Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Log in here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

100 percent of percent problems can be solved if we follow the correct steps. In this lesson, we'll practice solving a variety of different percent problems.

Meet Ashley. Here's Ashley's house.

It's what you might call a fixer upper. She could definitely use some help.

In this lesson, we're not going to help Ashley redo her floors or paint, but we will help her with some percent word problems. These problems are about as common as the termites in Ashley's walls. What? She didn't know there were termites. Oh no.

Well, while she fumigates, let's talk about how to solve these problems. First, the word **percent** just means per hundred. If you have 100 nails, 50% of that is 50 nails. If you have 8 paint brushes, 50% is 4 brushes. To figure this out, we can set up a simple equation: 50/100 = *x*/8. 50% is the same as 50/100.

In a percent word problem, we follow a few steps. First, read the entire problem. Makes sense, right? Next, identify the question. We can't solve it if we don't know what it's asking.

Third, identify the relevant details. This can be the tricky part. We're looking for a few key things. We might see a percent, which is identified with this symbol (%), unless that's what we're trying to find out. There might be a whole or a part. A whole is the original number. In our paint brush example, 8 is our whole. This is also sometimes called the base. 4 is our part; that's part of the whole, or base.

It's important that we figure out what's what so we can get to step four - solve the problem. As we'll see, there are often different, equally effective ways to solve percent problems. It's like fixing a leaky pipe. As long as you make it stop leaking, it doesn't matter if you solder in a new section or just put gum on it. Well, ok, gum isn't a long-term fix. But in percent problems, you may have multiple options.

Alright, time to help Ashley. She's retiling a bathroom and she runs into this problem: A bathroom requires 470 tiles. If Ashley has 355 tiles, what percent of the bathroom tiling can she complete?

Let's think about our steps. We read the problem. And what's the question? We're trying to find the percent of the bathroom she can tile. What details do we know? We know the whole; that's 470. That's the total number of tiles she should have. We also know the part: 355.

How do we solve it? There are a few different ways, but let's try an easy one to remember. Let's compare the part to the whole, so we have 355/470 = *x*/100. Here, x is the percent of the tiles. 100 would be all the tiles, which is 470. To figure out what *x* is, just cross multiply. So 470*x* = 35,500. Divide by 470, and *x* = 75.5%. That's our answer!

Sadly, that doesn't cover the walls with tiles. But at least Ashley knows how much coverage she'll have.

In that problem, we found the percent. What if we need to find the part? Ashley's at the hardware store and she encounters this: A table saw's original price is $250. If it's on sale for 15% off, what is the sale price?

This time, we want to find the part. The sale price is going to be a part of the whole price, which is $250. We know the percent: 15. But be careful. The saw is 15% off, so the part we're trying to find is 85% of the whole.

Ok, with that in mind, we could set up two fractions again, but there's another, simpler method. Let's convert 85% to a decimal. To do that, we just drop the sign and move the decimal point two places to the left. So it becomes .85. Now we can multiply .85 times the whole, 250. That gets us $212.50. So our sale price is $212.50.

Ashley was psyched to find a deal on a table saw. She hopes to also score a deal on some drywall. She needs a lot, and here's what she learns: A hardware store has 30% of its drywall on display, with the rest stored in the warehouse. If 72 panels are on display, how many in total are available?

We're trying to find the total number of drywall panels. So we want the whole. We know the part: 72 panels. And we know the part is 30% of the whole.

Let's try a new method. We can call the whole *x*. We know the 30% times *x* is 72. In other words, whatever *x* is, 72 is 30% of that. If we turn 30% into a decimal, our equation looks like this: 72 = .30*x*. Now we divide by .30, and we get *x* = 240. So the store has 240 drywall panels, including those on display and in the warehouse. That'll cover a lot of wall!

Let's try one more kind of percent problem. This one involves some electrical work. Sparky the electrician originally said his labor would cost $525 but now says it'll cost $610. By what percent did the cost increase?

