, and in the last 10 years he has hired a permanent research team that expanded studies on deathbed visions to include interviews with patients receiving hospice care at home and with their families, deepening researchers’ understanding of the variety and profundity of these visions.

There are a lot of ways to listen to ‘The Daily.’ Here’s how.

We want to hear from you. Tune in, and tell us what you think. Email us at [email protected] . Follow Michael Barbaro on X: @mikiebarb . And if you’re interested in advertising with The Daily, write to us at [email protected] .

Additional production for The Sunday Read was contributed by Isabella Anderson, Anna Diamond, Sarah Diamond, Elena Hecht, Emma Kehlbeck, Tanya Pérez and Krish Seenivasan.

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