3.15 Percent Word Problems - old

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Math Basics  >  Unit 3 Ratios and Percent  >  Lesson 3.15 Percent Word Problems

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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.

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