Before we can find the percent increase, we need to find the change in dollars. 610 - 525 is 85. So Sparky's charging $85 more. We can find the percent with a little division. To find percent change, divide the absolute change by the original. This works for increases or decreases.

Here, our original price is 525, and our difference is 85. 85 divided by 525 is .16. If we convert that to a percent, it's 16%. So $525 to $610 is a 16% increase. Let's hope Sparky spends that money on some safety equipment.

To summarize, we learned about solving percent word problems. Percent just means per hundred.

When we solve these word problems, we follow four steps. First, read the problem. Next, identify the question. Third, identify the relevant details. This includes looking for things like the percent in question, the whole and the part. Finally, solve the problem.

We looked at different ways of solving these problems, including setting up two fractions, converting percents to decimals and using a variable to stand in for our missing number. And maybe, just maybe, we helped Ashley fix her house. It's got to be at least, what, 5% better?

Following this lesson, you'll have the ability to:

- List the four steps that will help you solve percent word problems
- Solve percent word problems by setting up fractions, converting percents to decimals and using variables

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
6 in chapter 3 of the course:

Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- Ratios & Rates: Definitions & Examples 6:37
- How to Solve Problems with Money 8:29
- Proportion: Definition, Application & Examples 6:05
- Calculations with Ratios and Proportions 5:35
- Percents: Definition, Application & Examples 6:20
- How to Solve Word Problems That Use Percents 6:30
- How to Calculate a Permutation 6:58
- How to Solve Problems with Time 6:18
- Distance Formulas: Calculations & Examples 6:31
- Go to High School Algebra: Calculations, Ratios, Percent & Proportions

- SIE Exam Study Guide
- Indiana Real Estate Broker Exam Study Guide
- Grammar & Sentence Structure Lesson Plans
- Foundations of Science Lesson Plans
- Career, Life, & Technical Skills Lesson Plans
- Business Costs, Taxes & Inventory Valuations
- Using Math for Financial Analysis
- Assessments in Health Education Programs
- Governmental Health Regulations
- Understanding Health Education Programs
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- Intrapreneurship in the Hospitality Industry
- Saadat Hasan Manto: Biography & Works
- What is an Agile Environment? - Definition & Example
- Assessing a Patient's Nutritional & Gastrointestinal Status
- Functional Text Activities for Middle School
- Curt Lemon in The Things They Carried
- Religion in Jane Eyre: Analysis & Examples
- Quiz & Worksheet - Confucian Virtue Ethics
- Quiz & Worksheet - Achievements of President Jackson
- Quiz & Worksheet - Catherine Earnshaw
- Quiz & Worksheet - State & Federal Rights in the Civil War
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Art Lesson Plans
- Reading Comprehension | A Guide for Teaching Reading

- Holt Science Spectrum - Physical Science: Online Textbook Help
- Fahrenheit 451 Study Guide
- PECT PAPA: Practice & Study Guide
- Improving Customer Experience
- STAAR Reading - Grade 8: Test Prep & Practice
- SBA Math - Grade 6: Ratios, Rates & Proportions
- SBA Math - Grade 7: Operations with Decimals
- Quiz & Worksheet - Types of Behavioral Approaches to Job Design
- Quiz & Worksheet - Main Branches of Geology
- Quiz & Worksheet - Different Models of Aging
- Quiz & Worksheet - Causes & Effects of the Balkans Conflict
- Quiz & Worksheet - Group Decision-Making in the Workplace

- Impact of Word Choice on Meaning and Tone
- Epidemiology Lesson Plan
- Free LSAT Prep
- How to Study for SAT Subject Tests
- How to Pass the Living Environment Regents Exam
- Subtraction Math Games
- How to Pass Microbiology
- Anti-Bullying Programs & Organizations
- Science Word Walls
- Greek & Latin Roots Games
- Special Education Resources for Parents
- Common Core State Standards in Florida

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject