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

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to solve word problems like a pro. Learn how to setup your problem, write your equations and then solve your equations to find your answer.

In this video lesson, we are going to learn how to solve **multi-step algebra word problems**. These are problems written in English that require you to perform several operations to find the answer. I know, word problems are the worst thing ever. But keep watching and see whether or not you will find them easier to work with once you've learned what is in this video.

We begin with a problem. See, there is this concert coming up that I really want to go to. The tickets cost $200. That's just for one ticket! Anyways, I'm not complaining about the price, just saying it's expensive. My problem is I want to bring some of my friends with me, but I can only bring so many. I want to know how many friends I can bring with me. The amount of money I have to spend comes from working 20 hours at a job that pays $20 per hour. Can you help me figure this out?

Our first step to solve this problem is to really understand the problem and what we need to solve for. So, after carefully reading the problem and understanding its meaning, we highlight the important parts of the problem. We see that the tickets are $200 each. I worked 20 hours at a job paying $20 per hour. And I want to know how many friends I can bring. Those are my important parts of the problem. Everything else I can ignore.

Now that I have highlighted the important parts, we can label them with appropriate math symbols. I first want to label what I am supposed to solve for. I ask myself, 'What is the problem asking for?' After looking over the highlighted important parts of the problem, I see that the problem is asking for the number of friends that can come. I place an *x* next to that part to tell me that this is what I want to solve for. I can label the 20 hours worked with the words 'hours worked' and the $20 per hour with the words 'pay per hour.'

Now we need to think about how all this information goes together to help us find the answer. We want to find the number of friends that can come. In order to do that, we need to find out how much money we have to spend. To find the amount of money we have to spend, we need to find out how much money is earned after working the 20 hours. How do we do that? We need to multiply the hours worked with the pay per hour.

Once we have the amount of money we can spend, we then can split it into groups of $200 to see how many tickets can be purchased with that amount. One of the tickets will be for me and the rest will be for the friends. The number of extra tickets is what we are looking for.

We know how all the information is tied together now and what we need to do with the information. We can now write our mathematical equation. Sometimes, we may even need to write several smaller equations to get us our answer.

What was the first thing we needed to find out? We needed to find out how much money we earned after working 20 hours. What did we say we needed to do to find that out? We needed to multiply the hours worked with the pay per hour. So, our equation here is this:

money earned = 20*$20

Next we take our money earned and split it into groups of 200 to see how many total tickets we can purchase. What operation would we need to do that? Isn't it division? Yes, we divide our money earned by 200 to see how many tickets we can purchase.

number of tickets = money earned/200

But, I'm not just looking for the number of tickets. I'm looking for how many friends I can invite. So, what do I need to do to the number of tickets? I need to subtract 1 from it to account for my ticket.

number of friends = number of tickets - 1

Now that I have all my equations written down, I can go ahead and solve them. I take it one equation at a time, starting with the first. Why the first? I can't solve the second or third equation without the information from the first.

So, solving the first equation gives me money earned = $400. This $400 is the money earned, and I see that I need that bit of information for my second equation. Plugging in this information into my second equation, I get # of tickets = $400/$200 = 2. I see that after working 20 hours, I can purchase 2 tickets.

Now, my final step is to solve the third equation and for this equation, I need to know the number of tickets I can purchase. I already found this information, so I can plug that into the equation and solve.

number of friends = 2 - 1 = 1

Cool! I have enough money to take one friend with me. My last equation is solved, and I have finished solving my problem. My answer is 1.

What have we learned? We've learned **multi-step algebra word problems** are problems written in English that require you to perform several operations to find the answer. To solve them, we need to first carefully read the problem. We highlight the important parts of the problem and ignore the rest. We then label those important parts with symbols or other math labels. Then, we think about how all the information ties together and what operations will help us answer our problem.

We label the answer that we are looking for with an *x* and the other parts with appropriate labels so that we know what they are referring to. After everything is labeled and we have figured out how everything ties in together, we then write our equations to show how they are related to each other. Then we go ahead and solve the equations. As you can see from our example, sometimes we can end up with several smaller equations that lead us to the answer.

What do you think? Are you more confident about solving word problems now?

You will be able to explain how to solve multi-step algebra word problems after watching this video lesson.

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

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
- Go to High School Algebra: Algebraic Expressions and Equations

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