Solving Percent Change Word Problems

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Grade 7, Grade 8, Percentages, Word Problems

Introduction and Video

In our last video lesson, we learned how to calculate percent change, which is the amount that a value increases or decreases, but calculated as a percent. This concept is crucial in various real-life scenarios where we encounter percent change. In this video lesson, we will practice solving percent change word problems to see firsthand how percent change is applied in practical situations. Specifically, we will examine examples of percent increase and decrease.

Lesson Notes for Solving Percent Change Word Problems

Let's look at the details of the lesson including types of percent word problems and a detailed example.

Applications of Percent Change

There are many real-life applications of percent increase and decrease. Here are a few types that you might see in percent word problems.

Sales Tax: In certain regions, a sales tax is imposed, which is a percentage that is added to the price of a product or service. This additional amount contributes to the overall cost.
Inflation: Another instance where percent change is relevant is inflation. Over time, the value of goods and services tends to rise due to inflationary pressures. This increase affects the purchasing power of consumers.
Population Increase: Percent increase can also be observed in the context of population growth. As the number of individuals residing in a particular area rises, it can be represented as a percent increase.
Bank Interest: Additionally, banks utilize percent increase when dealing with financial transactions. For instance, they express the interest charged on loans or the amount paid for savings accounts in terms of percent increase.
Price Discounts: Percent decrease comes into play when we encounter discounts or sales. When purchasing an item on sale, the original price is reduced by a certain percentage, resulting in a lower cost.
Deflation: Another scenario where percent decrease is relevant is deflation. This refers to the decrease in the value of goods and services over time. Deflation can impact various aspects of the economy, including prices and wages.

List of real-life applications for solving percent change word problems. Examples shown of percent increase and decrease.

Example: Discount Price and Sales Tax

To illustrate the practical use of percent change, let's consider the following scenario: A video game is priced at $36, and Kelly has a coupon for 15% off. If a sales tax of 7% is added to the discounted price, we need to determine the final amount that Kelly will pay.

To approach this problem systematically, let's break it down into its essential components:

The original price of the video game is $36.
Kelly possesses a coupon that entitles her to a 15% discount, resulting in a decrease in the price (percent decrease).
Subsequently, a 7% sales tax is added to the discounted price, leading to a percent increase.

To find the final amount that Kelly will pay, we can follow these steps:

Calculate the discounted price:
- To determine the discount, we convert 15% to its decimal form (0.15) and multiply it by $36. This calculation yields a discount of $5.40.
- Subtracting $5.40 from the original price of $36, we arrive at a discounted price of $30.60.
Add the sales tax to the discounted price:
- To calculate the sales tax, we multiply 7% by $30.60, resulting in an additional cost of $2.14.
- Adding $2.14 to the discounted price of $30.60, we obtain a total amount of $32.74.

Based on our calculations, Kelly will pay $32.74 for the video game after applying the coupon and sales tax.

Solving Percent Change Word Problems. Detailed example for calculating a video game price after a discount and sales tax are applied.

Summary and Practice

When solving word problems with percent increase and decrease, it is important to approach them with careful attention to detail. By reading the problem carefully and focusing on one step at a time, we can effectively navigate through multiple steps and arrive at the correct answer. Remember, practice and patience are key to mastering problem-solving skills in math.

Try this practice activity to see what you learned. Click on the correct answer.

Video Transcript

In our last lesson, we learned how to calculate percent change, which is the amount that a value increases or decreases, but calculated as a percent. In this lesson, we're going to take a look at some word problems that involve percent change. So we'll get to see how it's actually used in real life.

So let's see how percentages can be used in real life. And we'll look at examples of percent increase and percent decrease. So when you're buying something, some places charge a sales tax, which is a percentage that gets added to the price.

You might even see the value of something being inflated over time. We call that inflation. For example, the cost of a gallon of milk at one time only cost a few cents, and now it cost a few dollars. And that's because its price has been inflated over time.

We can also see percent increase in the population as the number of people increase. A bank can also show percent increase in terms of the interest that they charge on a loan or the amount that they pay you for your savings account.

We might see percent decrease if something that we're buying is on sale and we're given a discount on that price and that would cause the price to go down. And just like items can inflate over time, we can also see deflation of something's value.

So for example, the more that you drive a car, its value goes down. So we would call that deflation. And just like population can increase, population can also decrease and we can represent it as a percent decrease.

So let's see how we can apply those concepts to help us solve this problem. A video game is priced at $36. Kelly has a coupon for 15% off. If a sales tax of 7% is added to the discounted price, how much will Kelly pay?

Well, first we need to take a look at the original price, which is $36. And then they tell us that Kelly has a coupon for 15% off. So that's going to cause a decrease in the price. So that 15% is a percent decrease. And then she also has to apply the 7% sales tax. So that's going to be a percent increase.

So we actually have two different percentages that we need to apply to the price to figure out exactly how much Kelly will actually pay for the video game. So first we'll calculate the discounted price, which means that we 're going to figure out what 15% of the $36 is.

And don't forget, when you're calculating with percentages, you have to convert it to a decimal or a fraction. So here we have the 15%, convert it to a decimal zero point 15 or 1500ths.

And then we multiply that by the $36 and that gives us $5.40. So that's how much is going to get taken off of the price of the video game. So we'll subtract that from the $36, which leaves us with 30 dollars sixty cents. So that's the discounted price of the video game.

Next we need to add the sales tax, which is 7% and they tell us that the 7% is added to the discounted price, not the original price of the video game. So we'll have to be careful to apply it to the $30.60, not the original $36.

So we'll calculate the 7% of $30.60. So we have 0.07 or 700ths times $30.60, which gives us $2.14 and that's what gets added to that discounted price. So we have $30.60 plus $2.14, giving us $32.74. So the total amount that Kelly will pay for the video game is $32.74.

So remember, when you're solving problems that involve percent increase and decrease, especially when there's more than one step like this one, just read the problem carefully and make sure that you focus on one step at a time until you get to your final answer.

Related Standard: Common Core 7.RP.A.3

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